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FOTD 25-06-08 (The Cubic Squared [8])
by Jim Muth 25 Jun '08

25 Jun '08

FOTD -- June 25, 2008 (Rating 8) Fractal visionaries and enthusiasts: My new formula, the DivideBrot2, appears to be another winner, which I will use often in future FOTD's. Today's image barely scratches the surface of the things it can do with the higher- order minibrots, all of which until now have looked pretty much the same. Today's image is one of the best cubic minibrots that I have yet stumbled upon. The parent fractal closely resembles the figure drawn by the marksmandel formula of Fractint when the exponent is set to 2. But the buds of today's parent, instead of being quadratic, are cubic. Today's image lies in the northern suburbs of this parent. I named the image "The Cubic Squared" because I felt like it. I rated it at an 8 because that's what I think it's worth. When I rendered the image, I used nothing more than the tradi- tional equal-iteration bands on the outside with a flat black on the inside. All the excitement is in the fractal itself. The calculation time of a mere 42 seconds can hardly be beat. But if running parameter files is not your cup of tea, forget the colloquialisms and beat it to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the completely rendered image is posted for viewing. The perfect weather at Fractal Central on Tuesday was appreci- ated to the fullest by the fractal cats, who enjoy plenty sun, low humidity and a temperature of 79F 26C. I would have enjoyed a day a little more peaceful, but the day I had was not too bad. The next FOTD, another good one, will appear in 24 hours. Until then, take care, and be fractally correct. Never mention undesirable things about fractals that everyone wants to continue denying are true. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Cubic_Squared { ; time=0:00:42.23-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot2 passes=1 center-mag=+0.014489004226624/+0.777624726013028/\ 2.005397e+007/1/-86/0 params=1/-2/1/0 maxiter=1800 float=y inside=0 logmap=53 periodicity=10 colors=000NOPOONDKU8If6JY5JQ4JH3JD2J81J30J05QRAXaF\ cnKjsPqwUwzYzzawxdrsgmrjgonaoqXotRowMoKDGUIKcKOhQS\ mSWrU_vWbk_ZacVSgSHkO7oK0sH4rIBrJIrKOrLVrMarNgrNZm\ ORhPJdQB_R3WR1WR2`Y3dc4hi4lo8fgCa_GXSKRLOMDSH5VC0_\ BIcA`g9sfBqeDodEmcGkbHiaJg`Ke_McZNaYP_YQZ_O`aNacMc\ eLdgJeiIgkHhlGicEhVChNAhJCiFDiCEi8Fj4Gj1HjLRnIWhG_\ cEcZBgT9kO7oJ4sD2w80z35y59w7Du9HtAMrCQpEUnGYmHWgHU\ aHfjIbfHZcHV_H7B`EJULQNfHkaN`XSR0z08r5IgB4SpwzelpX\ afPT_RSZOSYMSXJIU0MV5PWBi9QTOUSRPSULTosShfSbU3IECN\ FKSGMuWqP7hSB_VEpdvc`a0xVDjOsvLloKeiJZbICRgjkEcfFY\ aGLDpPNZ0K9ERDpzidhh_dZW`QOtrPnhQh_RzQNzcPzYQzSRzM\ kzYfzTwzPwzLwz0wz7wz9wzCwzFwzLwzJwz_wzQwzXwzTwzPwz\ Lwzdwz0wzpwzMwzvwzMwzCwz2wzRwzoFzqLzsRzuWzvczikzXs\ zKNzTlzJezIZzHezdazZZzTVzNUzuHzgOz0Qz9CzHKzHvzfCzQ\ nzqhzgbzZXzQjzK`zIQzaRzRBzcHzWNzOYzbVzSjz3ez7`zAWz\ E6zoHzY0zvwz0oz3gz8_zDCz0 } frm:DivideBrot2 { ; Jim Muth z=0, c=pixel, aa=real(p1), bb=imag(p1), dd=real(p2), ff=imag(p2)+100: z=z^aa/(z^bb+dd)+c |z| < ff } END PARAMETER FILE=========================================

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FOTD 24-06-08 (Strangeness [Rating--Not Yet])
by Jim Muth 24 Jun '08

24 Jun '08

FOTD -- June 24, 2008 (Rating Not Yet) Fractal visionaries and enthusiasts: At first glance, today's image appears hopelessly dull. It's another rendering of the Mandelbrot set, no big deal. But this Mandelbrot set is strange indeed, for it is the Mandelbrot set only on the surface. The deeper one delves into it, the more its elements change from the quadratic kind to the cubic kind. For a striking example of this strangeness, check one of the very small minibrots on the main stem, the smaller the better. You will find not a Z^2+C minibrot but a Z^3+C minibrot. The same is true throughout the entire parent fractal. And the most incredible thing about the formula is that by changing the imag(p2) parameter, the quadratic M-set can be made to have in its depths characteristics of any order whatever. The formula that does all this is pure serendipity. When I wrote it, I had nothing particular in mind. I simply wanted to see what the expression would do. And was I surprised! Today's image is not the last we will see of this formula. I have already found two outstanding cubic midgets, which will appear as the FOTD's for June 25 and 26. The name "Strangeness" is self-explanatory. The calculation time of 23 seconds makes running the included parameter file a breeze. And those who do not enjoy windy conditions may escape the breeze by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Fine weather prevailed here at Fractal central on Monday until nightfall, when a heavy thunder-shower moved in, leading to a pleasantly cool night. The temperature of 84F 29C and the plentiful sunshine during the day suited the fractal cats just fine. My day was made more interesting by the discovery of today's image, which promises an abundance of goodies. The next in the endless line of FOTD images bearing goodies will appear in 24 hours. Until then, take care, and the best is yet to come from this formula. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Strangeness { ; time=0:00:23.22-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot2 passes=1 center-mag=-2.879\ /0/0.17468 params=2/-1/5/1000 float=y maxiter=1000 inside=0 logmap=yes symmetry=xaxis periodicity=10 colors=000KB1JF8JJEIMKIQQHUXHXbG`hGcnSZpcVqoRrzNsp\ PrgQrZRrQTrHUr8VrEYpK`nPclVfj`ihekgXmhPnhHph9qh1rh\ 5sd9s`CsYGtUJtRNtNQtKMuOIvSEvWBwZ7wb3xf0xi2yg3ye5y\ c6ya8y_9yYAyXBuYCrYDoZElZEiZRjbbkenlizllfkfOkaSdZV\ ZWZTTaNQYQTUTVQWXNZZJaaFdcBge8igIdfS_f`WfjRfsNfrPg\ qQgqSgpTgpUgnXbl_ZjbUieQghMekHcnDbp9YoETnIOmNJlREk\ VFlQGmLHmGInBJo6Jo2KhKLaaMWrJVqGVpDVoAVn7VnFalMgjU\ mh`sfethjujnvkswmwxntveruYptQmrIkqAip2hn3gz3fz4fz4\ ez4dz5cz5cz5WzIPzVIzgHzcHz`HzYHzVHzRHzOHzLHzIMzKRz\ MWzO`zQezSjzUozWszYozakzegzhhz`hzTizMizEiz7ozFuzMz\ zTrzUkzUczUXzVPzVIzVGzdEzm1zzAzhJzRJzF`zErzDjzEczE\ WzFPzFPzLPzRPzXPzbPzgSzfVzeYzd`zcbzbXzkRztRzrSzoSz\ lTzjTzgUzeVzbVz_WzYWzVXzSXzQYzNYzLczNlzLhzPJzoKzqM\ zrNztPzuNzzQzvTzrWznZzkazgdzcgz`dzWazRZzMWzHTzCRz8\ QzEQzJPzPPzUOz_OzdQzbSz`Uz_WzYYzW_zVazTbzS`zYZzbXz\ gVzmTzrRzwPzuNztLzsKzrIzq } frm:DivideBrot2 { ; Jim Muth z=0, c=pixel, aa=real(p1), bb=imag(p1), dd=real(p2), ff=imag(p2)+64: z=z^aa/(z^bb+dd)+c |z| <= ff } END PARAMETER FILE=========================================

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FOTD 23-06-08 (Quartic Minibrot [?])
by Jim Muth 23 Jun '08

23 Jun '08

FOTD -- June 23, 2008 (Rating ?) Fractal visionaries and enthusiasts: Today's image springs from a new formula, one that I wrote on Sunday and named 'DivideBrot2'. The formula is so new that I have little idea what it does or how it works. Today's particular parameters create a parent fractal that resembles a Mandelbrot set with two main bays. But even though the parent resembles the M-set, the minibrots in it are quartic. And though today's image is located in what appears to be Seahorse Valley of the parent fractal, the elements in the image more closely resemble those of an East Valley. Since I have very little idea of what the formula can do, I had no idea how to rate the image. The name I gave it -- "Quartic Minibrot" -- is nothing more than a description. This formula appears to get more out of a quartic fractal than the simple formula Z^4+C. Hopefully it will do the same for some of the higher order fractals. I'll work with the new formula for a day or so before deciding whether to consign it to the storage bin. If anything of unusual interest turns up, I'll post it as a FOTD. Today's image is rather slow, taking almost 9 minutes to finish on the fastest machine. Any budding impatience may be nipped by visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the completed image there. The weather was good enough here at Fractal Central on Sunday, with sunny skies and a temperature of 84F 29C. The clouds that moved in at 5pm and the light thunder-shower than followed arrived too late to spoil the day. The fractal cats spent most of the day watching for squirrels and passing tomcats. My day was appropriately lazy, and if I have my way, tomorrow will be the same. The next FOTD will appear in 24 hours. Until then, take care, and if it doesn't make good sense, question it. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Quartic_Minibrot { ; time=0:08:58.05-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot2 passes=1 inside=0 center-mag=-1.045188369333446/+0.03206533434293096\ /1.098195e+012/1/82/0 params=2/-2/1/0 float=y maxiter=15000 periodicity=10 mathtolerance=0.05/1 colors=000YmXXhUWdRV_OUWLSRIRNFQICPE9O96N53M10O32P\ 44Q56R68T8AU9CVAEWBGYDIZEK_FM`GNZFOYEPXDPWCQUBRTAR\ S9SR8TQ7TO6UN5VM4VL3WK3WQDUVMT`WSedQknPpwOltTirYfp\ bbmg_klXipVfmTdjRagP_dNXbLV_JSXHQUFNRDLPBIM9GJ7DG5\ BD39B88GD7LH6PM6UR5YV4b_3fd3kh2om1tq1xq2Zq39o5Dn6G\ m8Kk9NjBRiCUgDXfF`eGccIgbJjaKm`Mk_OjZQiYShXUgWWfVY\ eU_dTacSbbOcaKc`Gc_CdZ8dY5dX6IRBNSGRTLVTP_UUcUZgVb\ lWgpWltXpxXjpUeiS_aPVVNPNKKGIE8F91DB6JDBOFGTHLYJQc\ LVhN_mPdrRhwTdqU`kVXeWT`YPVZLP_HJ`DEeGMjIUoKatMiyO\ qSvqOmgLeYIYOFQECI4FH8HHCJHFLGJNGMPGQSFTUFXWF_YEc_\ EfaEjcEm`FlZFkXGjVGjTHiRHhPIgNIgKJfIJeGKdEKdCLcALb\ 8Ma6MaTVgSThSRhSQhSOhSNhSLhSKhRIhRGhRFhRDhRChRAhR9\ hU8gW7gZ6f`6fc5ee4eh4dj3dm2co2cdWaVx_YwX_vVauSctQf\ tNhsLjrIlqGnpDqpBso8un6wm3ym1xj4xg6wd8waAvZCvXFuUH\ uRJuOLtLNtJQsGSsDUrAWr7Yr5_s4Ys4Ws3Us3Ts3Rs2Ps2Os1\ Ms1Ks1Jq2ICqb9sdNuc`vcZq_ } frm:DivideBrot2 { ; Jim Muth z=0, c=pixel, aa=real(p1), bb=imag(p1), dd=real(p2), ff=imag(p2)+64: z=z^aa/(z^bb+dd)+c |z| <= ff } END PARAMETER FILE=========================================

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FOTD 22-06-08 (Zitty Minibrot [7])
by Jim Muth 22 Jun '08

22 Jun '08

FOTD -- June 22, 2008 (Rating 7) Fractal visionaries and enthusiasts: Instead of writing a FOTD discussion on Saturday, I noticed the perfect weather and decided to go out with FL and enjoy the day, which we did quite well. (There is a little more [but not too much more] to life than fractals.) Today's minibrot is so unus- ual however that I must let it go without the usual description. The parameter file runs in 1-2/3 minutes. Run it and enjoy the result, or give Paul a chance to post the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view it there. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Zitty_Minibrot { ; time=0:01:40.48-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot5 passes=1 center-mag=-1.749153775791796/+0.00000097001782827\ /9.389332e+012/1/180 params=0/0/0/0/0/0/0/0/\ 2.000001/0 float=y maxiter=1500 inside=0 logmap=242 periodicity=10 mathtolerance=0.05/1 colors=000D69D8BCADBCEAEG9GI7IK6KL5MN4OP2QR2SS6VWB\ XZEZbJaeMciQelUhpXjs`lwcnz`ozZpzXqzUrzSszQtzOuzLvz\ JwzHxzFyzCzzAzz8zz6zzYzz`zzbzzdzzfzzHzzJvzLrvOmrRh\ mUchYZc`UZcQUgSPjUKmWHpYHt_IwaIzcIwaLt_NqYPmWSjUUf\ SWcQZ_P`XPbUOeRNgOMiNMkKK9KKAKKAKKBKKBKKCIKCGKC_K7\ rX2qY7qYBpZFpZJo_No_Ro`Vn`_nacmagmbklbolcslcwmdund\ toesperqfprfosfntgmuglvhjwhixihyigyif1GR0Lk1Ml1Nl2\ Om2Pm3Qm3Sn4Vn4Yo5`o5co6fp6hp7jq7mq7pqBunczlcziczg\ cziczkczlcyncxoHzqGzrFytEwuDvwCuxErtFtqGtnHsjIugJw\ dKxaNpeQiiTbmWWqZPuaIy`Hr`Gl`Gf`F`_EV_EP_DJ_DDhMPp\ U`xakfiXPqI8x3IuHRsV_phhnucnoZnjUnePn`KnWLkSMhNOeJ\ PbEQ_AOXBNUCMSDLPEKNFOJQSG`WDkGD`NHWTKSZNOdRKjUGpX\ Cv_8wZAxZByZCzZDzZEzYGz_HzaIzcJzeKzgLziMzkNzmNzoOz\ qPzsPzuQzwRzxRzySzzTzzTzzUzzVzzVzzUzzTzzSzzRzzQzzP\ zzOzzRzzTzzVzzXzzZzz`zzbzzdzzfzzhzzjzzkzz2zz2C03C0\ 3D04E04F05G05G06H06H07I27 } frm:SliceJulibrot5 {; draws slices of (-Z)^n Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=(-z)^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 21-06-08 (In Alien Territory [5])
by Jim Muth 21 Jun '08

21 Jun '08

FOTD -- June 21, 2008 (Rating 5) Fractal visionaries and enthusiasts: Wow! What a fractal! Talk about over-qualified! This is one of the most bombastic fractal images I have ever seen. It has no idea where to stop. The super-abundance of detail is so overdone that it actually detracts from the rating, which I could set at no more than a 5. The image is a scene in the Mandelbrot aspect of the East Valley of the same parent Julibrot that has supplied the past two days' images. I named the image "In Alien Territory", though I'm not sure where this alien territory is found. I used no gimmicks to produce the overwhelming detail in the image, which was rendered with the inside set to the color zero and the outside set to display equal-iteration bands. All the excitement lies in the numbers of the image itself. The calculation time of just over 3 minutes should give no one a case of impatience. And for even more convenience, the finished image is or soon will be posted for instant viewing on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A routinely pleasant day prevailed here at Fractal Central on Friday, with partly cloudy skies and a temperature of 77F 25C. The fractal cats noticed the conditions, then continued eating their dinner. My day was once again busier than I would have preferred, but not so busy as to affect the attention I gave to the FOTD, which failed to fulfill my hopes on its own account. The next FOTD is due to be posted in 24 hours. Until then, take care, and look before you iterate. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= In_Alien_Territory { ; time=0:03:10.62-SF5 on P4-2000 reset=2004 type=formula formulafile=slices.frm formulaname=MandelbrotMiN passes=1 float=y center-mag=+0.257194485268014/-0.0087089105892888/\ 3.721816e+008/1/-22.5/0 params=2.01/0/0/0/0/0 maxiter=2700 inside=0 logmap=297 periodicity=10 colors=000Zz0cz0hz0mz0rz0vz0zz0zz0zt0zt0zt0Ht0Kp0P\ p0Yp0dp0ip0Pt0Ct03t30tC0tI0zI0zI0zI0zI0zI0zI0zI0tI\ 0pI0iI0dI0YI0UI0PI0RI0UI0YI0`I0dI0hI0bI0YI0TI0PI0L\ I0II0FI0CI00I00I00I00I00I00I00I00I00I00I00J00K00L0\ 0M00N00O00P00Q00R00S00T00U00V00W00X00Y30_90aH0cP0d\ U0dd0ii0ip0pz0pz9tzKtzYtzpzzzzzzzzzzzzzzztzzpzzizz\ dzzYzzPzzKpzHizCdz9Yz3Ut0Ut0Pp0Pp0Ki0Ki0Hd0HY0CY0C\ U09U09P05P05K03H03H00C00C00900300903C09H0HK0PU0YY0\ id0ti0zt0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0tz0pz0dz\ 0Yz0Ut0Pt0Kt0Ct39p35p53p50d00p55tCCzKKzUUzddzppzzY\ zzKdz9Kz05z00z00r00r00m00m00m00h00c00c00c00c00c00c\ 30c90cC0cK0dU0dd0Yp0Uz0Pz5Pz9KzCHzHCzKCzP9zP9zP9zP\ 9zP9zU9zU9zU9zU9zU9zY9tY9pY9iY9dY9dd9Yd9Ud9Pd9Kd9H\ YCKd9Pd5Pd3Ud0Ui0Yi0di0di0ip0ip0pp0tp0tp0zt0zt0zt0\ zt0zz0zz0zz0zz0zt0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz\ 0zz0zz0zz0zz0zz0zz0zz0zi0 } frm:MandelbrotMiN {; Jim Muth b=p1, z=p2, c=p3+pixel: z=(-z)^(b)+c, |z| <= 16 } END PARAMETER FILE=========================================

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FOTD 20-06-08 (Independence Day [6])
by Jim Muth 20 Jun '08

20 Jun '08

FOTD -- June 20, 2008 (Rating 6) Fractal visionaries and enthusiasts: We finally have an image worth more than a rating of 5. True, the rating is only a 6, but mighty oak trees from tiny acorns grow. Who knows where this small improvement might eventually lead to. The image is a blow-up of what was barely a speck in the blank area of yesterday's image. The name "Independence Day" refers not to an invasion from space, but to the resemblance, at least in my mind, to an exploding skyrocket like those we see so many of here in the U.S. on July 4, which is Independence day. Is today's image a great fractal? No. Is there any such thing as a great fractal? Some fractal artists seem to think so, but I have yet to be convinced that any fractal could be called great. (Of course, if the multiverse can be taken as a fractal, as I suspect, then maybe there is a great fractal after all.) In contrast to yesterday's boringly slow image, today's image calculates in a little over 4 minutes. And even this short wait may be eliminated by visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and seeing the semi-glorious completed image there. The cool and cloudy weather continued Thursday here at Fractal Central. The high temperature of 68F 20C felt more like April than June, while the fractal cats remained in curl-up mode. My day was less hectic than the day before, but nowhere near the easy-going type of day I prefer. The next FOTD will be posted in 24 hours. Until then, take care, and fractals are the answer. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Independence_Day { ; time=0:04:06.34-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot5 passes=1 logmap=yes center-mag=+0.2148023/-0.3043594/202.832/1.26/-55/0 params=89.995/90/89.995/90/0.25567/0.00843/0/0/2.0\ 1/0 float=y maxiter=1000 inside=253 periodicity=10 colors=000kQIlOKmMLnKNoIOvKnmGkeCiY9fQ5dI2btbpp_nm\ XliUkfRicOh_MfXJeUGcQDbNA`K8_OD`RH`VM`YQ`aV`dZ`hb`\ kg`ok`rp`vt`yx`wsaunbsjcqedpadnXelSfjOghJhgFhcHc_I\ _WJWSKROMNKNJGOECPA8Q6AP7BP7CO7DO7EN7FN7GM7HM7JL7K\ L7LK7MK7NJ7OJ7PI7QI7TJAVKDXKGZLJ`LMbMPdNSgNViOYkO`\ mPcoQfqQisRluRnRbST_UUXVWUWXRXYOY_M_`J`aGacDbdAce8\ dcAabB_aDY`EW_FTZJRYLPXMNWNKVOIUPGTQESRBRS9QT7PU5S\ T7VS8YRA_QBbPDePEhOFjNHmMIpLKsKLuKMpLNkMOfNPaNPbQQ\ cTRdWSeYTf`UgcVheWihXjkYknZlp_mr`nsaitSbrAWoEMlHHi\ KMfOQcRV`U_YYcV`hSclPfhKWeFLaAAZ60V78R8GO9NK9VHAaD\ BiABp8S`7gL6w67s68p69m6Aj6Ag6Bd6Ca6DZ6EW6ET6DVEDXL\ DZSC`_CbfCdmCftHboM_kQWgVTb_PZcMVhIRmKMqUIvcEzmAwc\ 8mU6fP5`M3VQ2UP3UO4TN5TM5TL6SK7SK7RJ8RI9RH9QGAQFBQ\ FBPDDPCEPBFPAGP8IP7JP6KP5LSDSULYWSdZ_j`gqbnwcjvdgv\ edvf`vgYvhVviSvjOvkLvlIvmFvnBvo8vp5vq2vk4of6ha7aX9\ WRBPMCIHEBCF5LJX00KJczKcz } frm:SliceJulibrot5 {; draws slices of (-Z)^n Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=(-z)^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 19-06-08 (Straight and Narrow [5])
by Jim Muth 19 Jun '08

19 Jun '08

FOTD -- June 19, 2008 (Rating 5) Fractal visionaries and enthusiasts: Today's FOTD is late due to a work rush. The feathery scene is an almost-Julia set of the East Valley area of the (-Z)^(2.01)+C Mandeloid. I call the image an almost- Julia set because it is oriented within 0.005 degree of being a true Julia set. I named it "Straight and Narrow" after the blue stripes running diagonally through it. The rating of a 5 seems fair enough. The image is better viewed than described. One way of viewing the scene is to start the included parameter file and wait a while. A better way is to view it in finished form on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> But due to the unusual hour of the posting, it might be a while before the image is posted there. Cloudy, blustery and unusually chilly weather prevailed here at Fractal Central on Wednesday. The high temperature of 68F 20C was well below normal. The fractal cats adjusted by shifting from stretched-out mode to curled-up mode. In my department, the day was very busy. And it now looks like tomorrow may be the same. Despite all this, the next FOTD will likely be posted in 24 hours. Until then, take care, and ain't fractals fun? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= StraightAndNarrow { ; time=0:27:09.25-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot5 passes=1 logmap=yes center-mag=-0.000471978/0/1.138295/1/-90/0 params=89.995/90/89.995/90/0.25567/0.00843/0/0/2.0\ 1/0 float=y maxiter=32767 inside=0 periodicity=10 colors=000KKCLLDMMENNFOOGPPHQQIRRJSSKTTLUUMVVNWWOX\ XPYYQZXHWWMUWQRVUPVYNUaKUeITiFTmDSq9OxBSuCVsDZqFao\ GdmHhkIkiKngLreMucNxaPvZRtWTsTVqRXpOZnL_mJakGciDeg\ Agd8ia5kY2lV0kZ7jbDjgKieQhjXhkbgmifnohryfoudmrckna\ ik_ggZedXb`V`YUZUSXRQVNQQLPTKOVKNXJMZJM`ILbIKdHJgH\ IiGIkGHmFGoFFqEw`5FsEItDLtDNtCQtCTtBVtBYuA_uAbu9eu\ 9gu8ju8nz5lu8kqBimEhiHfeKeaNdYQbTTaPW_LZZHaXDdW9gS\ 0lV5jXAiZEhaJfcNeeSdgWccR__NWWITSEPO9MK5IF0DH1FJ2H\ L3JN4LP5MR6OT7QV7SX8UZ9V`AXbBZdC`fDbhDcjAnk8xhArfC\ lcEgaGaZIWXKRUMLSNGPRBTPFWOJZNNbMQeLUhKYlJ`oIdrHhu\ 9wuGkuN_uUOtb4u`CvZKwXSxV_yTgzRozPwyOvyNuyMtxLtxKs\ xJswItwHuwGvvFwvExvDyuCzuBzuAzu9zb_zK`zLazMbzMczNc\ zOczOczPZzQZzNZzQZzSZzUZzWZzYZz_ZzaZz_ZzYZzWZzVZzT\ ZzRZzPZzOZzMZzKZzKZzJZzIZzHZzGhzFhzEhzDhzBhzDhzEhz\ FhzGhzHhzIhzJhzLhzMhzNhzOhzPhzQhzThzRhzQhzPhzOhzNh\ zMhzLhzKhzJhzHhzIhzJhzKhz } frm:SliceJulibrot5 {; draws slices of (-Z)^n Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=(-z)^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD for June 19 to be delayed
by Jim Muth 19 Jun '08

19 Jun '08

>Fractal visionaries and enthusiasts: Due to the expected unexpected rush, the FOTD for June 19 will actually be posted on June 19 instead of late on June 18. Jim Muth

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FOTD 18-06-08 (Portal to Infinity [5])
by Jim Muth 18 Jun '08

18 Jun '08

FOTD -- June 18, 2008 (Rating 5) Fractal visionaries and enthusiasts: I seem to be in one of those occasional fractal ruts, where I just can't seem to come up with a fractal that meets even my lowly standards of fractal worth. Yesterday's image was probably the least impressive FOTD of the past 11 years, and that's talking about a lot of fractals. Today's image is a small bit of an improvement. It is a view of Seahorse Valley, a slit view that I can virtually guarantee has never before been seen. The view is almost in the Rectangular direction, oriented so close to it that it was necessary to stretch the scene about 75 times in the vertical direction before the remnant of Seahorse Valley became recognizable. (The rectangular orientation is determined by the imag(z) and imag(c) axes of the Julibrot.) Where is the rest of the Mandelbrot set? This is a question I cannot answer. It is probably off somewhere, a lost potentia in a space of five or more dimensions, making the quest absolutely futile. I have been trying unsuccessfully for 20 years or so to visualize something with only four spatial dimensions, so far without success. Apparently I need to have my consciousness expanded before higher-dimensional awarenedd becomes possible. Maybe the local mystic, Madam Zucchini, can be of help. I named today's image "Portal to Infinity" and rated it at a 5. The calculation time of under 2 minutes should cause no hardships. And to be doubly sure no hardships are incurred, the completed GIF image has been posted for instant viewing and enjoyment on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A very pleasant and refreshing day here at Fractal Central on Tuesday, with a temperature of 72F 22C, was made even fresher by a quick shower that passed over at 6pm, followed by a brilliant rainbow in the east. The fractal cats, not appreciating the small pleasures of nature, slept through it all. My day was busier than I would have preferred, but much better than yesterday, when I posted a hasty fractal that virtually duplicated and was a poor imitation of the not-all-that-great image of the day before. The current work rush has about ended however, so tomorrow's FOTD, which will appear in the usual 24 hours, will likely be a vast improvement over today's. Until then, take care, and walk with the fractal elite. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Portal_to_Infinity { ; time=0:01:51.10-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot2 passes=1 center-mag=0/0\ /33.52388/0.01407/90/0 params=89/88/0/90/-0.75/0/0\ /0 float=y maxiter=3600 inside=0 periodicity=10 colors=000JEYKGaLIfMJjNLoONsOOwRNtUNrLEDLDDLCCLBCf\ AQgCSgETgGUgIVgKWhMYhOZhQ_hS`hUaiWciYdi_eiaficgjfk\ iehhdegdbfc_ebXdbUcaRb`Oa`L`_I_ZF_Y9ZZCY_EX`GXaIWa\ KVbMVcOUdQTeSSeUSfWRgYQh`QibPidOjfNkhNljMmlLmnLnpK\ orJptKuyJpvIlsHhpGcnG_kFWhERfDNcDJ`CEZBAWA6TA2RD5U\ F7XH9_KCbMEeOGhXFjeElnDmkGjhIheKfbNd_PbXR`UUZRWXOY\ VL`TIbRGdPHeQIeQIeQJeQKeRKeRLeRMfRMfRNfSOfSOfSPfSQ\ fTQfTRgTSgTSgTTgUUgUUgWVg_VgcWigXkkYmoZosZnrZlqZjp\ ZgpZeoZcnZamZ_lZYkZVkZTjZRiZPhZNgZLg`KeaKdbJbcJadI\ _eIZfIXgHWhHUiGTkGRlFQmFOnFNoELpEKqDIrDHsCFtCEuCDu\ JGuQJuXMucPujSupUtnTslSrjRqhRpfQodPnbOnaOm_NlYMkWL\ jULiSKhQJhPJiNIjLHkJGoKAmJDkIFjHIhGKgGNeFPcESbDU`D\ X_CZYBaWAcVAfT9hS8kQ7mP7oR9nTAmUClWDlYEkZGj`HibIic\ KheLgfNfhOfjPekRdmScoTcpVbrWavT_tV`sXarYbq_cpadobe\ ndfmfglghkiijkjilkhnlgpmfqnesodupaywbwtcvqdtneskfq\ hfpegnbhm`ilYjjVjiSkgPlfM } frm:SliceJulibrot2 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 17-06-08 (Oblate Figure [5])
by Jim Muth 17 Jun '08

17 Jun '08

FOTD -- June 17, 2008 (Rating 5) Fractal visionaries and enthusiasts: Today's FOTD is late. My excuse -- too much work rush to finish the FOTD on time. Mandelbrot midgets are instantly recognizable. Julia midgets are more varied, but are almost as easily recognized. But what of the midgets in the other four planes of the Julibrot? Do they have certain characteristics that can instantly be recognized? Well, all the odd midgets resemble Julia midgets to some degree, but I can recognize certain Oblate features. Today's image, which lies in the Julibrot part of the second valley beyond Scepter Valley, is an Oblate figure, which explains the name "Oblate Figure". I rated the image at a 5. I have probably posted similar images in years past. The calculation time of 10 minutes is deceiving. About 90 percent of the total time is spent calculating the single center line, which lies along the real Z axis, and is actually the tiny space between the two branches of the valley. But why worry with slow center lines? Go to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and see the totally finished image there. A warm muggy day here at Fractal Central on Monday turned quite pleasant when a mild thunder-shower arrived in the afternoon, dropping the temperature from 86F 30C to 64F 18C. The fractal cats enjoyed the refreshing change. My day turned more pleasant in the evening when the work was finished. It's too bad the hurried fractal left much to be desired. The next fractal, however good or bad, will be posted in 24 hours. Until then, take care, and be at peace. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Oblate_Figure { ; time=0:10:33.29-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=Oblate passes=1 center-mag=+0.00449922\ 471287127/+0/113.4132/1.3729 params=-1.39404628522\ /0/-1.39404628522/0 float=y maxiter=350000 inside=0 outside=tdis logmap=17 symmetry=xaxis periodicity=10 colors=000JikImlHqlGnkGkjGhiFehFbgF_fFXfEUeERdEOcD\ LbDIaDF`DD`EC_FC_FB_GB_GAZHAZH9ZI9ZI8YJ8YK7YK7YL6X\ L6XM5XM5XN4WN4WO3WO3WP4VQ5VR6VS6UT7UU8UV8TW9TXATXA\ SYBSZCS_CR`DRaERbEQcFQdGQ`9AdGQjMflKemIdoGcpEbqCas\ A`t8_u6Zw4Yx2Xy0Wx6axCfwHkwNpwSutVqrYnp_jnbglddjg`\ giYelUcnRaqO_sKYvHWxEXxGYxHYxJZxK_xM_xN`xPaxQaxSbx\ TcxVcxWdxYexZex`fxagxcgxdhxfixgixhgviftidricpianj`\ ljZjjYhjWgjVekTckSakQ_kPYlNWlMUlKSlJRlWVUTXRQ_NObK\ LeGJhDGk9Dn2Em6ElAEkEFjIFiMFhQFgUGfYGeaGdeGciHbmHa\ qH`uH_xJ0tI3qI5oI7mI9jIBhIDfIFcHHaHJ_HLXHNVHQTHSQH\ UOGWMGYJG_HGaFGcCGeAGg8MV9Gi6Bz4Ax39w39u38t38r37q3\ 6p36n35m35k34j33i33g32f32d31c31b36eBBgJFiQKkYRrgOm\ dLibId_F`YCWV5PUASTEUTIWTNYTR_TVaT_cTceTggTehSdhRc\ iQaiP`jO_jNYkMXkLWlKUlJTlISmHQmGPnFOnEMoDLoCKpBIpA\ Hq9Gq8Fq7Gp9GoBGnDHmFHlHHkJIkLIjNIiPIhRJgTJfVJeXKe\ ZKd`KcbLbdLafL`hL`iKej000 } frm:Oblate {; Jim Muth real(z),imag(c) z=real(pixel)+p1, c=flip(imag(pixel))+p2: z=sqr(z)+c, |z| <= 16 } END PARAMETER FILE=========================================

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FOTD 16-06-08 (Royal Scepters [5])
by Jim Muth 16 Jun '08

16 Jun '08

FOTD -- June 16, 2008 (Rating 5) Fractal visionaries and enthusiasts: Yesterday's fractal showed a little-known scene in the Oblate view of Seahorse Valley. Today's fractal does the same with the next valley out the negative X-axis of the Mandelbrot set, the valley at -1.25, also known as Scepter Valley. I named the image "Royal Scepters" because it is filled with the scepter-like elements that give the valley its name. When the time came to rate the image, I could grant it a rating no higher than a humdrum 5. Just as was the case with yesterday's image, I suspect I have already posted at least one FOTD image nearly identical to today's. In addition to the less-than-outstanding rating of today's image, its calculation time is a snail's pace near-19 minutes. No wonder I recommend viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> And BTW, the 'Oblate' sets are the set of planes determined by the real(Z) and imag(C) axes of the Julibrot. They are kind of hybrids, half Mandelbrot, half Julia, though in today's image at least, the Julia characteristics appear to dominate. Near perfect weather prevailed here at Fractal Central on Sunday, with blue skies, puffy white clouds, and a temperature of 86F 30C. The fractal cats must have taken the good weather for granted, as they slept through most of the afternoon. I tried to enjoy things as much as possible, though yard work always seems to prevent a day from being as pleasant as it otherwise could be. The next fractal will be posted in 24 hours, more or less. Until then, take care, and they say that God knows everything. Why then, does He bother to create souls that He already knows are destined to be lost? Another question: what could a person do to save himself if he discovers that God knows he is destined to be lost? (Or is this just another version of the grandfather paradox?) Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Royal_Scepters { ; time=0:18:51.52-SF5 on P4-2000 reset=2004 type=formula formulafile=slices.frm formulaname=Oblate passes=1 center-mag=-1.70684/0/\ 48.56702/2.774 params=0/0/-1.25/0 float=y maxiter=1750000 inside=255 outside=tdis logmap=4 symmetry=xaxis periodicity=10 colors=000BEf8Ff5Gf3GfEOiPVl_aojhrd`m_UiUNePF`J8XE\ 1TK7OQDKWJGi6Kn2NpBSrJWtR_vZcxfgynkvomtpnrqopqpnrq\ lsrjtshttfupevmdwjqxlqylqzkpzkpzkpzkozkozjozjnzjnz\ jnzjozkpzlqzltzmuzlvzlwzmxznyznzzozzpzzWzzWzzXzzXz\ zXzzYzzYzzYzzZzzZzzZzz_zz_zz_zz`zz`zz`zzazzazzbWRt\ WPsXNsXLrYJrYHqYFq_GnaHkcIheJfgKciL`kLZiM`hMagMbfM\ ceMddNfcNgbNhaNi`Nj_Nk`PiaRgbTfcVddWbeYae__faYgcXh\ dVifUjhSjjQklPlmNmoLnqKosIotHmrGlqGjoGinGglGfkFeiF\ chFbfF`eF_dFZbEXaEW_EUZETXESWDQUDPTDNRDMQDLPDPNFTM\ HWLJ_KLcJNfIOjHQnGSqFUuEWxDXoKUfQSYXQQbOHiM8oK0uI1\ vG1wE1wC2xA2x82y62y52q62j72b82W92OA2HB2AC6CFADHEEJ\ IFLMGNQHPUIRYJTaKVeLXhMZeLabKc`JeYIgWHiTGkQFmOEoLD\ qJCsGBuEBwDDsCFpBHlAJi9Le9Nb8PZ7RW6TS5VP4XL4ZI5`K5\ aL6cN6dO6eQ7gR7hS7iU8kV8lX9nY9o_9p`AraAscAtdBvfBwg\ BxhAvaAtVArO9pH9nA9l4Cm8EmBHnFJnIMnLOoPRoSTpWWpZYp\ a`qebqhdqkbjl`dl_YlYSlWMl } frm:Oblate {; Jim Muth real(z),imag(c) z=real(pixel)+p1, c=flip(imag(pixel))+p2: z=sqr(z)+c, |z| <= 16 } END PARAMETER FILE=========================================

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FOTD 15-06-08 (A Pale Seahorse [5])
by Jim Muth 15 Jun '08

15 Jun '08

FOTD -- June 15, 2008 (Rating 5) Fractal visionaries and enthusiasts: I named today's image "A Pale Seahorse" and rated it at a 5. The unimpressive rating is due to the fact that I might have posted a couple very similar images during the long history of the FOTD. The name refers to the rather pale interior of the image, as well as the fact that it is an unfamiliar view (part of the Oblate view) of Seahorse Valley. Due to the extreme maxiter, the only way to color the image effectively was to use both the logmap and 'tdis' options. To give optimal proportions, it was necessary to compress the scene slightly in the vertical direction. The calculation time of 2-3/4 minutes is fair enough for most fractalists. And if the included parameter file fights back on an over-qualified machine, the finished image is easily viewed on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Lots of haze, clouds and high humidity made Saturday less than ideal here at Fractal Central. The high temperature of 88F 31C made things even worse. The rain threatened but never arrived. The fractal cats mostly ignored the outside conditions, but they did watch carefully as a chipmunk scurried about in the grass, stuffing his face with who knows what. My day was un-notable and I expect tomorrow to be the same. The next FOTD will be posted in 24 hours. Until then, take care, and use it, whatever it is, to the utmost. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Pale_Seahorse { ; time=0:02:42.22-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot2 passes=1 center-mag=-1.4048/0/7.48356/1.7871 params=0/0/90/0/-0.75/0/0/0 float=y maxiter=300000 inside=255 outside=tdis logmap=4 symmetry=xaxis periodicity=10 colors=000GX7GV7GS7IP7IN7IL7JI7JG7JE5LA5L95L75N35N\ 15N05N05S3AZ9GbCLhIPmLVqR`xVdz`jzdozjtzmzztzzxzztz\ zoqzlhzh`zdRx`JqXAmS3hP0dL0`J0XN0VR0SS0PX5N`ALbGIf\ NGjSElZAof9tl7vq3zz1zz0zz5zz9zzCzzIxzLvzPtzVqzZozb\ mxhlvljtohtvfqzdozbozZtvVvqRxoNzlJzhGzdCzb9zZ5zV1z\ R0zP0zS0zX1zZ3zb5zd7zh9zi9zjAzkBznDzqFzrHzuLzwPzyT\ zzXzz`zzdzxgzxhxxgtxgoxelxchzbbzaZzaSzbPzdLzfGzhCz\ j7zl3zl0zj7zhEzfLqdSjb```hRZoIXxAXzL`vVdodhjmjdzmX\ zqRzvLzxGzzJzzNzzRzzSzzXvz`qzblzffzj`zmXzoRztLzxIz\ zNzzRzzXmz``zfPzjCzo1zt0zx0zo5zhVz`xzVzxPzmLzfGzXC\ zPL00E0090310700C00G00J00L01N7CPENRN`SVlVdxXlzZtzZ\ zzdzzjtzoSzt3zx0zzSLzXJz`JzdJzhIzlIzoIzqIzV7z90z00\ zXEfVIjVLmSNqSRvRVzRXzR`zPdzPfzNjzNmzNoz9xx0z`0zE0\ zI0zJ0zL0zP0zR0xS0tX0qZ0o`0md0lf0jh0hj0db0`V5XNASG\ IP9NL1SI0ZE0dC0hG0jI0lJ0mL3qN9tPEvRIxSNzVSzXZzZdz`\ jzbmPNdJIREEEAA1CJ5ES7E`9 } frm:SliceJulibrot2 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 14-06-08 (The Bug-Eyed Tree [6])
by Jim Muth 14 Jun '08

14 Jun '08

FOTD -- June 14, 2008 (Rating 6) Fractal visionaries and enthusiasts: Today's strange image shows a kilroy-like alien head peering over the bottom of the frame. The top part of the image shows fractal stuff on the way to becoming a fractal tree. Combining both, I named the image "The Bug-Eyed Tree". The image is actually a near-Julia set of the (-Z)^sqrt(2)+C Julibrot. Actually, the slice is oriented 0.02 degree from the Julia direction toward the Oblate direction. This tiny rotation is quite important. To see how important, change the real (p1) parameter to 90 and do a thumbnail fractal. I rated the image at a 6. I have seen a few too many of this type of image to rate it any higher. The calculation time of under 3-1/2 minutes is rational, for all this is worth. The finished GIF image is available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Heat, haze and humidity moved back into the Fractal Central area on Friday. As the temperature reached 88F 31C, the fractal cats sought the cool air vent. My day was acceptable; the fractal, a bit goofy. The next fractal, goofy or not, will be posted in 24 hours. Until then, take care, and why must all space aliens have bug-eyes? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Bug-Eyed_Tree { ; time=0:03:28.90-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot5 passes=t float=y center-mag=0.190223/0/15.24794/0.8869/90/0 params=89.98/90/90/90/-1.124575/0/0/0/1.4142/0 maxiter=3600 inside=0 logmap=20 periodicity=10 colors=000KKVKKUKKTJKSIKRHKQGKPFKOEKNDKMCKLBKKAKI9\ KG8KE5KA2K73K93KB3KC3KE4KG4KH4KJ2KG4KK6KO7LS9LVBLZ\ CLbELfEHlFJjFLiFNhFPgFRfFTeFVcFVbFVaFT`FR_FQbFO`FM\ ZAKY6KW2IV4JT6KS8LRAMQCNPEOOGPNIQMKRLMSKOTGNSJNRMN\ QONPRNOTNNWNMYML`MKcMJeMIhMHjMGmGEkJFmMGoPHpSIrVJs\ SLqQMpNNnLOmIPkGQjERiBSg9Tf6Ud4Vc2Wb5Uc7ScARdCPdFN\ eHMeKKeMIfPHfRFgUDgWCgWBfWBfWBeWBeWBdWAdWAcWAcWAbW\ AbW9aW9aW9`W9`W9`NRbEgd6xfAq8Do9GmAJkBLjCOhDRfETeF\ WcGZaH``IcZJfXKhWLkUMnSNoLOpROpXOqaOqgOeOmtkMqlOol\ QmlSklUimWgmYem_bma`mcZneXngVniTnkPuvQqqRnlSjhSgcT\ c_UcVVcRVcMWcIXcDZc9`c6bb6dc6fd6gf6gg6gh6hj6hk6hl6\ in6io6ip6ns7io6di6`a5WU5PC1RI3SL5TP7VU8WYAXbCZhD_n\ F`uH_wWazKenPldUhcZdbc`ahcamf`ri_wlVzmXzn_znazoczp\ fzpizqkzrnzrpzuuzvwzzzztvzsszqovokrnhmmehmcdlbblb`\ kb_kaYjaWjaVj`Ti`Ri`Qh_Oh_MlYHjZJh_Lf`NdaPbbR`cSZd\ UXeWVfYTg_RhazYxgcmPhb3pR } frm:SliceJulibrot5 {; draws slices of (-Z)^n Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=(-z)^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 13-06-08 (Bat-Fractal [No Rating])
by Jim Muth 13 Jun '08

13 Jun '08

FOTD -- June 13, 2008 (No Rating) Fractal visionaries and enthusiasts: Today's ultra-quick image is simply a new view of East Valley of the Mandelbrot set. More accurately, it's an oblique view of the East Valley complex of the Z^2+C Julibrot. I named it "Bat- Fractal" after one of my favorite comic book heroes from long ago -- Batman. The large dark bat-shaped feature dominating the image inspired the name. I particularly enjoyed the Batman stories because Batman was, and still is, a mere mortal human with finely-honed but still normal human abilities as well as vulnerabilities. I could dream that one day I might be like the Batman, while heroes like Superman and Captain Marvel were total fantasies, far beyond human attainment. I also enjoyed the Green Lantern stories, about a hero who used psychokinesis, the power of his mind, to overcome his enemies. Too bad none of these old comic heroes ever heard of fractals. Well, there's not much to be said about the appearance of today's image, except that this is how one of the four- dimensional 'bridges' of East Valley appears when stretched about 100 times in the vertical direction. Some hints of the East Valley elephants are also scattered throughout the scene, though I could find no fully formed ones. Unfortunately, the image does not earn a rating, but it still has a bit of curiosity value. And the calculation time of only 3-3/4 minutes is not at all bad. The most convenient way of enjoying the image, as always, is to visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view it in finished form there. Near perfect conditions prevailed again on Thursday here at glorious Fractal Central. The clear skies and temperature of 84F 29C made everyone including the fractal cats happy. My day would have been a bit more pleasant if the work had been a bit lighter, but I'm not complaining. The next FOTD will appear in 24 hours. Until then, take care, and do what's right. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Bat-Fractal { ; time=0:03:37.44-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot2 passes=1 center-mag=+0.002707327725631/0/124.5/0.01064/-90/0 params=45/90/0/45/0.265/0/0/0 float=y maxiter=6400 inside=253 logmap=23 periodicity=10 colors=000mJKDNRH4DBCK6KRaW9otfblcQeaDYZYh7PcEH_K9\ VRDZOAXR7VT4TVRzoInh9bbvm4wQehRbUR`FRZcjRRloKfjEae\ 7W`w0t6l14f93aH2WPFkMAdQ5YU2Bt1Hl1MdmyIPgQl84`DCPI\ JDNQfsdTiaF_ZPbkHZf9VaIRMDRP9RS5RVP15DEJQvGJnLDfP7\ ZT8py5go3Ze1o11h91bH1XPpVfcUcRTaESZbaLKKuEjx9cn5Xe\ K`d2uF1jL1`RLhWbCPKcnpWLcUORTRESUh9CNINK53DDD7KNOd\ vZ7rIHgzdmj`hWYdGU`fWyWUqMTjBSc4i`3d_2_Z1VYrntdhnS\ bhEXbfSMWRPMRSBRVE9P7ITlQ3_T6ISK3T3VffGZab17KEKN9g\ CIa3Z42XC2VJ1TQp77RHKL73GCBBHI6MQpRJZROIRTA1T7AV4J\ WTCq7kQ5dT3YVDloHryBho6_e8jk4`cY1uNAlCJdJyHEpLAgP5\ ZT`F2JLIB2G7BM4JSPELHJP9NTOTjTmZJeYAYXHGIBKN6OS_RS\ ORUCRW1eBHzz9zzOzzvzzUzz2zzNzz`zzSzzJzzAzzDzzAzz7z\ z4zzFzz8zzozzyzzqzzUzzMzzFzz8zzQzzJzIDzN7zSZzqNzjC\ zcuzVLzYBzXUzvKzmAzd1zV1zWwzzUzzBz87zH4zPhzqYzkNzf\ zzwWzwXzw`zrcznfzjizfhzRhzzbzzYzzMzzBzzDzzFzzHzzIz\ zPzzVzz`zzfzzhzzM0`ozzbzz } frm:SliceJulibrot2 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 12-06-08 (Forever Down South [8])
by Jim Muth 12 Jun '08

12 Jun '08

FOTD -- June 12, 2008 (Rating 8) Fractal visionaries and enthusiasts: Today's image shows one of the most impressive minibrots that I have ever found in the exponent range between 1 and 2. The parent fractal was created by the formula Z^(1.5)+C as it appears 11 levels up the complex log ladder when the 'recip' function is applied. This parent resembles a fairly normal looking mandeloid with an unusually long zigzagging filament extending south from the main bud and curving east. A large minibrot lies on this filament, and today's scene is located in the East Valley area of this larger minibrot. The image consists of unmistakable East Valley Julia set stuff. It seems to be a universal fact that minibrots of all orders, which are located in the East Valleys of larger minibrots, have the same underlying appearance. The same is true, though perhaps to a lesser degree, of the minibrots in the Seahorse Valleys of larger minibrots. I named today's image "Forever Down South". I am not sure why I gave it this name, but the name is not totally inappropriate. After all, the scene does lie well south of the main part of its parent fractal. The rating of an 8 is due in large part to the coloring, which largely makes the image. The calculation time of 1-1/3 minutes is quite brief even in the eyes of the most impatient. And as always, the pre-calculated image is available for instant viewing on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A perfect day here at Fractal Central on Wednesday was fully appreciated by the fractal cats as well as the fractal-sapiens. The sunny skies, low humidity and temperature of 81F 27C could hardly be improved upon. With a repeat expected tomorrow, the satisfaction should only increase. The next FOTD is due to appear almost by magic in 24 hours. Despite the disagreement of skeptics, magic does happen, so expect the next FOTD image to appear on schedule. Until next time, take care, and also walk with care. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Forever_Down_South { ; time=0:01:20.71-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=recip center-mag=+0.4122069256216793/-2.500438043275711/\ 2.156969e+010/1/90/0 params=1.5/0/11/525 float=y maxiter=1500 inside=0 logmap=208 periodicity=10 colors=00000K00K00K00K00K00K00K01K23I65H86IB9IFCHI\ EGLGFNIGRLLWOPaRUfUXkX_oYbr_dx_gz_izblzcnzdpzeqziq\ zlpzoqzrtzvxzyzzzzzzzzzzzzzzzzzzzzzzzxrztkxobqkYkb\ VbVcVQmjNwzTwsKwkPqgJqaGhT8`I0060bzzF0L008000F9zzT\ zFztIzWDzVIzTNzTRnRVaQ__PdWPgVNkTLkRKlPKnNIqLGtKGx\ LPtNVqPalQgfRn_RzVQzWQzYQzYPz_Pz_PzaNzaNxbNtdLtdLo\ fLofKlgKkgKgiKfiLbfL_dLWbLVaNR_NQWNPVNLTPIRPIQPGNP\ FLQFKQFIQFGQGFTLKVQPYVR_YWbb_dfdggiikllnqnotkqoiql\ gqifrfdrbbrYatV_tRYtPWvLVxGTyDRz9Qz6Pz2Qz1Rv1To1Vk\ 1Qg8NdFKbKGbQDaV9_a6Yg2Yl0Wr0Vx0Tz0Tz0Wz0Yz2_y8avB\ drGfoKgnPikTkgWndaoadqYirVltTglKdd9aY1YQ0VK0WP0YT0\ YY0_b0_g1al6bq9bvDdzGdzKbzIazI_zIczIpzIzzIzzIzzIzz\ IzzIzzIPzLPyPPrRPlVPfYP_aPTbPNfPGiP9lP2oP0rP0vP0xz\ zz0t02z9BzK4zP0zT0zY0za8zNVz8zz0zz0zz1zz4zzBzzGzzz\ zzNzzzzzzzzrzzdzzgzzazzWzz8zzFzzLzzzzzkzzFzz0zz8zz\ zzznzz0zz0zz4zzGzzdzz_zzF } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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Re: [Fractint] a thought to clarify
by JackOfTradeZ＠comcast.net 11 Jun '08

11 Jun '08

Jim Muth say: "And it's just as hard to approve of the world's religions, which, after pronouncing conflicting doctrines for thousands of years, have still not found a way to demonstrate that the super- natural things they teach, such as God and the afterlife even exist" I would say: Now faith is the substance of things hoped for, the evidence of things not seen. Through faith we understand that the worlds were framed by the word of God, so that things which are seen were not made of things which do appear. (Hebrews 11) And I have always been intrigued by the fact that "worlds" is in plural, not just "world", as in only Earth ..... Keep dreamin' JoTz

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FOTD 11-06-08 (According to Hoyle [in doubt])
by Jim Muth 11 Jun '08

11 Jun '08

FOTD -- June 11, 2008 (rating in doubt) Fractal visionaries and enthusiasts: When the parent fractal of today's image is rotated minus 90 degrees, it resembles a Mister Potatohead toy, with a ridicu- lously large period-2 bud stuck on its left shoulder, a period-3 wart on its right shoulder, and a period-5 pimple on its butt. Today's scene lies in the western valley leading to the period-5 pimple. I have no idea what happened to a potential period-4 pimple. Anyway, today's image has little to recommend it. Due to the threat of lightning, I kept the computers unplugged most of the afternoon, which left little time for a proper fractal search. The only thing today's image has going for it is its striped appearance, which was created by rendering the scene with the outside set to 'tdis'. But even the stripes are so finely divided that they lose most of their effect. As a result, I gave the image no rating. The name "According to Hoyle" simply came to mind as I studied the image. (Perhaps a psych could do a fair analysis of me from the names I give the FOTD images.) The final bad news is the calculation time, which is a dragging 25 minutes. Run the parameter file if you wish, but I recommend visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the image is or soon will be posted for instant access. Tuesday here at Fractal Central started sunny and very warm. But a series of brisk thunder-showers moved in around 3pm and continued until dark. The temperature reached a high of 93F 34C just after noon, but by 6pm was down to a very comfortable 75F 24C. The fractal cats rejoiced. And if the next FOTD, which will be posted in 24 hours, is better than today's, I will rejoice also. Until the rejoicing starts, take care, and as the wise shepherd says, when you see a storm coming, get the flock out of there. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= According_to_Hoyle { ; time=0:25:16.83-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=recip passes=1 center-mag=+0.6839673892413574/+0.164658493324798/\ 184137.8/1/-102.5/0 params=1.25/0/0.2/0 float=y maxiter=32767 inside=0 outside=tdis periodicity=10 colors=000n4Pp2Nq1Mo3Ln5Lm7Ll9KkBKjDKiFKhHJgJJfLJe\ NJcOIbQIaSI`UIMMRHJOCGL7DI9DJBDJDDJEDJGDJIDKJDKLDK\ NDKP9HOBJODKNFMNGNMIPMKQLMSLNTLPVKRWKTYJUZJW`IYaI_\ cHWfI`dIdcJhaJm`KqZKuYKyXMuYNrYOoYPlYQiYSeYTbYU_YV\ XYWUYC8pXRYqiGpiFpiFpiEoiEoiEoiDniDniDniCniCmiCmiB\ miBliBliAliAkiAki9ki9ki9ihEggIfgMdfQbfUaeZ_ebYdfXd\ jVcnRfvUcrX`oZYlaWhcTefQbiNZkLWnITpFPsCMw9KuAJtBJs\ CJrDJqEJpFJnGJmHJlIJkIIjJIiKIgLIfMIeNIdOIcPIbQIaQI\ _VIYZIXbIW`KW_MWYOVXPVWRVUTUTUURWUQYTPZTN`TMbUNcTM\ cTLcTKcSJcSJcSIcSHcRGcRFcRFcREcQDcQCcQCcQBcPAcP9cP\ 8cP8cO7cO6cO5cO5cQ4cR4c_5hg6mo6rn9qnBpnDonFnmHmmKm\ mMlmOklQjlSilUhlXhkZgk`fkbekddpmekfdf_daTcYNcTGbO9\ bK3bL4`M4_N4ZN5XO5WP5VQ5UQ6SR6RS6QT6PT7NU7MV7LW7KW\ 8IX8HY8GN2HT5GY8FbBEhEDmHCrKByF3wMBvSIuYPtcXsicroj\ quqnlXpd4kcDgbLcaTZ`aV_iP`sRZqTXoUVmWTkXRjZPh_NfaL\ dbJbdIaeG_gEYhCWjAUk8Tm6R } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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FOTD 10-06-08 (How Now Brown Cow [4])
by Jim Muth 10 Jun '08

10 Jun '08

FOTD -- June 10, 2008 (Rating 4) Fractal visionaries and enthusiasts: Today's image lies in the debris along the southern shore line of the main bay of yesterday's fractal image, which is then the parent fractal of today's image. This fractal, when its inside is not decorated, resembles nothing as much as a quail brooding a clutch of eggs. But such things are for the birds. I named today's image "How Now Brown Cow", which I admit makes no sense at all. Of course this is no surprise. As FL often tells me, if I had any sense, I would devote far less time and energy to the useless FOTD. But then I tell FL that some people just cannot see the worth in these fascinating images. I rated today's image at a 4, which might be a gift. I found it in less than 5 minutes, and gave it far too little coloring effort. Hot weather makes me lazy. The calculation time of a mere 1-1/4 minutes can be improved upon only by viewing the already-calculated image, which is or soon will be posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Continued heat and blazing sun made Monday a very lazy day here at Fractal Central. The high temperature of 97F 31C made swim- ming and boating the activities of choice. The fractal cats' activity of choice was sleeping, and my activity was clearing away the work. The next FOTD will appear in 24 hours. Until then, take care, and if life serves up a lemon, make a lemon fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= How_Now_Brown_Cow { ; time=0:01:13.35-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=floor passes=1 center-mag=+0.1973598/-0.7442536/622.1558/1/22.5/0 params=1.237/0/14/0 float=y maxiter=1500 inside=0 logmap=92 periodicity=10 colors=000_QSYRSVTSTUSRVRPWRMXRKYQIZQG_QE`QC_OB_MA\ _K9`I8`G7aE6cC5cA4a83`62_41Z50YA4WF8TKCQPGOUKMZOKc\ SIhWMg_SecXcgbakg_omYsrWqsYps_os`nsbmsdlseksgjshht\ jgtlftmetodtqctrbttatuljkwaatZZqXWnVTlSQiQNfOKdLHa\ JEZHBXF9UGCSGFQGIOGLMGOKGRIGTFHWDHZBHa9Hd7Hg5Hj3Hl\ 8NhCSeGXbKa_OfWSkTWpQ_uNczKbxLbvLbuLasMarMapMaoM`m\ N`lN`jN_iO_gO_fO_dOZcPZaPZ`PYZQYYQYWQYVQXOXXHcXAjX\ 3pZ5o_7n`8naAmbBmcDleFlfGkgIkhJjiLjjMilOimQhnRhoTg\ pUgqWfrXfnWdkWchWaeW`bV__VYXVXUVWQUUNUTKURHUQETPBT\ N8TM5TL7UK8VK9VJAWJCWIDXIEXHFYHHYGIZGJZFK_FM`EN`EO\ aDPaDRbCSbCTcBUcBWdAXdAYe9Ze9lOIz6QnAUcDYSGaHJe6Mi\ 8IdAE`CAXAVW8oWMRk_3z`5y`6y`7x`8x`Ax`Bw`Cw`DwaFvaG\ vaHuaIuaKuaLtaMtaNtdJkgFbjCUm8Lo5C`CQNJb9PoASmBVlC\ XkD_jEbiEdhIfkMhmPjpTlrWnu_pwbryr8ppAnoClnDjmFilHg\ kIejKciLbhN`gPZfQXeSWdUUcVSbXQaYPZXRXXSVXUSXVQWXOW\ YLW_JW`HVbEVcCVeAVf9Xg9Zi } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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Using Fractint 20 in XP
by Robert Baker 09 Jun '08

09 Jun '08

Apologies if this has been raised before; I've just joined and don't know if there are any archives, or where to find them. Although 18 worked fine in a DOS prompt under Windows 95/98 (don't laugh), now I have a shiny new computer running XP, 18 and 20 both crash this (resulting in a, rare IME, BSoD) if I try to run them under a Command Prompt. Hence I have to run them under DOS-Box (0.72). * How do I set up DOS-Box to run Fractint (or the like) with maximum power? * How do I avoid the corruption of the output screen when I switch out of drawing and back within Fractint, or when I switch away from DOS-Box and back? BTW, 20 seems to have lost the Palette Editor, and not gained the promised 32767-pixel limit (the latter according to the help, which still says 2048). Can anyone enlighten me?

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Screen mode (widescreen) for a Packard-Bell laptop?
by Robert Baker 09 Jun '08

09 Jun '08

I have a PB laptop bought back in January, and want to be able to run DOS Fractint 20 in its native res of 1280x800(x2^32, although of course for Fractint purposes I'd like a colour depth of 256). I've tried to assign this mode to the F2 key with a fast hack of FRACTINT.CFG, but having done almost no machine-code programming on the PC I don't know what the register values should be, so I just left the existing ones. The resulting mode gives a display of sorts, but in graphics mode it's garbled. Does anyone have any idea what I should type? I don't know what chipset the onboard display adapter is, nor how to find out... (Would setting it as a VESA mode instead work? How do I do that?)

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FOTD 09-06-08 (On Fire Inside [8])
by Jim Muth 09 Jun '08

09 Jun '08

FOTD -- June 09, 2008 (Rating 8) Fractal visionaries and enthusiasts: While FL and I were sitting on the shore of a nearby lake Sunday afternoon, watching the duck families peacefully swim past, she innocently commented on how cynical I am becoming in my later years. She said that I seem to be turning against everything, especially science, religion and politics. She asked me what, if anything, I now approve of. Well, I replied, it's rather hard to approve of a science that fails to include the most important thing of all -- self-aware- ness -- in its search for a theory of everything. (This is why I refer to this theory as 'the theory of almost everything'.) Perhaps the omission is an oversight, or perhaps the physicists do not yet realize that self-awareness is included in the set of everything. If so, this omission should be acknowledged and corrected. Or could it be that they fear ridicule, or even worse, that their venerated scientific method is powerless? And it's just as hard to approve of the world's religions, which, after pronouncing conflicting doctrines for thousands of years, have still not found a way to demonstrate that the super- natural things they teach, such as God and the afterlife even exist. As I often comment, "It seems as though God gave us the faculty of reason so we couild understand his universe, but when we use this gift of reason, we are led to the conclusion that He does not exist." As the nuns used to say, 'it's a mystery'. Oh well, I guess a mystery is better than an accident. As for politics, the less said the better. And this is no mystery. But this leaves the big question unanswered. What do I approve of? Why I approve of fractals. And today's fractal is a typical example. The image consists of the entire parent fractal created by the formula Z^(1.237)+C as it appears 14 levels up the logarithmic ladder when the 'floor' function is used. Without the 'bof60' inside fill, the fractal is rather dull, but with this fill the inside explodes to life. And check those crazy orbit paths of the points around the edges of the circle inside the fractal. It's those wild orbits that led me to try the various inside options on the originally bland fractal. Too bad the orbits cannot be included in a parameter file. I rated the image at an 8. It's worth it. And I named it "On Fire Inside", which the fractal most certainly is. The calcula- tion time of just over 2 minutes means that no one will suffer fractal exhaustion waiting for the parameter file to finish running. An even better way to stay refreshed in such hot weather is to visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view the finished GIF image there. Hot sun, high humidity, and a temperature of 95F 35C made Sunday another lazy day here at Fractal Central. Luckily, Fractal Central is only 1/4 mile from Lake Augusta, where peeping duckling and gosling families make it seem 10 degrees cooler. The fractal cats see baby ducks and geese as food however, not as psychological air conditioners. So they spent the day safely indoors, keeping cool as best they could. My fractal search went well enough, and hopefully, tomorrow's search will go even better. The next FOTD fractal will be posted in 24 hours. Until then, take care, and if we don't know what we don't know, how will we know what we know when we find the answer? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= On_Fire_Inside { ; time=0:02:08.09-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=floor passes=1 center-mag=-0.58138/-0.286362/0.6230116/1/-12.5/0 params=1.237/0/14/0 float=y maxiter=1150 inside=bof60 outside=tdis colors=000G0XRKgVUhYci_ihanhcigecggZfiWfkSemPeoNdq\ RdsUcuXcw_bzcbzg_zlYzl_zneznjzppzrvzvzzzzzzzzzz8W9\ 9TAARABPBCNBCLBDJCEHCFECGCDGADH8DI6EF4EK2EUDIUOMcZ\ PmiTztWmmSVgPcaLUVISPESJBQLIONOMPUKQ_OKYSEWW9VVDSU\ HPTLNSPKtgXwo_ulYtiXsgWrdVqbUp_TnXRmVQlSPkQOjNNiKM\ hILfFJeDIdAHc7Gb5Fa2E`0D_1CZ1BY2BX2AW3AW39V49U48T5\ 8S57R66R66Q75P75O84N84M93M93NB5NC7ND9NEBNFDNHENIGO\ JIOKKOLMOMNOOPOPROQTPRVPSXPUYPV_PWaPXcPYe567FLPPZf\ _mzZlxZlwZluZltZlsYkqYkpYkoYkmYklXjjXjiXjhXjfXjeTg\ eXjd_lcbobeqaht`lxZkv_jt_jr`iq`hoahmagkbfjbfhcefcd\ ddWW_dcdmkiyuovsnsrnqqnnpmlominmgmldllbkl_jkYikVgk\ SfjQejNdjLciIbiGaiD`hB_h8Zh6Yh7Ye8Yb9Y_AYYBYVBYSCY\ PDYNEYKFYHGYEGYCFWGFVKFUNFSRFRUEQYEP`ENdEMgELkDHpE\ KnFMmGOlGQkHSjIUhJWgJYfK_eLadMdbMfaNh`Oj_PlZPnXQpW\ RrVStURxQSwSSvTSuUStVSsWSrXSrZSq_Sp`SoaSnbSmcSmeSl\ fSkgSjhSiiShjRlrShkTddT`Y } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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Rants (sorry but...)
by Robert Baker 08 Jun '08

08 Jun '08

1) FOTD date format: This is somewhat ambiguous at the moment, although it appears to be Short European (dd-mm-yy), which is probably a better choice than (Short) American even if only because it's more widely used. Remember that there are at least six numeric date formats; Short European, Short American (mm-dd-yy), Short Japanese (yy-mm-dd), and the Long versions (yyyy instead of yy; Long Japanese is more usually known as ISO-8601 or International). Of these, International is the only one that's completely unambiguous to everyone, hence the name. 2) Will people please not send large files, even off-list, as happened to me as a result of my problems with DOS Fractint 20; at my current account level, this account has quotas of only 16Mb storage and 40Mb/monthly bandwidth (which I think includes incoming BW), which are normally ample for me, but won't be if several people decide to send me large files (fortunately, it was only the one). Unsolicited large attachments (only 0.6Mb larger and it would have been bounced by my filters) are considered rude by many; kindly send a *link* to the file instead, and if I want it, I can then get it myself. Sorry about that; we now return you to your scheduled list. :-)

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Re: [Fractint] Using Fractint 20 in XP
by gnome＠hawaii.rr.com 08 Jun '08

08 Jun '08

I'm not sure you can fix it at Fractint's end at all. I used to experience that back in the days when I was dualbooting between Windows98SE and OS/2. Fractint ran fine under OS/2, with no problems whatsoever. NOTHING I tried with Fractint under W98 made a difference. The problem was in the Windows video drivers, not in Fractint - Windows would fight over the video hardware and die. It was specific to the Windows drivers for the video hardware - other people were (at the time) running Fractint under Windows98SE without any problems. That was one of the reasons I quite using Windows (that and the fact that Fractint could bring Windows to a standstill for any other uses when it was generating an image to disk, and not bother OS/2 at all). When I do fractals here now, I use XFractint. It would be particularly lovely with a dual monitor set up - put the text mode command window on one monitor, and stretch the image window out across the other monitor ... -- david gnome(a)hawaii.rr.com authenticity, honesty, community ---- Robert Baker <mandy(a)rjbaker.fastmail.co.uk> wrote: > On Sat, 07 Jun 2008 06:46:56 -0500, "Jonathan Osuch" > <osuchj(a)avalon.net> said: > > Robert, > > > > Did you try creating a shortcut to Fractint, then set the properties > > to run Fractint full screen (2 places)? > > Just tried that, as soon as I read your email. New shortcut worked > fine... until I tried switching out of Fractint (whilst in a text > screen), at which point I got the same BSoD as before. :( Since Windows > progs can grab focus and thus force a switch (and hence the BSoD if I > have Fractint running), this needs to be resolved... > > > If you have a machine where the manufacturer has tuned the XP video > > drivers to work with the hardware, you should be able to get this to > > work. > > Unfortunately my laptop (a Crappard-Bell) was optimised for Vista -- the > reason I'm running XP is because of Crappard-Bell's cheapskate policy of > making users roll their own recovery discs (which can only be done once, > so if it doesn't work (as it didn't for me), you're screwed). Still, I > find XP better than Vista, with the sole exception of dial-up > networking.

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FOTD 08-06-08 (The Dreg of Fractals [1])
by Jim Muth 08 Jun '08

08 Jun '08

FOTD -- June 08, 2008 (Rating 1) Fractal visionaries and enthusiasts: I found today's image in 3 minutes, which I think is a new short-time record. It calculates in 1-1/3 minutes, which is quite fast though not a record. The formula behind the image subtracts 1/2 part of Z^(-1.1) from 1/2 part of Z^2 and adds C. Today's scene lies very near the tip of a filament. The magnitude of 1*10^13 is actually a bit beyond the point of breakdown, but the slight bit of jaggedness is hardly notice- able. The magnitude does make the mathtolerance entry necessary however. The rating of a 1 shows what I think of the image. The name "The Dreg of Fractals" echoes the opinion. Even with its calculation time of 78 seconds, the image is most conveniently viewed on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> With a high temperature of 97F 36C, the weather was far too hot for comfort here at Fractal Central on Saturday. It was so hot that FL and I decided to take a day off in the surrounding wood- lands. The day in the woods was cool and enjoyable, but left no time for fractals. While we were out, the fractal cats spent the day stretched in the coolest spot they could find. The next FOTD is due in 24 hours, and as far as I know, it will appear on schedule. Until then, take care, and keep your cool. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= TheDregOfFractals { ; time=0:01:18.71-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=+0.1848571131062667/+1.389112151819734/\ 1.00707e+013/1/5/0 params=0.5/2/-0.5/-1.1/0/0/0/0 float=y maxiter=1500 inside=0 outside=tdis periodicity=10 mathtolerance=0.05/1 colors=000qFhjFidFiYFjRGkLGkEGl7Gm1Gm2Jj3Lh4Ne5Qc6\ S`7UZ8XW9ZU9`SEcRJeQNhPSjOXmN`oMerLitLdpN`lPXiRTeS\ PaULZWHVYDSZDUVDVRDWNDYJDZFD_BD`8Gb9Jd9Mf9Ph9Rj9Of\ AMbBKZCIVDFREDNFBJG9FH7CHBFLFHOJJRNLUQNXUP`YRcaTfe\ VihXlfZke_jdajccibdh`fg_gfZieYjdWlcVmbUoaTp`Sr_QsZ\ PuYOvXNxWMyWVxZcx`lwcuweod`tvdtudtudttdssdsscsrcsq\ csqcrpcrocrobrnbrmbqmbqlbqkbqkaqjapiapiaphapgapg`o\ f`oe`oe`od`EUrGVqIVpJWoLWoMXnOXmQYlRYlTZkUZjW_iX_i\ Z_h``ga`fcafdaefbdhbcicckcbldand`1DmCJjMPgWUee_bjC\ 5kE7kF8kG9kHBlJCD_mCdkBiiBnhDhjEckFZlHUmIOoJJpLEqM\ 9rN4sO9oPDlPHiQMfQQcRU`RYY_f_go`owamc`kK_j0_h6WfBS\ dHPbML`SHZXEXbAVg6Tl3Wj6Yh8`fAbdDecFgaHj_KlYMoWOqV\ QoUTnUVlTXkTZiTahScfSeeSgcRibRl`Rn_QpYQrXQtWRrWSpV\ SnVTmVUkUUiUVgUVfTWhTWiSWjSWkRXlRXmQXnQXoQYpPYqPYr\ OYsOZtNZuNZvNZwO`uPatQbrRcqSdpTenUfmVhlWijXjiYkhZl\ f_me`ndQUmG9vKBpOCjxEhxEg } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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Re: [Fractint] FOTD
by JackOfTradeZ＠comcast.net 08 Jun '08

08 Jun '08

. Animation of Jim Muth FOTD May 26, 2008 is posted: http://www.fractal-animation.net/vid/4dmorph_wmv.zip 9 MEG, 38 sec, WMV format .

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FOTD 07-06-08 (Count Fracula [6])
by Jim Muth 07 Jun '08

07 Jun '08

FOTD -- June 07, 2008 (Rating 6) Fractal visionaries and enthusiasts: A lot of flashy colors and a lot of filaments do not make a superior fractal. This description fits today's image, which rates only a 6. Today's fractal lies in the Z^(sqrt(2))+C Mandeloid as it appears 13 levels up the logarithmic ladder when no function is used. The most notable feature of the parent fractal is its incredibly long main filament. Today's scene is located deep in the East Valley area of the most prominent minibrot on this long zigzagging filament. There is a minibrot at the center of the image, though it lies far beyond the range of resolution. As it is, the magnitude of over 2*(10^12) is right at the limit, and requires the mathtolerance entry to assure that the parameter file calculates at the correct magnitude. I named the image "Count Fracula", though I can see little in it to connect it with that infamous monster. The calculation time of 5-1/2 minutes is about the fractal average. But it is always a convenient choice to view the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A cloudy morning gave way to a sunny hot afternoon here at Fractal Central on Friday, with a temperature of 86F 30C. The fractal cats, feeling the heat, remained in stretched-out mode. My day was unexpectedly busy, which explains the hasty fractal. Tomorrow will be slower, hopefully resulting in a better FOTD image. That image, however good, will be posted in 24 hours. Until then, take care, and wait for whatever is coming. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Count_Fracula { ; time=0:05:34.44-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-2.587188090720521/-2.220584310407471/\ 2.104486e+012/1 params=1.4142/0/13/0 float=y maxiter=1500 inside=0 periodicity=10 mathtolerance=0.05/1 colors=000LESLERLFQLFPLFOKFNKFMKFLKFKKFJXaLhwM_0Z`\ 5W`AU`ES`JP`ONaSLaXJaaGaeEajCanAbmEblHblKbkNbkQbjT\ biWciZchachdcggcfjcfmcepces`hpYjmVljSogPqdMsaKuZHp\ VFlRDgNBcJ9_GCaHFbHHcIKdIMeJPfJRgKUhKWiLZjL`kL_hKA\ 3KG4KH5JI6JK7JM8JO9IQAISBIUCIWDHYEH_FHaGHcKGfNFjRE\ mUDqXCt`BxcAzf9zj8zm7zp7zsBzuEzvHzuKzsNzqQzoTzmWzj\ ZzgazddzagzZLzXNz_OzaQzcRzfSzhUzjVzlXvoYrqZms`iuaj\ wblxdmxfoxhpxjrxlsynuypvyrxytyyvWom3fe3dd3bd3`c3_c\ 3Yb3Wb3Ua3Ta3R`3P`3N_3M_7SaAXcDbeGggJmiMrkPwlZZOgB\ 0fA5eAAdAEcAJb9Nb9Sa9X`9`_8eZ8iY8nY8rX9nWAkWBhVCdV\ DaUEZUFWTGSTHPSIMSJJPNNNQQLUTIXWG`ZEcaBge9jh7nk4qn\ 2uq0xt8xoFxkMyfTyb_yYfzUmzQnzOnzNnzLozKozIozHozGpz\ EpzDpzBzzAzz8qz7zv6pr8qm9khAmcBmZImUPmZWcdbUjiKpp9\ vwBrrCnmEjhFgcHcZI_UKWPLTKNPFOLAPI5IGDCEL6CT0B`c_b\ XPSQFHK56P97UC8ZF9cJAhMBlPBmOCnOCoNCpNCqMCrMDsLDtL\ DuKDvKDwKDtJGqJIoJLlINMET } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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FOTD 06-06-08 (The Age of Silver [8])
by Jim Muth 06 Jun '08

06 Jun '08

FOTD -- June 06, 2008 (Rating 8) Fractal visionaries and enthusiasts: Today's rather superior image lies in the fractal that is produced by the formula Z^5+Z^3+C, a fractal that consists of two large bays, one stacked on top of the other. The southern bay is partially cut off; the northern bay is less eroded, but its buds have the distinct look of being non-critical, with spurious arms pointing toward the mouths of the valleys. In the fractal world however, looks are sometimes deceiving. I found today's scene on the southern side of the extra arm that fills the large western bud of the north bay. The rather impressive silvery color palette is mostly serendipi- tous. The Fractint program should get most of the credit for creating the colors with one strike of the <enter> key. I did nothing more than tweak a few color registers. The image actually consists of half-inside, half-outside stuff. The inside parts have been rendered with the inside fill set to 'bof61'. The rating of an 8 might even be a bit of an under-estimate. The name "The Age of Silver" refers to the unusual coloring. The calculation time of 2-1/3 minutes is a far better value than was found in yesterday's loser. Downloading the finished 'gif' image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> is always a winning move however. A hot muggy day here at Fractal Central on Thursday gave ample warning that summer is not far off. The temperature of 84F 29C and humidity of 70 percent confirmed the diagnosis. The fractal cats must have reached the same conclusion. In the afternoon they switched from sleeping curled-up to sleeping stretched-out. I switched from being busy to having free time as the day progressed. The next FOTD will be presented to the breathless world within 24 hours. Until then, take care, and wait with anticipation. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Age_of_Silver { ; time=0:02:40.38-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-0.4553952426623336/+0.798314451690308/\ 2062443/1/-5/0 params=1/5/1/3/0/0/0/0 float=y maxiter=1500 inside=bof61 periodicity=10 colors=000gUOgVPgWQgXRgYSgZTg_Uf_Wf`XfaYfbZfc_fd`f\ eaffbfgcfhdfiefjgfkhflifmjfnkfolfpmfqnfrofspetrfsq\ fspfspfsofrofrnfrngrmgrlgqlgqkgqkgqjgpjgpihphhphhp\ ghoghofhofhoegqihpghoehndimbil`ik_jjYjiXjhVkgTkfSk\ fQkePldNlcLlbKmaIm`Hm_FnZDnYCnXAq`6pZ7oY8nX9mWAlVB\ kUCjTDiSEhRFgQFfPGeOHdNIcMJcKKbJLaIM`HN_GOZFOYEPXD\ QWCRVBSUATT9US8VR7WS3VR5WR6WQ7WQ8XP9XPAXOCYODYOEYN\ FZNGZMHZMI_LK_LL_KM`KN`KO`JPaJQaISaITaHUbHVbHWbGXc\ GYcF_cF`dEadEbdDceDdeDeeCgfChfBifBjgAkgAlg7lfAmgDi\ hGgiJdjMakP_lSWmVXnYUsZVp_Up`VpaWqbXqcYqd_re`rearf\ bsgcshdsietjgtkhtliumjumkunlvomvpovqpwrqwsrwtsxutx\ vvyuuxttwssvrruqqtppsoornnqmmpllokknkjmjilihkhgjgf\ ifehedgdcfcbebada`c`_b`Za_Y`ZX_YWZXVYWUXVTWUSVTRUS\ QTRPSQORQNQPMPOLONKNMJMLILKHKJGJIFIHEHGDGFCFEBDFCE\ GCEHCEHDEIDEJDEKDEKEFLEFMEFNEFNFFOFFPFFQFFQGGRGGSG\ GTGGTHGUHGVHGVHGgRLgSMgTN } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 05-06-08 (Monster at Large [0])
by Jim Muth 05 Jun '08

05 Jun '08

FOTD -- June 05, 2008 (Rating -- No Way!) Fractal visionaries and enthusiasts: Today's FOTD is a living corpse. Due to a pile of rush work, I had no time to do a reasonable FOTD. The image should have been discarded along with the day's discussion. But, undecided as to what to do with the fractal, I flipped a coin and it came up heads, so I posted the image and took about 5 minutes to write these few words. What is there to say about an image such as today's, which is nothing more than a mass of angular color patches splashed on the screen. The two heptagonal shapes near the center are actually 7-sided holes brought to life by the 'zmag' inside fill. The name "Two of a Kind" refers to these two heptagons. I must admit that the calculation time of 9-1/3 minutes for such a junky image is a real rip-off. Avoid being rooked by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> One thing for sure is that I don't hesitate to attack my own work when I think it falls short. Heavy clouds in the morning led to over 2 inches, 56mm, of rain in the afternoon here at Fractal Central on Wednesday, while the temperature hung around a very muggy 72F 22C. The fractal cats made the best of the wet conditions. As today's ho-hum fractal shows, my day was very busy. But things should be slower by tomorrow, and the next fractal will most likely be a vast improvement. Until then, take care, and keep trying. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Two_of_a_Kind { ; time=0:09:18.54-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+1.991689647207679/-1.720847520343586/\ 1608193/1/90/0 params=-25.3/-1.1/-2.3/-11/0/800/0/0 float=y maxiter=1750 inside=zmag periodicity=10 colors=0007AX78W68V37V68U89TAASCBSEBRGCQIDQKEPMFOO\ FOQGNSHMUILWILYJK_KJaLJcMIeMHgNHiOGkPFkLBlNDmPFmRG\ nTIoVJoXLpZMq`OsfNrdOqbPpaQo_RnZRnXSmWTlUUkTUjRVjQ\ WiOXhNXgLYfKZfI_eH_dF`cEabCb_8ZaA`bBbcCddEeeFgfGif\ ImgHjhGhiFejFckEakDZlDXmCVnBSoAQpAOp9Lq8Jr8Hs7Et6C\ v1Bu4At6As9ArBAqEApGAoJ9nL9mO9lQ9kT9jV9iY9h_8gb8fd\ 8eg8di8cl8cn8blBbkDbiFbhHbfJaeLacNabQa`Sa_UaYW`XY`\ V_`Ua`Sd`Rf_Pi_Ol_Mo_Lq_JvaLw`Jt_IrZHpYGmXFkWDiVCg\ UBdTAbS9`R8ZUAWXBTZCQaDOdELfGIiHFlIDnJAqK7wN6sL5pK\ 5mJ5jI5gH5dG5aE4ZD4WC4SB4PA4M94J73G63D53A437334231\ 1333544655867978B89C9BEACFCDHDFIEGKFHLGJMHKOILPJNR\ LOSMPUNRVOSXPTYQV_RW`SXaQY_PZYO_XN_VM`UKaSJaQIbPHc\ NGcMEdKDeICfHBfFAgE8hC7hA6i95j75j34j64j94jB4jE3jH3\ jJ3jM3jP2jR2jU2jW2jZ2ja1jc1jf1ji1gk0dm5amFZmPWmZTm\ hQmrNkwKivHguFgtIhsLirNjqQjpTkoWlnZmmamlcnkfojipil\ phoqgrpgvnftk`khUcgKUbAK_ } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 04-06-08 (Monster at Large [5])
by Jim Muth 04 Jun '08

04 Jun '08

FOTD -- June 04, 2008 (Rating 5) Fractal visionaries and enthusiasts: The more I watch those popularized 'science' programs on the leading 'science' channels, the more misinformation I notice in the shows, and the more I wonder who, if anyone, is checking the accuracy of the things presented as demonstrated fact. As a single example, on a recent show where the topic was condi- tions on other worlds, the narrator was describing the condi- tions we would find if we were to land on the surface of Titan, the giant moon of Saturn. Titan is thought to have weather much like earth's, with a surface covered with seas of cold liquid methane, which falls as showers from rain clouds as water does on earth. The narrator said that there is enough liquid fuel on Titan to power the earth for millions of years. This much seemed true enough, but then he said that if anyone were to strike a match on Titan, the entire moon would instantly burst into flame and burn into a barren airless world like our own moon Luna. When I heard this, my first thought was how fortunate it is that no lightning exists on Titan, and then I thought about how unlikely a total lack of lightning would be in an active plan- etary atmosphere with precipitation like earth's. But then I remembered that fuel such as methane burns by combin- ing chemically with oxygen, which on Titan must be as hard to come by as methane is on earth. On Titan oxygen would be the fuel! A resident on Titan would look enviously to earth and marvel at how energy-rich we are. On Titan, if it were possible to strike a match in the cold methane atmosphere, the match would sputter and instantly be snuffed out. It would not cause the entire planet to explode. Let's get our science straight, guys. In addition to wondering about inaccurate statements, I also wonder why the 'science' oriented channels load their schedules with so many programs about possible catastrophes, such as 'the asteroid strikes earth, civilization collapses and mankind is exterminated'. Maybe when people worry they buy more of the sponsors' products, but that's another story. Today's comparatively harmless fractal is unlikely to cause such worry. I found it lurking in the parent fractal that results when the formula Z^(1.237)+C is calculated 11 levels up the abstract logarithmic hyper-ladder when no function is used. This parent fractal resembles some kind of monster stretching out its filamentary arms to engulf the unwary fractalist. Today's image is located in the monster's right filament-arm. I named the image "Monster at Large" after this monster of my fancy. I rated it at a 5 because I don't particularly enjoy monsters, especially of the fractal kind. But the brief calculation time of 1-1/2 minutes is nothing to be afraid of. And if even this is too slow, the finished image may be accessed instantly on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Tuesday morning was fair enough here at Fractal Central, but clouds arrived during the afternoon, disappointing the fractal cats. The temperature of 81F 27C felt quite muggy due to the high humidity. My day was busy but thoughtful. All I needed was a subject fit to ponder. The next in the FOTD series is due to be posted in 24 hours, and the odds that this will actually happen are favor- able. Until next FOTD, take care, and settle your thoughts. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Monster_at_Large { ; time=0:01:34.64-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=+0.0153683212424909/-1.580096717232355/\ 1.376627e+011/1/-37.5/0 params=1.237/0/11/0 float=y maxiter=1750 inside=0 logmap=165 periodicity=10 colors=000cLmhY5wh0ca2UX3QS6NP9JKCGHF8DH6DF3CE5CDD\ BCKBARAKUAKWAKYAK`AKzA0mAUmm0mBUzP0mCUmCUzD0`DK_EK\ ZEKYFKXFKWGKVGKVGKPFUKFUFFUAFU5FW0FY3GW5HV8ITAJSDK\ QFLPIMNKNMNOKPPJSQHUQGZNJcLMhJOdLR`NTYPVURYRT_NUaK\ WcGYfD_h9aj6bl5ce4c_3cU9eQEfNKgKPiHVjD_kAem7jn4oo1\ lhAjbJhXReQ_cKhaEpdGqgHriIslJtnKuqLvsMwoPtlRqiTofV\ lcXi`ZgY`dUbaRd_OfXZpXXmVWjTVgRUdPTaORZMQWKPTIOQGN\ NFUTG_YGecHkhHohGrgGugFxgFviEukDslCrnCpoBoqAmr9lt9\ kv8iw7hy6fz6ez5cz4bz3az3bz2cw2cr2dn2ei2ee2f`1gX1gS\ 1hO1iJ1iF1hE0gD0fD0eC0eC0dB0cB0bA0bA0cB1dB1dB2eB2e\ C3fC3fC4gC4gC4YNOOXfRRjTXhVagWfeYld_qb`vaXn`Uf`Q_`\ NS`KL`ONaRPaURaXSb_UbbWbeXchZck`cnadqcdtedwfdnieek\ eXmeOpfFrf6tfArhEpiInjLrpNvuPyzRvvTtrVqnXokZlg`jcb\ g_deXfcTh`PjZLlWInUEpRArP6tN3pM7mLBjKEfKIcJM`IPYHT\ UHXRG_OFcLFfPGdTHcXIb`JadK`hL_lMZjPWXOGWLDWJ9WG6WE\ 3UF8TFCRFGQFKOFONFSTKMYPG } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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FOTD 03-06-08 (Ultimate Reality [4])
by Jim Muth 03 Jun '08

03 Jun '08

FOTD -- June 03, 2008 (Rating 4) Fractal visionaries and enthusiasts: An unexpected rush job came in Monday morning, which kept me occupied most of the day, leaving but little time for fractal work. But I did find something in the parent fractal of the past two FOTD's that barely passes muster as FOTD for June 3. The image is located in the handle of the fan of the parent, and required the outside to be set to 'fmod' and the inside to be set to 'bof61' before it barely made the cut. After a minimum of thought, I named the image "Ultimate Reality" and rated it at a 4. The name implies that the 'ultimate reality' of existence is as much a myth as a 'perfect fractal'. The standard image of God (invisible magician in the sky) falls short of being any kind of ultimate reality. The physical material universe falls even farther short. (We can no longer even be certain it's still there when no one is looking.) And the universe of fractals, ruled by its god the Mandelbrot set, is barely in the running. Pseudo-philosophy aside, today's fractal is not only a less than stellar one, it is also a rather slow one, taking 18-1/2 minutes to calculate on the fastest machine. Luckily, I have sent the image on ahead to Paul at the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where it is posted for instant enjoyment or ridicule. A near perfect day prevailed Monday here at Fractal Central, with lots of sun, low humidity and a temperature of 79F 26C. The fractal cats approved of the conditions by sleeping most of the afternoon. My day was quite busy, which accounts for the less-than-stellar FOTD. But tomorrow should be less busy, which should allow for an improved FOTD. Until that moment arrives, take care, and reality is every bit as real as you need it to be. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Ultimate_Reality { ; time=0:18:32.08-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-0.1595341138996228/+0.023810643049471/\ 1.958369e+010/1/-176/0 params=-11/-1.1/-1/-11/0/\ 380/0/0 float=y maxiter=12000 inside=bof61 proximity=1 outside=fmod periodicity=10 colors=000pjFpkEplDpmConApmCpmDpmEplFplGqlHqkIqkJV\ VdqjLrjNrjOriPriQriRriSshTshUshVsgWsgXtgZtf_tf`tfa\ tebuecuedudeudfudgwcjudhsefqfeogcmhbki`ij_gkYelXdl\ VbmU`nSZoRXpPVqOTrMRsLPtJOtINrJNpKNoLNmLNkMNjNMhOM\ fOMePMcQMaRM`RMZSLXTLWULUULSVLRWLPXLOXMMYNLYOKYOJY\ PIZQHZQGZREZSDZTC_TB_UA_V9_V8_U9`UA`UBaUCaUDbUEbUE\ bUFcTGcTHdTIdTJeTJeTKeTLfTMfTNgSOgSPhSPhSQhSRiSSiS\ TjSUjSUjRTiRShRRhRRgRQfRPfQOeQOeQNdQMcQMcQLbPKbPJa\ PJ`PI`PH_PH_RKXSMVUPTVRQXUOYWMZZJ``HacFceCdhAej8BY\ uCWrDVpDUmETkFShFRfGQdHPaHO_IMYILXJKVKJUKITLHQMGOM\ FLNEJNEHOGJPIKQJMRMNSNOSPQTQRUTSVUUWVVWXXXYYYZZZ_`\ _aa_bb`cdaeebfgcghdhidjkeklflmgnohophpriqsjstktvlu\ wlvxmwwnwxowypwzqwzqwzqwzqDNqENqFMqGLqHLqIKrJKrKJr\ LIrMIrNHrOHrPGrQGrRFrSEsTEsUDTVjsWClXcsYBsZAs_As`9\ yZ3s`9maEgcKadPXeUYfTYfSZgRZgQZgP_hP_hO_hN`iM`iLai\ LajKreLrfKqfJqgIqhHqiHqjG } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 02-06-08 (Eight Hooting Owls [8])
by Jim Muth 02 Jun '08

02 Jun '08

FOTD -- June 02, 2008 (Rating 8) Fractal visionaries and enthusiasts: Warning! Expect no answers in this discussion, only questions. There is a second fractal 'artist' here at F.C., one known as F.L., who usually prefers to lurk invisibly in the background, but sometimes says things that start an all-day line of thought going in my head. On Sunday she happened to catch a glance of today's image, and asked "why do the numbers you picked make a fractal that looks like a circle of eight owl's faces and not something like an icy tree?" I replied, "for the same reason that one plus one equals two and not three." But this is no answer at all. One plus one equals two because that's the way it is and it couldn't possibly be any other way. (I think it took B. Russell about 50 pages to prove that one plus one equals two, shortly before the whole point of his immense work was disproved by Godel.) But it's far different to state that one plus one must equal two than to state that today's fractal parameters must always equal a circle of eight figures vaguely resembling owl's faces. The first fact is intuitively obvious, the second must be accepted on the faith that the computer's fractal math routine calculates unambiguous truth. (Something I am not at all certain of.) During my no-longer-short life, I have 'wasted' countless hours trying to visualize the fourth dimension, and just as many hours wondering about things such as why I was born at a certain time to live a life as a U.S. citizen, and not 800 years ago to live a life as a nomad in Outer Mongolia or even as a deer to be devoured by a lion in central Africa. I also find it quite incredible that the universe should at this very moment be in the infinitesimal slice of time in which I will exist to observe and wonder about it. It must be true that a fool such as I can invent more questions than a wise man can answer. But this is not all. In addition, I have recently concluded that the perception of an outer universe (reality if you will) of three spatial dimensions is a function of the level of consciousness of humanity. As to why I am the person I am, and why the universe is in the infinitesimal period of time in which I will exist, it seems to be a matter of definition. How could it be any other way? Such an answer does not totally satisfy however. After all, does not the universe obey the mathematical laws of an objective three-dimensional space? But mathematics is a human invention, developed to be a symbolic statement of abstract human thought processes. Man certainly would never have developed a math that would be valid only in a perceived universe of four spatial dimensions. I now wonder whether our mathematics describes an objective reality at all, or if we intentionally designed and tweaked it to work with a three-dimensional space that we mentally create around us. The question of why the universe is in the tiny slice of time in which I exist might be a wrong question based on a wrong percep- tion. Relativity shows that there is no universal time which is true throughout the vast expanse of space. Each individual exists in his own unique present moment. We need to somehow re- phrase the question. I suspect that the question of why I am myself is also a wrong question, based on another misperception. So now, instead of searching for the correct answers, I find myself still searching for the proper questions. Perhaps it's time to turn to fractals. Today's image is named "Eight Hooting Owls" because that's what F.L. saw when she caught sight of it. It rates an 8 because I think it's a rather good image. The parent fractal is the same one that produced yesterday's image. But instead of lying at the edge of the fan, today's image lies almost at the dead center of the fan. The calculation time of 1-1/2 minutes is logical and provable. Just as logically provable is the fact that the image will soon be posted for viewing on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Near perfect conditions prevailed here at Fractal Central on Sunday, with low humidity, lots of sunshine, gentle winds, puffy cumulus clouds, and a temperature of 79F 26C 299K 21R. The fractal cats, unconcerned about which temperature scale to use, (Celsius is probably the best), found their comfort in the sunniest window. My day was pleasant enough, though thanks to F.L., the nagging and unanswered questions simply would not go away. But despite this, the next FOTD will be posted in 24 hours. Until then, take care, and there must be aleph^(aleph) questions that never have been and never will be asked, much less answered. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Eight_Hooting_Owls { ; time=0:01:28.38-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+3.400279501439892/+0.0000082660249179/\ 3.599998e+010/1/-39/0 params=-11/-1.1/-1/-11/0/\ 525/0/0 float=y maxiter=1750 inside=0 logmap=165 periodicity=10 colors=0000Ob0Xe0zi0bm0zp0ig0kZ0dR0\ XI0TA2I0460820000T00b00z00z20z0Ma0xi0thErbTniimTxi\ zzgMzeozdGzdCzdAzd6xd4rd0md0gd0bd0Xd0Rd6IrM8z`0zX8\ zVEzTMzRRzOXvMdrKinInkGngGneGndEn`EnZELXEnTCnRCnPC\ QMCnKAnIAnEALCAVACQAEVAEVAGV8IV8KV8KV8MV8OV8PV8RV8\ TV8VV8XV8Zi8`i8zrvzptzprzppzpnzpmznkxnivngvnetndrn\ brm`pmZpmXnmVrtOvzGzz8zzAzzCzzEzzGzzGzzIzzKzzMzzOz\ zOzzPzvRzmTzgVzbVz`RzZOzZKzXGzXCxV8tV4pT0kT0gR0dR0\ gK0kE0m86p2Cr0Iv0Ox0Rz0`zCgzOnz`xzmzzxzzzzzzzzzttz\ nnzigzdbzZXzTRzOMzIEzC8z62z00z00z00z00z00z40tE0kO0\ bX0Ve0Mn0Cx04z08z0Az0Cz0Ex0Gv0It0Kr0Mp0On4Pm6RkK`m\ Ximgrntznbzpzxpxinz`2zb8zdEzeKxgOviTviZtkdrmgpnmnp\ rnpxmrzktzivzgxzgxzZzzRznIzZAzI0z00z00z04z0Az4GzAM\ zGRzMXzRbzXgzbmzgrzmkzkdziXzibzeezbkz`nzXtzVxzRzzO\ zzMzzIzzGrzdVzzRzxPzxMzxKzvGzvEzvAzt8zt4zt2zr0zr0z\ r0zp0zp0zp0zp0zn0zm0zk0zi0zg0ze0ze0zd0zb } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 01-06-08 (Edge of the Fan [8])
by Jim Muth 01 Jun '08

01 Jun '08

FOTD -- June 01, 2008 (Rating 8) Fractal visionaries and enthusiasts: Today's FOTD image is a true case of serendipity. I had another image ready to be posted as the FOTD for June 1, but one of the fractal cats, (Cassandra), leaped onto the keyboard and caused the program to terminate before I had saved the parameters or image, which I had named "Fish Ladder" and rated at a 7. In frustration I re-booted the program and found a second image, this one in the parent fractal that is created when 11 negative parts of Z^(-1.1) are combined with 1 negative part of Z^(-11) and (1/C) is added, a combination that creates a parent fractal with an outstanding fractal 'fan' unfolding east from the origin. Today's scene is located on the northeast edge of this 'fan', which explains the name "Edge of the Fan". Surprisingly, the second FOTD for today rates an 8, a full point higher than the first, which was a rather similar image The calculation time of 5-1/2 minutes is reasonably convenient. A short trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to see the finished image is equally reasonable. Morning rain here at Fractal Central on Saturday gave way to afternoon sun and a temperature of 82F 28C. This made the fractal cats happy, and they showed their satisfaction by doing what cats usually do when they are satisfied. They curled up and went to sleep. My day was slow enough to permit two satisfactory fractals. Tomorrow should be slow again, which promises that another satisfactory fractal will appear here in 24 hours, plus or minus a few. Until then, take care, and I thought the wonder years were long past. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Edge_of_the_Fan { ; time=0:05:31.05-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+4.535322291620997/+1.211627703364356/\ 1.238e+009/1/-60/0 params=-11/-1.1/-1/-11/0/525/0/0 float=y maxiter=5200 inside=0 periodicity=10 colors=000KzeIzdHzcGzaGz`EzZEzZDzYDxWBuWBtVArTAoT8\ mR8jQ7iQ7eO5dN5cNAdOEdQHdRLdTOeVTeVWeW`eYdgZgg`lg`\ ogaticwidzieziezegzcix`jwYluVmtRorOppNrmKtlHujEwiB\ xg8ze5zd2zc1zY2mZ5pW5iV8dTAaQBTODOLEHKGBIH5GI0EK0D\ L0GODIRKLVROYZR`aVc`YeYWgVclTYjQeoOKj80g04i08j0Dl2\ Gm4Ko7OpATrDWtE`uHdwKixNlzOpzRuzVzzYzzZzzYzwWxtWwp\ VumTtjTteRrcRp`QoYOmVOlRNlONmLRoIWoHZpEcpBgrAjr7ot\ 4tt2wu0zu0zw0ww0px0jx0dx0Zu0Vt0Rr1Op5LoBIlGGjLDiQA\ gW7e`4ic7leAmgDpjGtmHuoKxrNzuQzwTzzVzzYzz`zzczzdzz\ azz`zwZztYzoVzlTziRzdQzaOzYLzVKzQIzNHzKG01u10w70xD\ 0xI0zN0zL1tK5mIBiHGcHKZGQTEVOD`IDdEBi8Ao48t08x0Ar0\ Bl0De0E`0GW0HQ0IK0KE0KA0HE0EI0BN48RA5WG2`N0dT0iZ1g\ V4gR7eNAeKEeHHdDKdANd7Qc2Vc0Yc0`a0ca0ea0ZW0TR0NN0H\ I0AD04800400000000202A0AH0HO0OW0gc0dj0zr0tz0zzezz0\ zzUzz0zm0xl0zU0rZ0tK0mN0oG5dAO`4gW0zV0wT1tR2pR2mQ4\ jO5gO7dN7cL8`LAYQwlOzjLzi } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD for June 01
by JimMuth＠aol.com 01 Jun '08

01 Jun '08

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FOTD 31-05-08 (Coronal Crisis [6])
by Jim Muth 31 May '08

31 May '08

FOTD -- May 31, 2008 (Rating 6) Fractal visionaries and enthusiasts: When I was in Catholic elementary school (I did survive it.) and the subject turned to religion, I had a way of asking questions that on several occasions caused me to be told in effect to sit down and shut up. I'm still not sure what I did wrong. Maybe I asked the wrong kind of questions. Or maybe I just had too much trouble believing in things that neither I nor apparently anyone else could see. (This was before I realized that the scientists known as physicists are even better at inventing theories about things that will never be directly seen.) Anyway, one sunny day in May, shortly after Sister Mary Thomas told the class that if we were good on earth, we would all have a seat at the right hand of our Savior when we went to heaven. So far, so good, but then I had a sudden insight. Not only did the thought of an eternal church service seem boring, but I remembered the baseball game I had attended a few days earlier. The crowd there had numbered about 45-thousand, a tiny fraction of the millions of Catholics who would go to heaven and sit next to the Savior, yet even that tiny fraction at the ball game took up so much space that those on the outer fringes were hundreds of feet from the field. If a hundred-million Catholics all had seats at the right hand of the Savior, the stands would stretch for miles. Those in the outer bleachers would be unable to even see Him. Feeling a surge of perhaps foolish bravery, I raised my hand and asked how millions of people could fit by one man's right hand. After a minute's thought, the sister said it's a mystery and told me to sit down and shut up. (Actually she said something like 'the question is silly, so sit down and pray for guidance.) Unfortunately, after all these years, guidance has yet to come. But in the meantime, fractals *have* arrived on the scene, and today's rates an acceptable 6. The parent fractal was created by iterating the formula Z^sqrt(3)+C at a level 123 levels up the logarithmic ladder when no function is applied. This parent is shaped roughly like a distorted Mandelbrot set rotated so that its main bud, which is actually only 0.732 of a bud, faces southwest. This bud is shaped quite like the main buds of the Z^3+C Mandeloid, with a small valley directly opposite its mouth. Today's scene is located in this valley. The colors are unusually brilliant. In fact, they are so brilliant that they actually detract from the worth of the image. But in this case, applying such extreme brilliancy was the only way to add life to the scene. Today's parameter file will reveal its secret in only 3-3/4 minutes running time on a 2000mhz machine, which is about the same time it will take to surf down to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view the completed image there. Thursday was absolutely perfect here at Fractal Central, though Friday brought a few too many clouds for perfection. The temp- erature hovered around 79F 16C (13 Reaumur) on both days, while the fractal cats kept an eye on the yard, watching for intruding tomcats. My day on Friday was a lot less busy than Thursday, when I had no time for the FOTD. And speaking of the FOTD, the next one will be posted in 24 hours. Until then, take care, and if you don't know the answer to a question, humiliate the one who asked it by calling the question silly. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Coronal_Crisis { ; time=0:03:47.28-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-0.8004024479835327/-0.735937934452532/\ 348789/1/-12.5/0 params=1.732/0/123/0 float=y maxiter=5000 inside=0 logmap=174 periodicity=10 colors=000V1TX3VZ5X`7Zb9`dBbfDdhFfjHhlJjnLlpNnrPpt\ RruSsuTsuUsuVsuWsuXsuZsu`subsudsufsuhsujsulsunsups\ uqsursursursursursursurou0eu0Su1Iu69u60uB0uF0uK0uP\ 0qP0lU0gZ0cc0Zc0Ug0Pl0Kq0Fu0Bu06u01u01u00u00u00u00\ u00u00u00u40u90uI0uN0uX0ua0uj0uo0us0us0us0us0us0us\ 0us0ps0ks0ls0ms0nscoskpswzzzzzzzzswoluecuXZrIgl9lg\ 0u_0uU0uP0uM0uS0uZ0uc0ul0uu0uu0lu00u00u00qe0Bs0Ps0\ ca0q90u00u06u0Pu0gu0Uu0Fu01g00K000I00j00s00s00s0u0\ 0u40uD0lI0cS0PX0Fe06j00s00s00s00s00s00s00s00s00s00\ s00s00s00s00s00o00e00X00N00D0040000000000101606F0B\ K0FP0KU0Pc0Ug0Zl0cq0g00g00q00u00u00u00u00u00u00u00\ u00u00u00u04u09u09u0Du0Iu0Nu0Nu0Su0Xu0Xu0ju1su6su6\ suBslFsUFsBKs0Ps0Ps0Zs0gs0ls0us0us0us0us0us0us0us0\ us0us0usBusUusquNuu0uu0uu0uu0uu0uu00us0us0us0us0us\ 0us0uo0ua1uNFu9Uu0gu0uu0uu0uu0uu4uuDuuSuuauujuusuu\ suusuusuusuuscusBuj0uI0uX } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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No FOTD for May 30
by Jim Muth 30 May '08

30 May '08

Fractal fans: Due to a very busy day, there will be no FOTD for May 30. The FOTD for May 31 will be posted on schedule. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com

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FOTD 28-05-08 (A Stitch In Time [7.5])
by Jim Muth 28 May '08

28 May '08

FOTD -- May 29, 2008 (Rating 7.5) Fractal visionaries and enthusiasts: I saw on the news this morning that the cameras on the latest Mars lander have picked up something in the distance that suspiciously resembles an intelligently designed artifact. I assume we'll soon be hearing that the artifact was left there by aliens from Vega-3, who have been spying on earth from this secret base on Mars, and neglected to clear all signs of their presence when they returned to their home world to report that the earth is ready to be invaded and conquered. I am sorely disappointed. I thought the space aliens were an alliance from the yet-to-be-discovered third star in the Sirius system and the fourth planet circling Procyon. Whatever, I will be watching the Pennsylvania skies very carefully in the days to come. And I can't help wondering whether fractals exist in the universe as perceived by the aliens. I often wonder whether fractals really do exist, or are mere inventions of the human fancy. Since aliens, by definition, must lack human minds, fractals might not exist in their world. One thing certain however is that something exists somewhere, for today's FOTD is a picture of it. The parent fractal was created when I mixed various negative portions of Z^(-1.732) and Z^(-7.32), then added (1/C). This parent fractal is little more than a chaotic mish-mash of fractal stuff, but even so it has at least some worth. Today's scene lies at the terminal of a filament extending from a small bud in the southernmost part of the parent. Most of the artistic effect is a result of my quasi-skilled coloring efforts. The extreme magnitude of 4.5*(10^12) requires the mathtolerance entry. The rating of 7-1/2 includes 1/2 point for my coloring. The name "A Stitch In Time" has nothing at all to do with the image, but then again I have no idea what "the tropic of Sir Galahad" has to do with "the tin man", yet it's in the song regardless. The calculation time of 2 minutes means immediate relief from fractal congestion. A trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to view the completed image, will bring even more relief. With a temperature of 66F 19C, Wednesday was just a bit too chilly for comfort here at Fractal Central, but the light winds and strong sun kept it from being uncomfortably cold. The fractal cats enjoyed the unbroken sun. I enjoyed a day that was not too busy. Tomorrow looks promising also. The next FOTD fractal will be posted in 24 hours. Until then, take care, and where will you be when the aliens arrive to carry off all of us as slaves? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Stitch_In_Time { ; time=0:02:06.01-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+0.6271399461988936/-1.226465429540339/\ 4.493818e+012/1/60/0 params=-5/-1.732/-1/-7.32/0/\ 0/0/0 float=y maxiter=1800 inside=0 logmap=226 periodicity=10 mathtolerance=0.05/1 colors=000LKzNNzPLzSJzTIzVJyWKyYLyZNy_PyZRxYTxYVxX\ XwXZwW`wVbwTdvSfvQhvShyPivNfsKepIbmF`jDZgAXd6Xe7Wc\ 8Ub9TaAR`AQ_BOZCNYDLXEKWEIVFHUGFTHESzzcptzA80AB0AE\ 0PHMTJKWMI_PGbREfUCiXAmZ8pa6td4wf2sa4p`5mZ7iW8fU9c\ RB_PCXMEUKFQHGNFIKCJGALD7MA5NA7PA8QA9RAASABTACUAEV\ AFWAGXAHYAIZAJ_8LY7MW6OU3NP4OR5PS6QT6RU7SV8SW8TX9U\ zAV_AWzBWaCXzCYcDZzE_eC`zE_fG_zHZmJZzLYtMYzPXjRXYR\ VWSTUSSSSQQTOOTNMTLKUJIUIGVGEVECVDAWB8W96X72z85W88\ z8BV8Ez8HU8Kz8NT8QT8TS8WS8ZS8aS8aR8`R8`RK`QKzQK_PK\ zPKZOKzOKZOKz000000000MKXMKXLKXLKWKKWKKWKLzJLVJMzI\ MUINUHNUHOUHOTGPTGPTFQSFQSERSERRESRDURDcQCcQzUQBmP\ zzPAmPzWOAmOzzO9mNzYN8mNzzM7mMz`M6aLzbL5cLzdK4eKzf\ KQgtzhjFiazjTFkSzlREmRznREoRzpRDqRzrQDsQztQCuQzvQC\ wQzxQCyPzzPBzPzzPBzPzzPAzPzzOAzOzzOAzOzzO9zOzzOWzT\ zzOYzKzzF_zBzz6`z2zzCSzLzzMQzMzzMPzNzzNOzNzzOMzOzz\ OLzPzzPCznzzlBzmzznGzozzp } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 28-05-08 (Fortune Always Calls [5.5])
by Jim Muth 27 May '08

27 May '08

FOTD -- May 28, 2008 (Rating 5.5) Fractal visionaries and enthusiasts: Today's image shows one of those generally disappointing mini- brots lying in the Mandeloids with exponents between 1 and 2. This one lies in the Z^(sqrt(3))+C as it appears 4 levels up the complex logarithmic ladder. Due to its modicum of organization, it squeaks by with a rating of 5-1/2, barely worth the honor of being declared a FOTD. At this not-very-lofty log level, the parent fractal resembles nothing more than a numeral 8 listing to starboard. Today's scene is located on the northern side of the west branch of the prominent valley dividing the main bay into the figure 8. Choosing the square-root of 3 as an exponent was done in jest. Significant numbers such as this apparently have no effect on the quality of the fractals they create. The name "Fortune Always Calls" has nothing whatever to do with the image, or with anything at all connected with fractals for that matter. It's simply a cute phrase, nothing more, nothing less. The calculation time of just over 1 minute is unexpectedly fast. But the trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> is equally fast, and going to the web site will avoid the minor hassle of copying this FOTD into your Fractint directory (or folder) in text format with a .par extension and running it as you would any other Fractint parameter file. A rather muggy day on Tuesday was interrupted by a shower of rain (what else?) in the afternoon, which knocked the tempera- ture down from 86F 30C to 73F 23C. The fractal cats watched the 15-minute shower with disinterest. My day was busy but under control. Tomorrow, when the next FOTD will be posted, should be the same. Until then, take care, and isn't the thought of the perfect fractal heavenly. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= FortuneAlwaysCalls { ; time=0:01:24.04-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-0.199082275456053/+0.1545238480953167/\ 39000/1/-75/0 params=1.732/0/4/0 float=y maxiter=2000 inside=0 logmap=83 periodicity=10 colors=0009KnBJjCIgDHdFHaGGZHFWJETKEQLDMNCJOBGPBDR\ AAS97T84U81SC3RF5PJ7OM9NQBLTDKXFJ_HHcJGfLFiNDkPCmR\ AoSFmVKkMPhOUeQZbSa_UcXWaVY`T_ZTaYWcXYeV`gUciUfkUi\ mUloUoqVqsXsuZtwauyctxesxhqxjpxlowonwqmwslwrkvrjvr\ ivrhurgurgurftretrdtrcsrcsrbsrarr`rr_rr_rq`nq`jp`f\ p`bo`_o`Wn`Sn`On`Ln`Ln`Km`Jm`Jm`Im`Il_Hl_Hl_Gk_Gk_\ Fk_FjZEjZDjZDiZCgY8iZCiZBhYBhYAhYAgY9gY9gY8zW5yX6y\ X6xX6xX6wX6wX6wX6vX6vX6uX6uX6uX6tX6tX6sX6sX7sX7rX7\ rX7qX7qX7qX7pX7pY7oY7oY7oY7nY7nY7mY7mY7mY8lY8lY8kY\ 8kY8kY8jY8jY8iY8iY8iY8hY8hY8gY8gY8WgRXfPYeOZeN_dL_\ cK`cJabIbaGcaFc`Ed_De_BfZAgY98bb9aaAaaAa`Ba`Ba_Ca_\ CaZDaZDaZEbYEcYFdXFeXGfWGgWHhWHiVIjVIkUJlUJmTKnTKo\ SLpSLqSMrRMsRNtQNuQOvPOwPPxPPyOzzOzzNzzNzzMzzMzzLz\ zLzzLzzKzzKzzJzzJzzIzzIzzIzzHYzHYzGZzGZzF_zFJzmKzh\ MzdNz`OzWQzSRzNSzJUzFVzAWz6Xz2Vz6Uz9SzCRzFPzIOzLMz\ OLzRJzUIzXGz_FzbDzeCzhAzk } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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FOTD 27-05-08 (Depths Without End [7.5])
by Jim Muth 27 May '08

27 May '08

FOTD -- May 27, 2008 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image returns to yesterday's scene in the Seahorse Valley complex of the Z^2+C Julibrot. I zoomed in on the lower right part of yesterday's image and turned the view upside down to produce an image that gives the impression of massive striped arms floating above an infinite depth. No wonder I named the image "Depths Without End". I created the banded effect by hand rather than using the banding feature included in the program. Though the view is double-rotated only two degrees or so (my estimate) from the Julia orientation, the ghostly remains of Mandelbrot buds are clearly visible along the top of the image. The fact that the circular bud outlines are undistorted shows that both parts of the double rotation are equal. (Mandel-bud remains are impossible in the exact Julia orientation because their outlines have enlarged to infinity.) I rated the image at a 7.5. Despite its several flaws, it still has something to offer. Just to the right of the center of today's image lies a cluster of tiny bright dots. These dots are actually holes in the surface stuff. Beneath the surface at this location lies a minibrot with its main bud facing left. When blown up, these holes prove to be julia sets of whatever part of the underlying minibrot they happen to be on top of. The minibrot itself is located somewhere in Seahorse Valley, though I have not the slightest idea of its actual Mandelbrot coordinates. The calculation time of the included parameter file is only 3/100 of a second in excess of 5 minutes, a bit slow but nothing that cannot be quickly accomplished. The finished GIF image is or soon will be posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Monday was a repeat of Sunday here at Fractal Central, though with a few more clouds and a bit higher humidity. With all the sun, the temperature reached 84F 29C. Now, at post time, the wind is stirring and lightning is flashing in the distant west. Rain is threatening, but the day is finished, so let it rain. The fractal cats have their eyes on the sky however. The next FOTD will be posted in 24 hours. Until then, take care, and if you can't find the fourth dimension, try to be satisfied with the third. It's only a consolation prize, but it's still better than nothing. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Depths_Without_End { ; time=0:05:00.03-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=EvenMoreSlices passes=t center-mag=0.953034/-0.257883/17.1836/1/-167.8/0 params=2/0/0/0.15/-0.78/0/0/0 float=y maxiter=15000 inside=255 logmap=22 periodicity=10 colors=000088re8097re70A6rg60B6rh50C5rj40D4ql30E4p\ k50F5oj60G6ni70H7mh80I9lg90JAkfA1KBjeB2LCidD2MDhcE\ 3MEgbF4MFeaG5MHd`H5MIb_I6MJaZJ7MK`YK7ML_XM8MMZWN9M\ NZVO9MOZUPAMQZTQBMRZSRCMSZRSCMTZQUDMUZPVEMVZOWEMWY\ NXFMYXMYGMZWLZGL_VK_GK`UL_HK`TK`HKaSKaIKbRKbIJcQJc\ IJdPJdIJdOJeJIeNIfJIfMIgJIgLIhKIhKHiKHiKHiLHjLHjLH\ kLGkLGlLGlMGmMGmMGmMFnMFnMFoNFoNFpNFpNFqNEqOErOErO\ ErOEsOEsODtPDtPDuPDuPDvPDvOCwPDvPDvPDuQEuQEuQEtREt\ RFtRFsRFsSFrSGrSGrTGqTHqTHqTHpUHpUIpUIoVIoVInVJnVJ\ nWJmWJmWKmXKlXKlXLlXLkYLkYLjYMjZMjZMiZMwZNw_Nw_Nw_\ Ow`Ow`Ow`Ow`PwaPwaPwaPwbQwbQwbQwaRwbQwbQwbQwcQwcQw\ cQwdPwdPwdPwePweQweRwfSwfTwfUwgVwgWzgWzhWzhWzhWziW\ ziWziWziWzjWzjWzjWzkWzkWzkWzlWzlWzlWzmWzmWzmWznWzn\ WznWzoWzoWzoWzpWzpWzpWzrWzqWzpWzpWzoWzoWznWznWzmWz\ mWzlWzlWzkWzjWzjWziWziWzhWzhWzgWzgWzfWzfWzeWzeWzdW\ zcWzcWzbWzbWzaWzaWz`Wzmzz } frm:EvenMoreSlices {; Jim Muth ; P1--exponent, P2--angle, ; P3--M center, P4--J center, z=pixel+(p4), c=p3+(pixel*p2): z=(-z)^(p1)+c, |z| < 16 } END PARAMETER FILE=========================================

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FOTD 26-05-08 (The Fourth Dimension [Rating Arbitrary])
by Jim Muth 26 May '08

26 May '08

FOTD -- May 26, 2008 (Rating Arbitrary) Fractal visionaries and enthusiasts: The unknown fascinates me, and what could be more unknowable than space of four dimensions? The problem is, while our math has no difficulty dealing with 4-D, and computers can be programmed to deal with it as logically as they do 3-D, we pathetic humans can do nothing more than twist our faces into a look of astonished puzzlement when asked to visualize something as simple as a 4-D tesseract. Today's image is a scene in Seahorse Valley of the Mandelbrot set, an object every tyro fractalist becomes familiar with the day after he discovers fractals. But the image bears little resemblance to either Seahorse Valley or its Julia set, yet what we are seeing is all part of the great Seahorse Valley complex. What has changed in the image is the angle at which we are viewing the valley. We are seeing it sliced at an angle very close to but not exactly in the Julia orientation. The Seahorse Valley Julia set (actually the -0.78,0 set) may be seen by changing the (p2) parameter to 0,0. The Mandelbrot aspect, which is Seahorse Valley itself, may be seen by changing the (p2) parameter to 1,0 and the (p4) parameter to -0.78,0. I can logically deduce what is going on in all these changing views of the same 4-D object, but I am no closer to visualizing the entire 4-D Seahorse Valley complex than I was that day 20 years or so ago, when I realized that the Julia sets and the perturbed Mandelbrot sets are differently oriented slices of a single 4-D object, the Julibrot figure. Perhaps what we call dimensions are simply another way of describing levels of consciousness, and mankind is now at the three-dimensional level of consciousness. This would imply that space appears three-dimensional because that is the only way we can perceive the abstract reality. If this is so, it is only to be expected that we would naturally develop a mathematics that would be compatible with and would confirm our perception. Enough philosophical rambling already. I named today's image "The Fourth Dimension" for obvious reasons. I gave it no rating, or rather left it to the individual viewer to decide its worth. The calculation time is but a few seconds, so have no fear when running the included parameter file. But if fear strikes, rush to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view the finished image there. BTW, tomorrow's image will be a zoom into today's. Absolute perfection wrapped in a package -- that describes the conditions here at Fractal Central on Sunday. How can cloudless skies, low humidity, light winds and a temperature of 77F 25C be improved upon? The fractal cats must have agreed, for they sat in their window for an hour, watching me finish the yard work, while FL supplied encouragement and occasional refreshment. And despite all this activity, I still found time for the FOTD. The next FOTD will appear in 24 hours or so. Until then, take care, and seek total fulfillment in your endeavor. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= TheFourthDimension { ; time=0:00:14.15-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=EvenMoreSlices passes=1 maxiter=1800 center-mag=0/-0.0486/0.86 params=2/0/0/0.15/-0.78\ /0/0/0 float=y inside=0 logmap=yes periodicity=10 colors=000IJJ97P7DU6IY5Nb4Sf3Yj2bo1gs0lw6muCnsHoqN\ ooSpmUmkWjiYgg_deaaccZaeW_gTYiQWkNUmKSoHQpEOpBMmCK\ kEIhGGeIEbKC`MAYOBVQCSSDQTEPUDPVDOWDOXDNYDNZDM_DM`\ DLaCLbCKcCKdCJeCJfCIgCIhCHiBHjBGkBGlBFmBFnBEoBEpBG\ qEHrHJsJKtMLuONrNPpNRmNTkMUiMWfMYdL_aL`_LbYKdVKfTK\ gRJiOJkMJmJInHIoFIpCHqAHr8HpAIpBJoCJoDKoEKnFLmHLlI\ MlJMmKNmLOnMOoNPpPPqQQqRQqSRqTRqUSqVSoWTmXUkYViZWg\ _Xe`YcaZab__c`YcaWcbUccScdQceOcfMcgKchIciHcjHckHcl\ HcmHcnHcoHcpHcqHcrHcsHctHcuHcvHcwHcxHcyHczHczHczHc\ zHczHczHczHczHczHczHczHczHczHczHczHczHczHczHczHczH\ czHczHczHczHczHczHdzHezHfzHgzHizHkzHzzHzzHzzHzzHzz\ HyzHxzHzzIvzJuzKtzPszUrzZqzcozhmzmzzrzzvzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:EvenMoreSlices {; Jim Muth ; P1--exponent, P2--angle, ; P3--M center, P4--J center, z=pixel+(p4), c=p3+(pixel*p2): z=(-z)^(p1)+c, |z| < 16 } END PARAMETER FILE=========================================

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FOTD 25-05-08 (Second Chance [No Rating])
by Jim Muth 25 May '08

25 May '08

FOTD -- May 25, 2008 (No Rating) Fractal visionaries and enthusiasts: Since I was busy on Saturday, out having fun for a change, I had no time for a FOTD search. But to avoid fractal disappointment I resurrected a fractal that I found several weeks ago, and gave it a second chance. I named the image "Second Chance". One glimpse will show why it failed its first chance. The mixed-up fractal has little going for it but a random scattering of randomly colored elements rendered with the outside set to 'tdis'. I did not dare rate the image. I hate to give a fractal a rating of a negative number. I think the image is located in a string of holes down the center of a valley of its parent, but I'm not sure. One thing I am sure of however is the 3-1/2 minute calculation time on my fractal-dedicated 2000mhx machine. The time is automatically written in the parameter file. As almost always, the finished image is available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> F.L. and I made the most of the perfect weather that prevailed here at Fractal Central on Saturday, while the fractal cats complained about being left alone most of the day. The next FOTD will very likely be posted in 24 hours. Until then, take care, then seek and find. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Second_Chance { ; time=0:03:31.53-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident float=y center-mag=+0.0089893132145013/+0.6702539704283154\ /3453.553/1/142.5/0 params=-5/-1.45/-1/-4.5/0/0/0/0 maxiter=5000 inside=0 outside=tdis periodicity=10 colors=000faFhaFjaFkaEmaEnaDpaDraDsaCuaCvaCtZDsXDr\ VDqTDpRDoPDnNDlLEkJEjHEiFEhDEgBEf9Ee7Ed9HcAKcBNbCQ\ bDTaFW`GZ`Ha_Id_JgZLjYMmYNpXOsXPuRVrL`oFflDehCeeBe\ bAe_9eX8eU7dQ6dN5dK4dH3dE2dB3cD4bF5bG6aI7aJ8`L8`M9\ _OA_PBZRCZSDYUDYVHUbLQjOMrHFEMPQRY`Wgl_pwbmtdjqfgn\ hdkkahmZeoWbqT_sRYUYj4dw5ev5fv5gv5hv5iv5jv6ju6ku6l\ u6mu6nu6ou6ouUerpWpoVnoUmnTlnSkmRjmQilPhlOfkNekMdj\ LcjKbiJaiI`iI_sYgkQhdIiXAjQ3kS6lT9lVCmWFmYHnZKn`No\ aQobSoYOpULqQIqMFrICrE9sA6s63t20t8BqELoKVmQdjWlhZn\ cYpbVn_SjXPdUM_RJVOGQLDLIAGF7BC4795AC6DE7GG8JIAESC\ 9`D5iEBfFHcFMaGSZHYXHbUIhSJnPJsNYvXkxfyzpxyqwyrwyr\ vysuytuyttyutyusxvrxwrxwqxxpxypxyoxzoxzjfgfQPb96`C\ B_EFYGJXJNVLRUNVSPZRSbPUfOWjMZnL`rJbvIdzRixZmvfrtn\ vrvzpryqoxqlxqiwqfvrcvr`urYtrVtrSssPrsMrsJqsGqsHnr\ IlqJiqKgpLdpLboM_oNYnOWmPTmPRlQOlRMkSJkTHjTFjWHhZI\ faJddKbgM`jNZmOXpPVcaGeaG } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 24-05-08 (Lilacs in Blueoom [7])
by Jim Muth 24 May '08

24 May '08

FOTD -- May 24, 2008 (Rating 7) Fractal visionaries and enthusiasts: A very heavy work load means a short FOTD discussion, which is what we have today. The day's image resulted when I subtracted Z^(0.35) from Z^(2.7) and added straight (C). The parent fractal is a slight variation on yesterday's parent. The image is actually surprisingly attractive, considering that almost no effort went into it. The rating of a 7 is due almost totally to serendipity. The name "Lilacs in Blueoom" came to mind when I glanced out the window and noticed a lilac bush that had just finished blooming. The calculation time of 3-1/2 minutes on a 2000mhz fireball is about average. Combined with an average image, everything should be under control. But to assure control, the finished image is or soon will be posted for instant viewing and total enjoyment on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Friday turned out to be a really nice late spring day here at Fractal Central. The blue sky was decorated with puffy cumulus clouds, the wind was gentle, and the temperature reached 68F 20C. The fractal cats as well as the ducks on the nearby Susquehanna River agreed. The cats purred and stretched in the sun, while the ducks quacked and swam on the water. Swamped in work, I had little time to do the obligatory FOTD, much less enjoy the quacking ducks. But the worst of the work is finished -- at least for the present -- so the next FOTD has an 80-percent chance of appearing on schedule in 24 hours. Until the next time, take care, and beneath every mountain lies a hidden fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Lilacs_in_Blueoom { ; time=0:03:29.71-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=+0.9436889113880975/+0.646306059851099/\ 5.986522e+010/1/-40/0 params=1/2.7/-1/0.35/0/0/0/0 float=y maxiter=2400 inside=0 outside=tdis periodicity=10 colors=000rEwrDwrBxr9xs8xs6ys5ys3ys2ym4sh5nc6iZ7dT\ 9ZOAUJBPECK9DF9LE9SE8QI7OM6MQ6KU5IY4Ga4Ee3Ci2Am29q\ 5Ao8AnBBmDBkGCjJCiMDgODfRDeUEcXEbZFaaF_dGZgGYiGXjH\ WjIWjIVjJVjJVjKUjKUkLUkMTkMTkNTkNSkOSkOSOYb0gm4ej8\ dhCbfGadK_aOZ_SXYWWW_UTcTRgRPkQNnPLlRJkTIjUHiWGhYF\ gZDf`CdbBccAbe9ag7`h6_j5Zl4Ym3Xl5Wl7Wl9VlAVlCUlETl\ GTkHSkJSkLRkNQkOQkQPkSPkTQlQQmOQnMQoKQpHQqFQrDQsBQ\ t8Qu6Qv4Qv2Or5Mn8KjBIfEGbHE_KCWNASQ8OT6KW4GZ3Da2Hd\ 2Lf2Ph2Tk2Xm1`o1dr1ht1lv1ox5ms9knDiiGhdjNHZIMODQNC\ OLCLKBJIAGH9EF8BE89LJ7RT5Yc4cm2iw1hp9gjGfcOfYVgZUg\ _Ug`UgaUgbThbThcThdTheShfSifSigSihRiiRijRijRhhQhgP\ gfOgeOgdNfbMfaLf`Le_KeZJeYJfXLgWMhWNiVPiVQjURkTTlT\ UmSVmSWgW_bicXjgSkkMloHmsBnw6pzPnyblofjocip`jlchn`\ ijbjf`lcYi_WjXWcVWYTSRSNLQIEOE8NxPZtO`pObmNdXXHiNf\ fMhbMjt9bmEefIhZfd__g_TiwnN`VOylyuhwqdum`sjXqfTobP\ mifagccf`ddYfcVgaSiqHwrGw } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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Re: [Fractint] Fractal question
by Paul N. Lee 23 May '08

23 May '08

On Mon, 19 May 2008 at 22:35:00, Tony Fisher <tfisher(a)hccs.hunter.cuny.edu> wrote: > > Greetings! I am a high school math teacher working > with some exceptional students. While my field is > originally group theory, I have been trying to work > with my students on fractals. I have used Fractint > for many years and am impressed... I have what I > think should be a simple question, but I have had > trouble finding the right program for what I want to > do. Fractint's "Newtonbasin" identifies points in > the complex plane by their ultimate destination, > through Newton's method, to solutions to the equation > z^3 - 1 = 0. I would like to do the same but with > the equation z^3 - z = 0. The movement of z changes > from: > z'=(2z^3 - 1)/(3z^2) > to: > z'=(2z^3)/(3z^2 - 1) > > However, one should still get a tricolored fractal as > long as one identifies points by destination rather > than speed. Is Fractint the way to go to create this > fractal? Or [other fractal generator]? Any assistance > you could give, either directly or in the form of > pointing me toward the best person to ask, would be > much appreciated. > The above was sent to me about 26 hours ago, but I have been way to busy to give it my full attention (as seen by the way the FOTD's are running late on the website). Would somebody care to assist this individual, please ?? Sincerely, P.N.L. ------------------------------------------------- http://home.att.net/~Paul.N.Lee/PNL_Fractals.html http://www.Nahee.com/Fractals/

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FOTD 23-05-08 (Dark Kisses [5])
by Jim Muth 23 May '08

23 May '08

FOTD -- May 23, 2008 (Rating 5) Fractal visionaries and enthusiasts: The recipie for today's 5-rated image subtracts Z^(0.4) from Z^(2.5) and adds (C). The parent fractal is a strange thing, a main unit divided into several large bays, the whole thing surrounded on the west by a horde of minibrots of varying sizes. Today's scene lies in scattered debris just off the negative X-axis just west of the main fractal unit. I named the image "Dark Kisses" because that's the first thing I thought of when I saw the scene. Much of the pizazz is due to the image being rendered with the outside set to 'tdis'. The rest of the pizazz is due to luck. The calculation time of almost exactly 2 minutes is just what the doctor ordered as a cure for fractal fatigue. Another good prescription is to go to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view the completely calculated image posted there. But if the image is not yet available, be patient. Paul has been busy lately. Brilliant sunshine alternated with showers of rain through the day on Thursday here at Fractal Central, while the temperature of 55F 13C and a brisk northwest breeze made it quite a bit too cool to enjoy the spectacular clouds and rainbows. The fractal cats enjoyed the sunny intervals and searched for their catnip rat while the rains fell. My day was very busy, and I would not be surprised if tomorrow is the same. Unless the unexpected happens, the next FOTD will be posted in 24 hours. Until that semi-glorious moment, take care, and is there any such thing as a totally new fractal? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Dark_Kisses { ; time=0:02:00.01-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=+0.416383005818/+0.002891533387/2599786\ /1/22.5/0 params=1/2.5/-1/0.4/0/0/0/0 float=y maxiter=1800 inside=0 outside=tdis logmap=76 periodicity=10 colors=000GHaGIdGIgIOiKTjMZkNclPhnRnoTspUxqXGDUFBR\ EAOD9LC7IB6FA5D94HD6LG8OKASNCVRDZUFaXHe`JicLlgMpjO\ snQwqSztTvrVspXpnYll_ijafibbgd_efXcgTaiQ_kNZlRXiUV\ gXTe`RccP`fNZjLXmJVpIT3LH5KI6JJ7JK8IL9HMBHNCGODFPE\ FQFERHDSIDTJCUKBVLBVMAVMAVM9WN9WN8WN8WMAXLCYKEZKG_\ JI`IKaCciIMbHObGQcGSdFUeEWfEYgD_hCaivxI2S53T84UB4V\ E5WG6WJ6XM7YP8ZR8_U9_XA`_AaaBbdCcgUd1Tc3Sc4Sc5Rc7R\ c8Qc9QcAPcCPcDOcEOcGNcHNcIMcJMcLLcMLcNKcPKcQJcRJcS\ IcUIcVHcWHcYGcZGc_Fc`FcbEccEcdDcfDcgCch_1tY5sW8rUB\ qSEpQIoOLnMOmKRlIVkGYjE`iOjeIfg4TS5UT5UT5UT5UU5UU5\ VU5VV6VV6VV6VV6VW6WW6WW6WX6WX7WX7XY7XY7XY7XY7XZ7XZ\ 8YZ8Y_8Y_8Y_8Y_8Z`8Z`8Z`9Za9Za9Za9_b9_b9_b9_b9_cA`\ cA`cA`dA`dA`dA`dAaeBaeBaeBafBafBbfBbgBbgBbgCbgCbhC\ chCchCciCciCcisI2pK5nL7lM9iNCgOEePGbRJ`SLZTNWUQUVS\ SWUPYXNZZL_`I`cGaeEbgfvgeuhduhdthcthbthbshasharh`r\ h_rh_qhZqhYqhYphXphFFWGGZ } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 22-05-08 (Lack of Symmetry [7])
by Jim Muth 22 May '08

22 May '08

FOTD -- May 22, 2008 (Rating 7) Fractal visionaries and enthusiasts: Today's fractal was generated when I iterated Z^(1.14)+C at ground level of the complex logarithmic ladder with no function applied. The parent fractal resembles a distorted extracted tooth with an unusually large area of debris spread well to the southwest of the main bay. Today's image is located far out near the edge of this debris field. I named the image "Lack of Symmetry". The name is was inspired by the distorted-tooth shape of the parent fractal. Then, when I saw the finished scene, I rated it at a 7. The image is just another star-burst low-order minibrot, but it is a better-than- average one, IMO worth its rating. The calculation time of 1-1/2 minutes will be easy going. Equally easy will be downloading the finished image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> but Paul is very busy, so there might be a delay before it is actually posted. The older and more experienced people grow, the more cynical they tend to become. It must be a hazard of old-age. But whatever it is, it is certainly happening to me. I wish I could believe that a certain candidate for the US presidency really would bring a change for the better if elected, but I have heard this promise and been disappointed too many times to have any hope of meaningful change. I also wish I could believe that those corporations who claim to care about global warming were truly concerned with warming and not with their profits. In fact, if global warming actually exists, I wish it were possible to do something about it. The fuel situation is little better. A few weeks ago a customer stormed in the front door, complain- ing that he could no longer pay the high cost of gasoline. He supposed that the service stations were getting rich at the consumer's expense. I replied that the money we pay for fuel untimately ends up in the hands of the petroleum suppliers and speculators, and I doubt that even they are getting as rich as it appears. When he asked what I thought we could do about it, I told him to stop driving his oversized van and get a bicycle. If enough people stop driving large fuel-hungry vehicles, the demand for fuel will drop and the cost will soon follow. When he said he needs his large van to make his living, I told him that in that case he must continue paying the high price of fuel, and he should bite the bullet and stop complaining. I doubt that my comments made him happy. Luckily, the weather is much more enjoyable than the customer was. The partly cloudy skies here at Fractal Central on Wednesday were interrupted in the afternoon by a brief thunder-shower, which is pretty routine for this time of year, but the tempera- ture of 55F 13C was much too chilly for late May in central Pennsylvania. The fractal cats, who have still not remembered where they hid their catnip rat, agreed. My day was as close to average as a day could be. The next FOTD will appear in 24 hours. Until then, take care, and be assured that truth will prevail. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Lack_of_Symmetry { ; time=0:01:33.23-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-6.983235396309989/-8.54444043927656/\ 1.817357e+010/1/-85/0 params=1.14/0/0/525 float=y maxiter=5000 inside=0 symmetry=none periodicity=10 colors=000mTTjWReZRaaQYeQTgOOkOKmOLkQLjRLgTLfULdWL\ bXL`XLZYLXZLW`LTaLRbLOdLNdNQfNRiNTkNWmOXpOYrOZtOav\ ObyQezQgzQjzQlzQnzOqzOszOuzOxzOzzOzzOzzOzzOyzOzzOz\ zOzrOzqOzpHt`BjHEXYGHjTBZH0uL0tN2sO2rQ4qR4pT7nU7mW\ 9lX9kYBjZBi`CgaCfbEef4`dEdbLfaTi`YkZbmXiqWmsUsuTxx\ BzzRzzdzynvxztvzruzmuvjupfuibuaYuUUuLQuBLuKKvQHxWG\ yaGzfEzkCzqBzuBzz9zz7zz4zz4zz9zvCsnGkeKbWNULOLOROR\ URUXUXZXZaYad`dfbfieikgkmimpkprmrtptvrvzzuxstkdsYN\ uK0sH0qG2nG7lE9jECgCGeBHbBL`9OY4NZ9QZCRZGTs0dZHU0e\ HBZKOTKiEKkCKq2Ku0Hy0Kt0Kp0Lk0Lf4Na7NXBORCOLGQGENE\ HQELREOTEQWETYEW`EXbEZeEagEbjEelEgnEiqBem9aj4Yf2Wb\ 0RZ0NW0HR0EO0GR0GU0GY2Ga7He9HiCHlEHnKGmOGmTGlXEl`E\ kdEkgCjkCjnCirBiuBgyBgz9fz9fz9ez9ezLjxUnqasjivfeqd\ alaZgYflUlqQruLxyKzqHziHz`GzREzGEz2Qz4Ys4fj4mZ7uO7\ zB7z07z0Nz0Zz0jz2tz2zs2rg2fX2UH2E020K00X00i04s07z0\ 9z0Zz0Xz2Wz7WzCUyGUuLTqOT } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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Spidrons
by Tony Hanmer 21 May '08

21 May '08

A relatively new area of geometry, with much to explore in 2d and 3d, and much which could be developed in various fractal programmes. See: http://www.szinhaz.hu/edan/SpidroNew/ Tony Hanmer Tbilisi, Republic of Georgia www.geosynchronicity.blogspot.com

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FOTD 21-05-08 (Ghostly Apparition [8])
by Jim Muth 21 May '08

21 May '08

FOTD -- May 21, 2008 (Rating 8) Fractal visionaries and enthusiasts: I named today's image "Ghostly Apparition" because the minibrot near its center barely exists. The spooky apparition manifested itself when I combined 6 negative parts of Z^(-1.66) with one negative part of Z^(-6.6) and added (1/C). The parent fractal consists of a number of irregularly shaped bays surrounded by countless interesting nooks and crannies to explore. But instead of exploring the nooks, I checked a blob of material near the inside center of the fractal, near the point where two large bays appear to merge. I found there a strange arrangement of bits and pieces, which when enlarged formed the skeletal outline of a ghostly minibrot. To return the ghost to life, I rendered the scene with the inside set to 'bof60' and the outside set to 'atan'. The result is an image different enough to rate a 8. The calculation time of under 11 seconds can hardly be a burden. And the already-calculated image is posted for instant viewing on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> About a week ago I told of a 152-year-old book I recently found in a local antique emporium while tagging along with fractal lady on one of her antiquing expeditions. The book is a popular- ized presentation of the scientific and practical knowledge of the day. Some of the old ideas are now absurdly, almost comically wrong, while others are still totally accurate, and still others, such as how to shoe a horse, and how to bank a fire, are still true, but of importance to very few. While idly turning the weathered and stained pages, I sometimes wonder how our current scientific and practical ideas will seem 152 years from today. Will our descendants laugh at our futile search for a 'theory of (almost) everything'? Will they wonder how we could possibly fail to grasp the obvious (to them) mean- ing of our own quantum discoveries? Will they shake their heads at our silly addiction to 'cell phones' and the rhythmic noise we now call music? But most frightening of all, are we now see- ing the beginning of a new era of techno-civilization or is it actually the start of a neo-dark age? Rain fell steadily all morning and most of the afternoon here at Fractal Central on Tuesday, while the temperature hovered just above 50F 10C. The fractal cats spent the day looking for the catnip rat, which they have somehow misplaced. I spent the day working and thinking deep (IMO) thoughts. The next FOTD will be posted in 24 hours or so. Until then, take care, and I had a clever closing comment in mind, but I forgot to write it down, and have since forgotten it. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Ghostly_Apparition { ; time=0:00:10.55-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+0.12324718494693840/-0.146235048606272\ 10/133.4492/1/50/0 params=-1/-6.6/-6/-1.66/0/0/0/0 float=y maxiter=1500 bailout=10000 inside=bof60 outside=atan periodicity=10 colors=000v`SvYQvWPuTOuRNuPM8CmCBnGAoK9oO8pR8pQBlP\ EiOHeOKbNNZMQWMSSLVPKYLK`IJcEIfBHo7Ik8Ih8Je8Jb8K_9\ KX9LU9LR9PI0NL5LO9JREHUIFXMD_RBbV9eZBdWDcUFcSHbPJb\ NAFgAGhAHiAIjAJkAKlBLmCMnCNoDOpDPqEQrERsEStFTuFUvG\ VvGVxGVyHVyHVxIVvIUwJUvJTvKSuKRtLQtLQsLPsMOrMNrNMq\ NLqOLpOKpPJpPIpPIoQHnQGmRFmRElSElSDkTCkTBjRAkTBjUC\ jVDiXDiYEhZFh_FgaGgbHfcHfeIefJegJdhKdjLckLclMbnNbo\ NapOaqP`sP`tQ_uR_vR_rQZoPZkOZhNZeNZaMZZLZWKYSJYPJY\ MIYIHYFGYCGYCEWCDVCCTCBSCAQC9PC7NC6MC5KC4JC3HC2GD4\ FE5FF6FG8FH9FIAEJBEJDEKEELFEMGDNIDOJDPKDQLDQNCROCS\ PCTQCUSCVTBWUBXVBXXBYYBZZA__A`aAabAbcAec5bdA_eFXfJ\ UgORhTNk_PhXQeVRbTS_QTXOUUMVRJWOHXLFYICZFA_C8`A6ZC\ 8YD9XFAWGBVICUJETKFSMGRNHQPIPQKORLNTMMUNLWOKXPIYRH\ _SG`TFbUEcVDdXCfYBgZAi_9j`8kb7mc6nd5pe4qf3rgSigp`g\ gVJfZHc_EeaGgbIhcJjeLkfMmgOnhPpjRrkTslUunWvoXxpZzv\ bys`yq_xnZxlYxiWwgVweUwbT } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 20-05-08 (The Total Distance [6])
by Jim Muth 20 May '08

20 May '08

FOTD -- May 20, 2008 (Rating 6) Fractal visionaries and enthusiasts: After all these years, I think I might be growing bored with quadratic minibrots. But despite my best efforts, the ubiquitous things keep coming. Today's little fellow lies in the parent fractal generated when negative Z^(1.25) is combined with negative Z^(3) and (C) is added. This parent is shaped somewhat like a lopsided eggplant, with some pretty ordinary Mandelbrot buds on the east shore but a more chaotic landscape along the west shore. A very prominent minibrot lies a bit inland on the western shore, and today's scene is located in the East Valley of this minibrot. Today's FOTD is a full five point improvement over yesterday's. But yesterday's image rated only an abysmal 1, which means that today's rates a 6, a rating that, while not too bad, is nothing to celebrate either. I named the image "The Total Distance" since it was rendered with the 'outside' set to 'tdis', which colors the points according to the total distance they travel before escaping beyond the specified bailout radius. Perhaps the best thing about the image is its speedy calculation time of 1-1/4 minutes. And the next best thing is that the pre- rendered image is available for immediate viewing on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> As the FOTD progresses, I find myself getting more and more involved in the philosophical aspects of fractals, which are so obviously made of numbers. But after trying to get through a few advanced books of quantum theory, I find that atoms are made of numbers also. And I wonder whether the quantum world determines the numbers or the numbers determine the quantum. I guess we might soon have to admit that the world, including ourselves is composed of numbers, which begs the question 'what are numbers?' Sometimes I wish I could return to the days when things were so much simpler, when I thought the real world was really real and atoms were tiny solar systems made of little orbiting particle-energy things which existed even when no one was looking. But like my faith in the mysterious invisible things of religion, my faith in the equally mysterious invisible things of science has vanished also. In my opinion, Santa Claus is unreal, God as described by religion is unreal, and atoms as described by science are unreal also. If it's all a dream however, who or what is doing the dreaming? Chilly and blustery conditions made Monday quite unseasonal here at Fractal Central. The temperature of 55F 13C and brisk winds made it feel more like mid-March than mid-May. The fractal cats watched the scudding clouds for a few minutes before they got into a spat over who would claim the best window shelf. Cassie won the dispute with a good slap on Nicholas' head. My day (Monday the 19th) was unexpectedly busy, and tomorrow (Tuesday the 20th) will be just as busy. But despite the rush, there will most likely be another FOTD posted in 24 hours. At this time, I'll make no predictions as to its potential quality. Until then, take care, and sometimes putting it off until later is the best choice. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Total_Distance { ; time=0:01:16.23-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-1.00704998814352/+0.2867813765415/3518\ 04.6/1/-23.5/0 params=-1/1.25/-1/3/0/0/0/0 float=y maxiter=1200 inside=0 outside=tdis periodicity=10 colors=000uzeuzouruubukOuG5uV6ukLuuXuVzuRzuNzuLzuG\ zsBzm9zf3z_0zT0zN3zT9zYEzbIzfPzkTzoYzsbzuhwumruqou\ uiuuduu`uuXuuSuuQuuQuuQuuQuuQusQuoOumOuhOueOubOuYO\ uVOuTLuTJuTJuTGuRDuRDuRBuRBuP8uP6uP6uP5uP5uT6uV8uY\ Bu_DubGueJufLukOumQuoSuqVusXuuZuWBNZ5Pa5Rb5P`5P_5N\ Y5NV5LT8LRDIUFIUHG9SG3XE1`E0bN0dT0g_0if0lm0os0pu0r\ u0uu0wu0yu0zu0zu0zu0zu_`uu5uuguuzuozuezuRuuIruGouG\ luGduGZuESoEFhE5bE1VB0PB0IB0BB03B00eXEudTTzkVzfYze\ _z_buYblTedRfZNhSLhLIkSGmZEmbEoiBIz0ooBuLbu5uu5uu5\ uu5uu5uu5uu5uu5uu5uu5uo5uh5ue5sY5sR5ZI5hN5hP5hT5hV\ 5k_5fb5ee5bh5Yk5Vo5Rq5Pu5Lu5Iu56u5Gu5No5Tk5_f5f_5m\ VBsPGuLLuGSu9Xu3`u0du9guGguNguTgu_guhiuoiuuiuuiuui\ uuluuluuluuluuluuluuluulsuosuoquoquoouooupmupmupku\ pkuz0uphuphurfurfureureureuubuubuu_uu_uuYuwYuwVuwV\ uwTuOVuOYuLbuJeuGfuGkuDmuBouBquJsuQuuXuubusiuqpuow\ umzukzuhzuGzufzuuzuuzm_5u } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 19-05-08 (A Nothing Fractal [1])
by Jim Muth 19 May '08

19 May '08

FOTD -- May 19, 2008 (Rating 1) Fractal visionaries and enthusiasts: Warning: I'm in a strange mood today, so have fun. Since today's fractal image is nothing to write home about, or to write about anywhere else for that matter, I might as well start the discussion by broaching the topic of the nature of the mind and reality. Only a fool would claim it is foolish to waste time discussing the nature of reality, a problem which can never be solved. At the same time, only a fool would actually waste his time writing about it. Since I must be a fool, I will discuss the problem. But expect no solution. One thing I think is certain is that my awareness exists, though sometimes I doubt even this. I never ask myself where my awareness goes when I go to sleep. Only a fool would do so. But for countless days it has been there to greet me when I wake up in the morning, unchanged from the evening before. I am not foolish enough to wonder what it is that stays the same while the material of my brain as well as my thoughts constantly change, but it might be a soul, whatever that is. Oops, I just forgot that souls are supposed to be a by-product of the body, so this is no answer either. Let's make an assumption -- whatever my self-aware mind is, it does indeed exist, and it is somehow miraculously generated by the electro-chemical interactions of the neurons in my brain. If this is so, the question now becomes how unconscious matter can create self-awareness. I have read over a dozen books about this miracle, but I am no closer to grasping what is going on in my brain than I am to grasping what is going on in the quantum realm. But one thing for certain is that speculation among the cognitive scientists is currently rampant. One of the most recent theories is that I am a strange loop, whatever a strange loop is. I rather enjoy being a strange loop. It's rather like being a fractal, and if I am a fractal, then everything else must also be one. The universe is a big fractal, with God doing the iterating. (I assume He uses Fractint.) Oops, I forgot that God is supposed to be only a feel-good superstition. I have no idea where I'm going with this, so I guess it's time to turn to the fractal. As for that fractal, it's a disgrace. It's the first FOTD ever to rate a humiliating 1. And it doesn't even deserve its 1. It actually deserves a zero. The image lies in the parent fractal created by the formula Z^(1.618)+C when it is calculated at ground level of the log ladder with no function applied. I named the image "A Nothing Fractal", which is exactly what it is. At least the calculation time is a mercifully brief 41 seconds. And the finished image is posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Morning rain here at Fractal Central on Sunday was followed by early afternoon sun and late afternoon rain squalls, while the temperature hung around a very chilly 61F 16C. The fractal cats noticed the rain, but were more interested in the pigeons scrounging for sustenance on the sidewalk. For me the day was busier than I would have preferred, but not as busy as I might have feared. The next FOTD will be along, if I feel like doing one, in 24 hours or so. Until then, take care, and if nothing is really real, are illusions real? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Nothing_Fractal { ; time=0:00:41.47-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-0.567480167420823/-0.8351769720835365/\ 159.2013/1/-105/0 params=1.618/0/0/0 float=y maxiter=3600 inside=0 logmap=37 periodicity=10 colors=000w_`vZ_uYZtWYsVXqUWpSVnRTmQSlPRjNQiMPgLNf\ JMdILcHKbGJdEGfCDhBAj97l84gE6bJ8YNATRCOVEJZFKXILXL\ LXNMXQNXTNYVOZYO__P_bQ`eQ`gR`jS`mS`oT`rT`tHei6j_5q\ N4xB6wF8wI9vMBvPCuSEuWFtZHtbIseKshLrlNroOrrQsqRsqT\ tqUtqWuqXupZvp_vpavpbwpdwoexogxohyojyokyoYmlKai6Qg\ 8Rh9ShAShBThDThEUhFUhGVhIWhJWhKXhLXhNYhOYhPZhQZhbv\ kbul03z46v89rCCnGFjKIfOLbSOZWRV_URcXNg_JkbFoeBrg7m\ j9imAeoBdlGciKbgPadT`bX`_a_YeZViYTnXQrXOvVNsTMpRLm\ PKjNJgLIeJHbHG_FFXDEUBDS9CP7BM5AJ39G19E87CF6BL5ALW\ TLukNpjPliQhhScgT_fVWeXRdYNc_Jb`EabA`c6`gDekKioRnr\ YroWomVmjUjhZhecfchc`maZrZWvXUzVRzUOzTLzSIzRFzQCzP\ 9zOAzkEzjIzjMziPziTzhXzh`zhczggzgzzfzzfzzfzzczzazz\ _zzYzzWzzUzzSzzQzzPzzNzzMzzLzzJzzIzzGzzFzzEzzCzzBz\ zAzz9zz8zzAzzCzzDzzFzzHzzIzzKzzLzzNzzPzzQzzSzzUvzV\ rzXmzYhz_czaazb`zd_zfZzgYziYzjXziXzhXzgXzfXzeXzdXz\ cXzbXzaXz`Xz_XzZXzZWzXWzV } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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FOTD 18-05-08 (Flight of Fancy [6])
by Jim Muth 18 May '08

18 May '08

FOTD -- May 18, 2008 (Rating 6) Fractal visionaries and enthusiasts: We're already 10 or 12 hours late with today's FOTD, so I'll keep the discussion short. Today's image is named "Flight of Fancy". It's an appropriate name. After all, are not all fractals flights of fancy? But we have seen many such squashed-pancake images over the history of the FOTD, making it difficult to rate today's image higher than a 6. Perhaps the main feature of the image is its celestial blue colors. The colors might be celestial, but fractals need more than just fancy colors to gain a superior rating. The parent fractal came about when I iterated the formula Z^(1.57)+C at a level 0.57 units up the logarithmic ladder, while applying no function. This parent reminds me of a sopping wet dish cloth slung over the edge of a shelf, but it has a curious something just off to the west of its main bay, with a trail of debris leading to this odd thing. Today's image is located where the debris joins the oddity. The calculation time of 4-2/3 minutes is barely within reason, so waste no time in setting up the included parameter file and running it. The image may also be seen on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Due to the odd hour of my posting, give Paul a chance to run the parameter file and post the finished image there. Saturday began sunny but unusually chilly here at Fractal Central. Dark clouds moved in during the afternoon, with several light showers passing over. The high temperature of 57F 14C was most un-springlike. The fractal cats ignored the weather, and spent the afternoon chasing each other up and down the hallway. In my section, things were rather busy, and will probably remain so for several weeks. The next FOTD will appear in around 12 hours. Until then, take care, and move forward. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Flight_of_Fancy { ; time=0:04:40.14-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident center-mag=-1.114717333522346/-0.1301401672941029/\ 3.823849e+009/1/-90/0 params=1.57/0/0.57/0 float=y maxiter=3600 inside=0 periodicity=10 colors=0008rX8rX7o_7ma6kd6if6gi5ek5cn5ap4_s4Yu4WwC\ _vJcvQgvXjvcnujruqvuxyuvwrtuorslqqioofmmdkkajiZhgW\ feTdcQcaOfeNhiMjmLlpLhmRdkX`haXfgTclParM_wNXrNUnNR\ jNOfOLbOJZOGUODQPAMP7IP4EP2AS6FVAJYDN`HRcLVfO_iScl\ WgoZkrbotespctlbtiate`ub_uZZuWYvSXvPWvLVwIWwEVzBWz\ 7Rz4OxCPnJOeQNXYMNdLEkL5lO6mR6nU6oX7p_7rb7td8ug8vj\ 8wm9xp9ys9zu9zwJzzSdiaZejTasX`n__ibZeeY`iYXlXSoWOr\ VJuVFrUHpUJnULlUNjTPhTRfTTdTUbSW`SYZS_XSaVRcTReRRg\ PRhROgSLgTJgVGgWDgXBgVEcTG`SIYQKVPNSNQPMTMKWJJZGHX\ IFUJDRLBOM9L07I05F03D05G06J07LP9OOARNBTNDWMEZLF`KH\ cJIfIJhINbTQXcTRnWLxZLkaL_dLOgLCiL0cK1YJ2SI3NI3HH4\ BG56G5IiFKdGL`GMXGNSHPOHQKHRFISBIT7IR6MP6QN5TM5XK5\ _I4cH4gF3jD3nC3qE4rF5rH7rI8sK9sLAsMCtODtPEuRFuSHuU\ IvVJvWKvTHrRFoPDkNBhL9dJ7aH5YF3VD1SH5PL8MPBKTEHWHE\ _KCcN9gQ6jT4dX4__4Vc4Qf4Li4Gm4Bp46s4DqBJpHQoNWnTal\ Zhkdnjjtipmdlf_i_Vf8sY8sY } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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FOTD 17-05-08 (Under the Equinox [8])
by Jim Muth 16 May '08

16 May '08

FOTD -- May 17, 2008 (Rating 8) Fractal visionaries and enthusiasts: On a recent visit with fractal lady to one of the nearby antique emporiums, I came upon an old book printed in 1856 and titled "Wells's Familiar Science". Being in a state of moderate bore- dom, I opened it and found it to be a book of popularized science as science was understood in the middle of the 19th Century, with the text presented in a question-and-answer format. Since the price was quite reasonable, I purchased the book, which now lies on the desk beside me. I have yet to read it thoroughly, but the small part I have browsed through is quite interesting. It is surprising how much our scientific understanding of some phenomena have changed in the past 152 years, and how little our understanding of other phenomena have changed. The velocity of light is given as around 190,000 miles per second, a bit too fast. And there is a section explaining the constitution of the so-called luminiferous ether. One of the greatest questions about light at the time was what happens to it when it is absorbed by a dark body. The source of the sun's energy was a complete mystery, though it was speculated that the sun emits heat and light as a bell emits sound when it is struck, without exhausting its reservoir of sound. I'll relate further interesting tidbits from the book as I come upon them, but now we have a fractal to investigate. The fractal was generated by calculating the formula Z^(1.375)+C at a level 1.375 units down the logarithmic ladder, while applying no function. I'll not describe the parent fractal in much detail. It is basically a distorted Mandeloid standing on its head. Today's unusually gaudy scene is located in a small valley near the parent fractal's 'nose'. I gave the image the rather poetic name, "Under the Equinox", though I have since forgotten what moved me to give it this name. The rating of an 8 might be a bit optimistic, especially for an image with no true minibrot at its center. The central blue triangle is no real substitute. To add some extra zip, the image was rendered with the outside set to 'tdis'. The calculation time of 16-1/3 minutes is admittedly slow, but instant gratification is available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Steady rain all day and a very un-springlike temperature of 52F 11C made Friday a day to be forgotten here at Fractal Central. The duo of fractal cats watched the dripping water for a few minutes, then viciously attacked their catnip rats and mice. My day was close to normal. The next semi-glorious FOTD will appear in 24 hours or so. Until then, take care, and don't be too sure of things you're not sure of. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Under_the_Equinox { ; time=0:16:21.46-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=+0.05758293098342480/-0.989073028706620\ 60/2.569865e+007/1/152.5/0 params=1.375/0/-1.375/0 float=y maxiter=2200 inside=255 outside=tdis logmap=1175 periodicity=10 colors=000HJ4HN4HY4Hf4Nm2Ym2fn1qn1zq0zq0zs0zs0zu0z\ y0zw0qu0fs0Yq0Nn0Jn0Lm0Lk0Li0Nf0Nf0Ne0Pc0Pa0PZ0SZ0\ SY0SW0UU0US0US0UP0WN0WL0WJ0YJ0YH0YG0ZE0ZC0ZC0aA0a8\ 0a60m40w40z20zU0zZ0zZ0y00k10Z20Y40W60U80SA0PC0NE0L\ G0JH0HJ0GL0EN06W0CP0HL0LH0SE0YA0a62f26k0Cq0Gw0Jz0P\ z0Uz0Yz0Uz0Sy0Pw0Ns0Ln0Jk0Hi0Ee0Ca0AY08W06S04N02L0\ 1H00E10A108204201400600600800800A00C00C00E00E00C00\ C00C00C00C00C00C00C00C00C00A00A20A40A80AA0AC0AG0AH\ 0AL0AN08S08U08W08Z08a08e08f08k08m08n0Am0Am0Am0Ak0A\ k0Ak0Ai0Ai0Ai0Ai0Af0Af0Af0Ae0Ae0Ae0Ae0Ac0Ac0Ac0Aa0\ Aa0Aa0Aa0AZ0AZ0AZ0AY0AY0AY0AY0AW0AW0AW0AU0AU0AU0AU\ 0AS0AS0AS0AP0AP0AP0AP0CN0CL0EJ0EJ0GH0GG0HG0HE0JC0J\ A0LA1L84N66N68P4AP2ES1GS1HU0LU0NW0PW0UY0WY0YZ0aZ0c\ a0ea0fc0kc0me0ne0sf0uf0wi0zi0zk0zk0zm0zm0zn0zn0zm0\ zm0zk0zk0zi0zi0zf0wf0qf0me0ke0fc0ec0ca0Za0YZ0WZ0SZ\ 0PY0NY0JW0HW0GU0CU0AU08zz } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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FOTD 16-05-08 (Celestial Festival [7])
by Jim Muth 16 May '08

16 May '08

FOTD -- May 16, 2005 (Rating 7) Fractal visionaries and enthusiasts: When I was but a small child, I was fascinated by the sound produced by striking the top of the metal bed post with a coin. The indescribable sound was strangely familiar. I was sure I had heard it long before but had forgotten where. Then quite a few years later, I heard the same sound on a record of unusual sound effects, with the note that the sound reminds most people of something very familiar from the distant past, but long ago forgotten. We'll file the nature of this haunting sound as mystery of life number 13,702. Today's fractal is not nearly as mysterious. It is a scene in the parent fractal that results when 4.5 negative parts of Z^(-1.05) are combined with 0.8 negative parts of Z^(-8.8) and (1/C) is added. This parent fractal is a grossly inflated thing requiring several outzooms to fit onto the screen, and featuring an incredible feather-like 'fan' attached to an even larger circular bay. Today's scene skips the 'fan', and is found instead at the end of a filament extending from a bud on the shore of the circular bay, and terminating in a scalloped ring. I named the image "Celestial Festival", not that there's anything particularly heavenly about it. Then I rated it at a 7, which is not at all a bad rating. With a running time of 31 seconds, the included parameter file will bring the agony of impatience to no one. The finished image is or soon will be posted to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Partly cloudy and mild weather prevailed here at Fractal Central on Thursday, with a high temperature of 72F 22C. The fractal cats greeted the periods of sunshine with enthusiasm. My day slowed down as the day progressed, but there was still a bit of hastiness when FOTD time arrived. The next FOTD will be posted in 24 hours. Until then, take care, and when the world turns against you, open a gift shop selling candles, teddy bears, and pseudo-country items with feel- good slogans on them. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Celestial_Festival { ; time=0:00:31.15-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip center-mag=-3.777300433225537/-0.4621972219516149/\ 1.218883e+009/1/-80/0 params=-4.5/-1.05/-0.8/-8.8/\ 0/0/0/0 float=y maxiter=1100 inside=0 logmap=86 periodicity=10 mathtolerance=0.05/1 colors=000FSQAOKBOKBNKBNKBMKBMKBLKBLKBKKBKLBKLBKMB\ KMBLNBKNBJJBJLBIKBHJBGJBEIBCHBAGB8GDCJFGMGJPINSKQU\ LUXNY_P`bQdeSggUkjVomXrpZvs_yuaxscwqevpgunhuljtkls\ inrgorfnpdnobnnamm_mlZmkXmjWlhUlgTlfRkeQkdOkcNkbLj\ `Kj_IjZHiYFiXEiWCiVBkSClQDmOEnLEpJFnHGoEGiCHkAIf7I\ g5Jb3Kc1KiEVUQeFazH`zJ_zLZzMYzOYzQXvRWrTVpVUpWUpXS\ nXRmXPkXOjXMhYLgYJeYIdYGbYFaZE`ZCZZBYZ9WZ8V_6T_5S_\ 3Q_2P_1Oc`AhfEmkHrpLvuOzzRzyQzyPzyPzyOzxNzxNzxMzxM\ zxLzwKzwKzwJzwJJvIKvHLvHMvGNvGOuFPuEQuERuDSuDQtHOt\ KMsOKsRIrVGrYEr`CqdAqg8pk6pn4or2ou1ox2mu3ls4kq5jo6\ il7hj8gh9ff9ed8ac8Yc8Ub8Qb7Mb7Ia7Ea7Aa8Cb9EcAGcBId\ CKeDMeEOfFQgGRgHThIViJXiKZjL`kMbkNhlOmmPrmRviSzeTz\ bUzZVzWWzSzzPzzLzzIzzEzzBzzEzzHTzKRzNPzQMzTKzWIzZF\ zaDzdzzfzzdzzczzazz`zzZzzYzzWYzV`zUczSezRhzPkzOnzM\ qzLszKozJkzIgzIczH`zHXzGTzGPzFMzFLzEKzDJzCIzBIzAHz\ 9Gz8Fz7Fz7Gz9GzAWzDQz8KzH } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 15-05-08 (Looping the Loop [No Rating])
by Jim Muth 15 May '08

15 May '08

FOTD -- May 15, 2008 (No Rating) Fractal visionaries and enthusiasts: Due to the busy conditions here at Fractal Central, today's FOTD is a very hasty one that deserves no rating. The unusually fast image lies in the fractal that results when the formula Z^(1.37)+C is iterated at level 1.37 of the complex log ladder when no function is applied. This parent fractal is shaped something like a garden mole pulling itself halfway out of its burrow. The mole's head appears as a large period-2 bud, with a pointed snout. Today's scene is located on a zigzag filament in a clump of debris on the northeast shore of the main bay. To add a bit of interest, the image was rendered with the outside set to 'tdis'. I named the image "Looping the Loop" for no good reason. The fireball-fast calculation time of under 23 seconds is made possible by the unusually small magnitude of 35. And as always, the finished image is available for immediate viewing on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Wednesday started sunny here at Fractal Central, but by noon the sky had clouded over, and by late afternoon light rain had moved in. The fractal cats observed all this with disinterest. In my department the day was unusually busy. Thursday will be another busy day, though not as hectic as Wednesday. If all goes as planned the next FOTD, as unimpressive as it might be, will be posted in 24 hours. Until then, take care, and search for good fractal fortune. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Looping_the_Loop { ; time=0:00:22.81-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident center-mag=0.802447/0.710266/35.36239/1/77.5/0 params=1.37/0/1.37/0 float=y maxiter=1500 inside=0 outside=tdis periodicity=10 colors=000uzlrzkozklzjizjfzjczi`ziZzibzdez`hzXkzTc\ zZWzdOzjGzplzjazfSzbIzZ8zWBzSEzPGzLJAIMAFOABNA8LA5\ FA98AD8AH8AL9AP6GTDIWJKYQM_WObbQdhSfnThocjpnljjief\ g_ceV_cQXaRYdSYfSYiTZkTZnUZpUZrWXoYWm_Vk`UhbTfdSde\ RagQ_iPYjOWQagP`dP_aPZZPYWPXTPWRPVOPULPTIPSFPSDMV9\ JY6G`2Db0JZ8OVGTRPZNXcJehGmgOkfVieagdhecod_m_WkVTi\ QPgMMeHIcCFa8MZ9SXAZVAdSBkQCqOCoOEmOGkOIiOKgOMeOOc\ OQdQRdRSdTSdUTdVTeXUeYVe_Ve`WeaWccYbe_`fa_zbZzdXzf\ WzgVziTzkSzlQznPzpOzqMzsLzuKzvGzpCzk8zezz`zzWzz_zz\ czzfzzjzzmzzjzzgzzdzzazzZzzWzzTzzQzzNzzKzzHzzEzzBz\ z8zz5zzIzzVzzfzzczz_zzWzzSzzPzzLzzHzzDzz8zz9zz9zz9\ zzAzzAzzAzz4zz6zz8zzAzzCzzEzzGzzIczK`zJYzIVzHSzGPz\ FMzEBzAJzDGzCDzBlzk_zZNzM0zE2zD3zD4zC5zC6zC7zB8zB9\ zAAzATzbSz`Rz_QzZPzXOzWOzVNzTMzSLzRKzPKzOJzNIzLHzK\ GzJFzHFzGEzFDzDCzCBzBIz1Hz2Gz3Gz4Fz4Fz5Ez6Dz7Dz7Cz\ 8Cz9BzAYzYWzWUzUOz1Pz0Qz0 } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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Fractint version 20.4 patch 8
by Jonathan Osuch 15 May '08

15 May '08

Folks, Fractint (and Xfractint and Winfract) version 20.4 patch 8 is now available on the developer's web sites: www.fractint.org or www.fractint.net What's new: Fixed a bug in the virtual video code where the screen width was being reduced when going from a text screen back to the graphics screen. Revised logic that calculates the maximum X and Y resolutions possible with a given initial virtual screen size. Because of the variable type being used, the maximum size is 32767 even if sufficient video memory is available to support higher resolutions. Added back in code that forces passes=1 when either the X or Y resolution is greater than 2048. This was inadvertently removed with patch 5, and is needed because other passes= options are hard coded to use arrays of this size. Xfractint changes: Jean-Pierre Demailly provided extensive changes to eliminate the use of ncurses with Xfractint and also updated the MakeFile. Included a patch from Andrew Church and the people at Gentoo that fixes a filename buffer overflow that affected the help compiler. Also included their xioerror patch. Fixed a seg fault in Xfractint caused by not unstacking all the screens before exiting. Removed the shell-to-DOS option in Xfractint. Jonathan

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Re: [Fractint] FOTD 13-05-08 (At Attention [6])
by Jacopo Longo 15 May '08

15 May '08

Sorry to bother you but I keep on not being able to see the fractal images posted after May 6th. Is there any general problem or I am the only one experiencing this situation? Thanks and Best regards Jacopo, Italy > > FOTD -- May 13, 2008 (Rating 6) > > Fractal visionaries and enthusiasts: > > I named today's image "At Attention" because of the two dark > red, strikingly erect elements at the sides of the frame. > > The parent fractal is a typical double-negative Z thing based on > a variation of sqrt(2). The scene of today's action is in a > valley between two circular bays of the parent. > > The rating of a 6 seems appropriate for an image that is little > more than a sprinkling of confetti. > > The task of calculating the image from the parameter file can be > avoided by visiting the FOTD web site at: > > <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> > > where the finished image is posted. Doing this will save a > whopping 1-3/4 minutes. > > Light rain continued on Monday here at Fractal Central, with a > very unseasonal temperature of 55F 13C. The fractal cats spent > most of the day resting by the window. My day was peaceful > enough. Tomorrow should be a repeat. The next FOTD will be > posted in 24 hours. Until then, take care, and relax. > > > Jim Muth > jamth(a)mindspring.com > jimmuth(a)aol.com > > > START PARAMETER FILE======================================= > > At_Attention { ; time=0:01:44.88-SF5 on P4-2000 > reset=2004 type=formula formulafile=allinone.frm > formulaname=MandAutoCritInZ function=recip passes=1 > center-mag=+0.7486893055325985/-1.400758443118599/\ > 1933.74/1/82.5/0 params=-5/-1.4142/-1.4142/-5.4142\ > /0/2500/0/0 float=y maxiter=1800 > inside=0 logmap=50 periodicity=10 > colors=000ZFIRSWRTYRU_SW`SXbSYdP`dwZeVYeuXs`WfcVgf\ > UgiThlShoRirQiuPjxOjzNkzMkzLlzKlFJEHKGILHJLIKMKLML\ > MNMNNOOOPQPQRPSSQTTQUURWVRXWSYUR`XSZZTY`UXbVWeWVgX\ > UiXTkYSmZRp_Qr`PtaOvbNzgJzdLxbMu_OrYPnVRkTShQUeOVd\ > QVbRVaTV`UU_WUYXUXZUW_UU`TTbTScTQeTPfTOhSMiSLkSKlS\ > JmSKlTKkTKkTKjUKjUKiUKhUKhVKgVKgVKfVKfWKeWKdWKdWKc\ > XKcXKbXKbXKaYK`YK`YK_ZK_ZKZZKYZKY_KX_KX_KW_KW`KV`K\ > U`KU`KTaKTaKSaLT`KSaKSbKScKRcKRdJReJRfJQfJQgJQhIPi\ > IPiIPjIPkIOlHOlHYmHYnHYoHYoGYpGYqGYrGYrGMsFLtFLuFL\ > uFKvFKwEKxEKxEJyEJzEJzFIzEJzEJzEJzEJzEJzEJzEJzEJzE\ > JzEJzEJzEJzEJzEJzEJzEJzEJzEJzEJzEJzEJzEYzEYzEYzEYz\ > EYzEYzEYzEYzEJjEJjEJjEJjEJjEJjEJjEKjEKjEKjEKjEKjEK\ > jEKjELjEMjEYzE_zEazEdzEgzElzEqzEqzEqzEqzEqzEqzEqzE\ > qzEqzEqzEqzEqzEqzEqzEqzEqzEqzEqzErzEuzDxzEzzFzzFzz\ > GzzGzzHzzHzzIzzIzzJzzKzzKzzLzzLzzMzzMzzNzzNzzOzzOz\ > zPzzQzzQzzRzzRzzSzzSzzQzz } > > frm:MandAutoCritInZ {; Jim Muth > a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), > g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), > k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): > z=k*((a*(z^b))+(d*(z^f)))+c, > |z| < l } > > END PARAMETER FILE========================================= > > > _______________________________________________ > Fractint mailing list > Fractint(a)mailman.xmission.com > http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint > o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o-o- La Luna non si spegne mai, ma brilla di luce riflessa; la candela si può spegnere con un soffio, ma ... brilla di luce propria.

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Late FOTD for May 15
by Jim Muth 15 May '08

15 May '08

Fractal visionaries and enthusiasts: Due to an unexpected rush, the FOTD for May 15 will be delayed about 12 hours. If all goes well, the FOTD for may 16 will appear on schedul;e in 24 hours. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com

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Re: [Fractint] FOTD 13-05-08 (At Attention [6])
by Jacopo Longo 14 May '08

14 May '08

So did I. No change at all. Jacopo > Tried refreshing many times with no change. > > John W. wrote: > > Me neither. > > > > This seems to happen periodically, and it's usually curable by refreshing > > the page a few times. Why? I don't know. In any case this doesn't seem > > to work in this present mess. > > > > John W > > > > ----- Original Message ----- > > From: "Bill Jemison" <billjemison(a)cableone.net> > > To: "Fractint and General Fractals Discussion" > > <fractint(a)mailman.xmission.com> > > Sent: Tuesday, May 13, 2008 4:18 PM > > Subject: Re: [Fractint] FOTD 13-05-08 (At Attention [6]) (...)

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FOTD 14-05-08 (The Blue Minibrot [6.5])
by Jim Muth 13 May '08

13 May '08

FOTD -- May 24, 2008 (Rating 6.5) Fractal visionaries and enthusiasts: Today's image, which I named "The Blue Minibrot", came about when I subtracted Z^(1.1) from Z^(-1.1) and added C to produce a parent fractal consisting of one multi-bayed main part and a smaller disconnected Mandeloid which is partially obscured. Today's scene is located in the East Valley area of this smaller Mandeloid. I named the image "The Blue Minibrot" because of the intensely blue minibrot at the center. I could just as easily have named it after the colorful art-nouveau-like features surrounding the minibrot. After not too much thought, I rated the image at a 6.5. I am only moderately impressed by it. The calculation time of a fire- ball-fast 41 seconds will make running the attached parameter file a pleasure. Another way to see the image is to visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where it (hopefully) is or soon will be posted. Thursday turned into an absolutely perfect day here at Fractal Central, with crystal clear skies and a temperature of 72F 22C. The fractal cats were more concerned with scampering squirrels than the fine weather. And I was more concerned with work than the weather. The next FOTD will appear in 24 hours. Until then, take care, and be one of them. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Blue_Minibrot { ; time=0:00:41.24-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-2.4660478735/+1.253346387/1310.263/1/\ 66.5/0 params=-1/1.1/1/-1.1/0/500/0/0 float=y maxiter=1500 inside=0 logmap=44 periodicity=10 colors=000QxzNuzKrsHopElmBij8fgCcdF`ZJYTMRNQKHTEBU\ K9UP7UU6UZ4Uc2Uh1N8ILAMKCQQKLVSH`ZDef9jm5YeMMZaBIJ\ 1114JK7_b9pt6_l3Jd03Y28Q3CI5HA6L36VD6cN6lX6ueObheL\ kv3mr4jn5gj6df7ab8ZZ9WVAT83MRARiNmiKdiHWj1Ji8MiFOi\ LQiSTiYVidXknYijZggZedZc`_aY_VMa`V_fbZljXrrWmkYhd_\ cY`ZRbXOkUKcSGXPCPN9IpU_lRUiOOfLIkM2cIDWFNJ7UPCXVH\ _`MbfQelVhr_kwcmn_keWihltiisjfskcsk`slYsmWsmTsnQso\ NroKrpIrqFrqCrr9rs6rs4rq7spAtoDtmGulIukLvjOvhRwgUx\ fWxdZycaybdzafz_dyYbyWaxU_xTYxRXwPVwNUvMSvKQvIPzGN\ zFMzIQzKTzMXzO_zQczSfzPczN`zLYzIVzGSzEPzBMz9Jt7GzB\ JzELzHNzKPzNRzRTzUVzXXz__zbazfcziezlgzoizrkzumztlz\ tlzskzskzrjzrjzqizqiznfzlczj`zgYzeWzcTz`QzZNzXLzUI\ zSFzQCzOAzUFzZKzcPzhTzmYzrbzwfzB4zL7zV9zdBzmDzcAzU\ 7zK5zA2z00zCEzKKzSPzZUzVRzSPzPNzMLzIIzFGzCEz9CzIGz\ QKzZOzfSzoWzw_zcezKjzPlzTnzYozaqzfszjtzerzapzYnzUl\ z9yzVkzpZzL2zO7zQCzTHzVLz } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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Re: [Fractint] FOTD 08_30_2000
by JackOfTradeZ＠comcast.net 13 May '08

13 May '08

. Yes, FOTD 8 years ago! Finally got around to animating Jim Muth's flying boobs: http://www.fractal-animation.net/vid/alienboobz.zip 640x480, WMV, 45 second, 8 Meg .

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FOTD 13-05-08 (At Attention [6])
by Jim Muth 13 May '08

13 May '08

FOTD -- May 13, 2008 (Rating 6) Fractal visionaries and enthusiasts: I named today's image "At Attention" because of the two dark red, strikingly erect elements at the sides of the frame. The parent fractal is a typical double-negative Z thing based on a variation of sqrt(2). The scene of today's action is in a valley between two circular bays of the parent. The rating of a 6 seems appropriate for an image that is little more than a sprinkling of confetti. The task of calculating the image from the parameter file can be avoided by visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the finished image is posted. Doing this will save a whopping 1-3/4 minutes. Light rain continued on Monday here at Fractal Central, with a very unseasonal temperature of 55F 13C. The fractal cats spent most of the day resting by the window. My day was peaceful enough. Tomorrow should be a repeat. The next FOTD will be posted in 24 hours. Until then, take care, and relax. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= At_Attention { ; time=0:01:44.88-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+0.7486893055325985/-1.400758443118599/\ 1933.74/1/82.5/0 params=-5/-1.4142/-1.4142/-5.4142\ /0/2500/0/0 float=y maxiter=1800 inside=0 logmap=50 periodicity=10 colors=000ZFIRSWRTYRU_SW`SXbSYdP`dwZeVYeuXs`WfcVgf\ UgiThlShoRirQiuPjxOjzNkzMkzLlzKlFJEHKGILHJLIKMKLML\ MNMNNOOOPQPQRPSSQTTQUURWVRXWSYUR`XSZZTY`UXbVWeWVgX\ UiXTkYSmZRp_Qr`PtaOvbNzgJzdLxbMu_OrYPnVRkTShQUeOVd\ QVbRVaTV`UU_WUYXUXZUW_UU`TTbTScTQeTPfTOhSMiSLkSKlS\ JmSKlTKkTKkTKjUKjUKiUKhUKhVKgVKgVKfVKfWKeWKdWKdWKc\ XKcXKbXKbXKaYK`YK`YK_ZK_ZKZZKYZKY_KX_KX_KW_KW`KV`K\ U`KU`KTaKTaKSaLT`KSaKSbKScKRcKRdJReJRfJQfJQgJQhIPi\ IPiIPjIPkIOlHOlHYmHYnHYoHYoGYpGYqGYrGYrGMsFLtFLuFL\ uFKvFKwEKxEKxEJyEJzEJzFIzEJzEJzEJzEJzEJzEJzEJzEJzE\ JzEJzEJzEJzEJzEJzEJzEJzEJzEJzEJzEJzEJzEYzEYzEYzEYz\ EYzEYzEYzEYzEJjEJjEJjEJjEJjEJjEJjEKjEKjEKjEKjEKjEK\ jEKjELjEMjEYzE_zEazEdzEgzElzEqzEqzEqzEqzEqzEqzEqzE\ qzEqzEqzEqzEqzEqzEqzEqzEqzEqzEqzErzEuzDxzEzzFzzFzz\ GzzGzzHzzHzzIzzIzzJzzKzzKzzLzzLzzMzzMzzNzzNzzOzzOz\ zPzzQzzQzzRzzRzzSzzSzzQzz } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 12-05-08 (Minibrot In Sight [9])
by Jim Muth 11 May '08

11 May '08

FOTD -- May 12, 2008 (Rating 9) Fractal visionaries and enthusiasts: With too much other work to be done, I had no chance to write the discussion and post the FOTD for May 11. But the image was ready on time, and has lost none of its luster in the 12 or so hours that have passed since it was originally scheduled to appear. To avoid distracting the reader's attention from the attractive- ness of today's fractal, which rates a 9, there will be no arm- chair philosophy to dilute this discussion. The philosophy will return shortly however, so feel no disappointment, as no sacred cows, especially science and religion, will go untouched. I named today's image "Minibrot In Sight". This is certainly a fact with most FOTD images, and need hardly be stated. The rating of a 9 is my own opinion, due mostly to the colors, which add an unusual amount of life to the scene. The parent fractal was created by subtracting Z^(1.01) from Z^2. For some strange reason this mixture creates a Mandeloid that closely resembles the one created by the formula Z^(2.01)+C, in which the main spike has split into two infinitely divided main spikettes, each spike with a large minibrot of its own. Today's parent fractal has a fragmentary third minibrot between the two well separated main ones, and today's image is located in a valley of this minibrot fragment. The calculation time of 4-1/2 minutes fails to bring totally instant gratification. For gratification that is more instant go to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the image will soon be posted. But.....due to the unusual time of this posting, it might be a little while before Paul gets the image up on the web site. (Hmmmm, is postponed instant gratification really instant?) Light rain fell on Saturday here at Fractal Central; Sunday was merely cloudy, but with more rain forecast. Both days brought chilly temperatures around 61F 16C. The fractal cats were them- selves during this time. The next FOTD, the one for May 13, will appear in 34 hours or so. Until then, take care, and how do we know the real truth, when it keeps changing? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Minibrot_In_Sight { ; time=0:04:31.66-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident center-mag=-1.001490826049229/+0.0015796701297154/\ 5.024341e+010/1/-175/0 params=1/2/-1/1.01/0/0/0/0 float=y maxiter=6000 inside=0 logmap=449 periodicity=10 mathtolerance=0.05/1 colors=000BARCETDFVEFXFE_GBbHAeI9hL8kO7lRAkUCjXFi_\ IhbLgeNfhQekTdnWcqYbt`awc`ye`xfbwgcvhdvheuiftjhski\ skjrlkqmlpnnpnooopnpqmqrmqsnqnnpiopdoo_ooVmnSmnPmm\ MmmJmlHmkEmjBmi8nh5og3pfBqgJrgRshYtheuimvitqhpmgmh\ gidff_fbWe_SeXZdSedOlcKscGzcCzgazkzwlxulvrmtpmrnmp\ knninlfojdohbof_pdYpbVq`TqZRqYOheM_mKSuJUkJWbIXUIZ\ KH`BHa2I_AJZIJYPKWXLVdLUkKShKReJPbJO_IMXILUIKRHIOH\ HLGFIGEFGDCFHEKKFPOHURIZUJcYLh`MmcNrgPvjQzmRzqTztU\ zwVztUzqTzoTzlSziSzgRzdRzaQy_QuYOqWNmUMiSLeQKaOJYM\ IULGQJFMHEIFDEDCABB69A38949B4AD4BF5BH5CJ5DL6EN6EP6\ FR7GT7HV7HX8IZ8J`8JbFPaMV`S``Zf_dl_krZqxZdqbSjfGrz\ HrzIrzKmzMmqNdrPcsRbsSatU`uV_vXZvZYw_Zxa_yb`y_awXb\ vUctRdsOeqLfpIgnFhmCik9jj6ki5lh5mh5oh5qg5tg5wg5zg5\ zf5zfmzfmzemzemzemzemzgmzimzjzzlzzSzzQzzOzzMzzKzzJ\ zzHzzGzzFzzDzzCzzBzzQzzdzzaRzZOzWLzTIzQFzNCzK9zH7z\ EDzMIzTOz`TzgYzn`zKbzL_zP } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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NO FOTD FOR MAY 11, MAY 12 FOTD TO POST IN 12 HOURS
by Jim Muth 11 May '08

11 May '08

Fractal fans: Due to circumstances not entirely beyond my control, there will be no FOTD for May 11. But the FOTD for May 12 will appear about 12 hours earlier than scheduled. Until then wait with bated breath. The image will rate a lofty 9. Jim Muth

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FOTD 10-05-08 (Volcano [7])
by Jim Muth 10 May '08

10 May '08

FOTD -- May 10, 2008 (Rating 7) Fractal visionaries and enthusiasts: Once again, the philosophy, or whatever it is, leads off the discussion. To reach the fractal stuff, skip ahead seven para- graphs. I recently watched a 'skeptical' (read Atheist) show supposedly devoted to debunking paranormal claims. Not surprisingly, after demonstrating that Madam Zucchini, the local psychic, could not predict the future, the topic soon wandered to the so-called 'delusion' of spiritual life after death. During the entire show, the announcer repeatedly stated that extraordinary claims, such as the existence of spirits of the dead, demand extraordinary evidence. So far, so good, but the point of the program was to show the viewers that ghosts are nothing more than images created in the brain and mistaken for reality, or else outright fabrications. But with legends of ghosts, etc. existing in every culture on earth, and with many of those who see ghosts aware of the possi- bility of mistaking a hallucination for reality, the claim that absolutely everyone who claims to see a ghost is either mistaken or inventing the story is in itself quite extraordinary. Accor- ding to the 'skeptics' own words, this claim also must demand extraordinary evidence. But such evidence cannot be found. The high (or low) point of the show came at the end, when the announcer said that, since it is impossible to prove a negative, there can be no scientific evidence that ghosts do not exist. And since there is so much admittedly non-scientific and anecdotal evidence that ghosts do exist, this totally negated the entire message of the show. The only thing the show convinced me of is that skeptics and Atheists are out to convert others to their belief system. IMO, this makes Atheism as much a religion as any other religion on earth. And now on to the fractal stuff. In today's image I see a picture of an erupting volcano as viewed from a few thousand feet directly above the crater, complete with billowing clouds of ash, zig-zagging lightning, and oozing lava. The name 'Volcano" is quite appropriate, since a volcano is currently erupting in Chile. The formula behind all the volcanic action adds straight Z to Z^(2.1) to create a parent fractal that is quite hard to describe. Perhaps the best description would be a disembodied Mandelbrot main bay with two lopsided sausages where the single large bud should be. A large field of scattered zig-zagging debris lies off to the west of the two sausages, with today's image located very deep in one of these zig-zags. It lies so deep in fact that the resolution is starting to break down. Luckily, this is hardly noticeable, but I did include the mathtolerance entry to assure that the parameter file calculates at the correct magnitude. The rating of a 7 is arbitrary, but the calculation time of 42 seconds is as fast as a photon. As always, the finished image is posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> An all day rain and temperature of 54F 12C made Friday less than ideal here at Fractal Central. The fractal cats took one look at the water running down the sidewalk and returned to attack their catnip rats. My day was average. With any luck at all tomorrow will be the same. Look for the next FOTD in 24 hours. Until then, take care, and if I had not seen a ghost, I would never believe that they exist. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Volcano { ; time=0:00:42.24-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident center-mag=-1.68679550605384600/-0.833917252303289\ 20/2.434378e+013/1 params=1/2.1/1/1/0/0/0/0 float=y maxiter=390 inside=0 logmap=132 periodicity=10 mathtolerance=0.05/1 colors=000670880A90CA0EB1GC2ID3LE3PG3UJ4YL4aO4eR4j\ T5pW5uX5zd5zf6zj6zo6zr6zo5zm5zi5zg5we5tc5ra5p`5nY5\ lX5jU5hT5fR5dQ5cWBbaGagL`mQ_sV_y_YtXXoUVkRUfOSaLRY\ JUzBbmVk`mmaloakqbjrbitcivchwcgydfzdezeezedzfczfbz\ fbqkM`p6LBxPDuTEsXFq`GodHmhIklJipKgtLexMczNazO_zPY\ zNVzLTzJRvHPsFNpDLmBJi9Hf7Fc5D`3Bc8FfCJhHMkLQmQUpU\ XsZ`ubdxggzkkzpoztrzqmzoizlezjazgXzeTzbPz`LzZHzXOz\ VUzT`zRfyPlvNksLjpKimIhjHggFgdDfaCeZAdW9cT7bQ6bSAW\ UEOP`URXRSUPTRNUOLVLJzdgy`ctY_oVWjRSeOO`LKZiFYbGOc\ qM`oKYnIVlGSjEPiQUpaYwlfrvompkckhUfdKaaAaLRa4fc7je\ 9mfBphDsjFvkHyXpoUqpSrpPspNspLtpIupGvpEvpRwgbwZnwR\ trbzmnzhztgtjfn_ehQdbGcYR`R`YKkVEuS7zP1zylzcnzJolN\ mYRl_TdaUXcWPdXHbUH`RHZOHYDJXLH_Y8ZVAYSBYQDXNEWKGI\ 0cK3_M6XO8UQBQSDNUGKOc0Q_3RX5SU8TRAUODVLFz4Ow6Ns8M\ oALkBKgDJcFI_HHuqRh_MZiqXWZL77OAARDCUGFhPMeNLcMKaL\ J_KIYJHOMzPLtQLnRKhNLJMJG } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 09-05-08 (Ruffled Flourishes [6])
by Jim Muth 09 May '08

09 May '08

FOTD -- May 09, 2008 (Rating 6) Fractal visionaries and enthusiasts: The philosophical blather continues today. Those who are not philosophically inclined will find the start of the fractal stuff nine paragraphs below. Though materialism (Is it now called energism?) was more popular in the 19th Century, I still sometimes hear claims that physical matter is the ultimate reality. I find this philosophy naive almost to the point of comedy, but some still hold fast to it. The first question that comes to mind is, 'what is physical matter made of?' The answer of course is atoms. But the regress continues, for then we ask, 'what are atoms made of?' and find they are made of sub-atomic particles, mostly protons, neutrons and electrons. If we dare go farther and ask what protons are made of, we find they are made of quarks, but when an electron gets into the mix, the proton becomes a neutron. Only a fool would ask what quarks are made of, but if he did, he would probably find they are currently thought to be multi-dimensional vibrations of super- strings or membranes. And I assume the strings and membranes are made of pure energy. With the electron, things are no better. The electron has both wave and particle aspects, as do all sub-atomic particles when not observed. When an electron is observed, it collapses for the observer's convenience into whatever the observer is looking for. When it spins, and all electrons do something called spin, it must make two full turns before presenting the same face to the observer. And anyone foolish enough to ask what is waving when the electron is in its wave mode will find that nothing is waving. I only hope no one asks how nothing can actually start waving and thereby become something. The last I heard, it is logically impossible for something to come from nothing. Mass and energy have been shown to be different forms of the same thing. Mass is a parcel of energy tied into a knot. But what the heck is energy? Yes, we know it is the ability to do work, but what is it made of? No one seems to know. They say the question is silly. (And maybe it is!) It appears we have come to the end of the line and answered absolutely nothing. Physical matter is not the ultimate reality, nor are the atoms that matter is made from. Sub-atomic particles are even less real. Energy is the ultimate reality, and without invoking a god, no one has the slightest idea what it is or where it comes from. And if we invoke a supernatural god, we must then ask where that god came from and what he, she or it is made of. Something is wrong somewhere in this dead-end line of thought. Something, perhaps many things, or even everything we assume to be a fact must be wrong. But I have been searching for over half a lifetime for the flaw. Dogmatic religion has no answers, equally dogmatic science has no answers, and dreamy-eyed mysti- cism, though it might have some answers, is as much a failure in communicating those answers as are the quantum physicists at communicating exactly what goes on down there. All this leaves the questioning segment of humanity lost in the wilderness, which for all I know might be our natural predestined state. Now as for today's fractal image, it rates a 6. There have been worse and there have been better. I named it "Ruffled Flour- ishes", which has nothing to do with the chief of state. It was created when I subtracted 1/4 part of Z^3 from the Mandelbrot set to produce a M-set rotated 180 degrees, with lots of extra nooks and crannies (not crooks and nannies) along the X-axis. Today's image is located in one of these extra crannies in the East Valley area of the main M-set of its parent. When rendered in the usual manner, the image falls flat, so I have rendered it with the outside set to 'tdis', which gives it just enough life to make it worth being declared FOTD for May 09. The calculation time of 1-1/2 minutes is gloriously fast. But it would be even more glorious to surf over to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and enjoy the finished image posted there. Thursday started with light rain here at Fractal Central. The rain ended before noon however, leading to a cloudy bright afternoon with a temperature of 73F 23C. The fractal cats enjoyed the weather from the comfort of their window seats. My day was once again slow. Who could ask for more? The next FOTD will be posted in 24 hours. Until then, take care, and my philosophical muse is still raging. Also, if such a thing as absolute truth exists, where does it lie and how do we recognize it? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Ruffled_Flourishes { ; time=0:01:28.30-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident center-mag=-0.059072035782852/+0.0135011860476962/\ 2.357457e+007/1/67.35/0 params=1/2/-0.25/3/0/0/0/0 float=y maxiter=1500 inside=0 outside=tdis periodicity=10 colors=000q`5pY6oU9nRCYQAHP9caOynayf_yZZySYxOPxLGw\ I7wF5nU6ehDXwJZvH_vG`vFauEbuDcuCohMzWVzJczLUoNLePB\ VR5LS5K_5Kf9JnHJuPNmSRfVU_YYT`aar`ardarhL_kQUoWNLp\ BFoBTb5fR5lT5rU5xVAzWFzXKzaIqeGhjE_nCRrAOMWWVaccgk\ lmafeS`YzpOziKzbHyXEuQBqJ8nD5rCMnLIkTEhaAei6bq5ZpC\ VZKRnTNm`KmhQSiVli`lielikliplivlizliunfppdkrbet_`v\ YWxWPxTRyUTyUUzVWzVYzWZzW`zXzrPrwTazXDzZHz_Lz`PzaS\ zaWzb_zcczdfzddtbcl`beZaYXQS_`RWkQTvPPzOMxWJobGfjD\ HzrVrEZqBbq9fp7jp5no5ro5vn5PZZzk5yn5wp5tr5rt5to5vk\ 5xf5zb5zY5zU5yS5uQ5qO7GzeXiPmN9qTDuZGxcJziMzoOznPz\ mQwlRskRojSkiThiT`oCzzGTu5ti5gc5VY5SV7QSHOPQMM_KJi\ IHrJNjJScJYXKbQKhJKmCEq5Hr5Kr5Nr6Pr6Ss7Vs8Ys9_s9bm\ AegAhaAwF_xN5kXAZfRElqNogVqZcsQkuHtw8xKozy5wu5srAn\ oFjlKeiPafUGU_PZZYcZQgJYgRegZDzFVtTlgeuzNzlbzVrwZj\ pbcifWUZjZd_cjPicMnYKsSHzKDzLExMFwNGuOGsPHrQIpRJoR\ JmSQkTWiUagVgog5tk5sg5rd5 } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 08-05-08 (Tongues of Fire [6.5])
by Jim Muth 07 May '08

07 May '08

FOTD -- May 08, 2008 (Rating 6.5) Fractal visionaries and enthusiasts: I am often puzzled by dimensions. What are they? Are they merely the number of mutually perpendicular lines that can be erected through a single point in a given space? Or are the lines a mere indicator of dimension? Where do dimensions come from? Why is our universe limited to three spatial dimensions when a higher number would allow for far more varied phenomena? Since stable planetary orbits are impossible in spaces of dimensions greater than three, maybe intelligent life is possible only in our familiar 3-D space. But then why is it so easy for computers to work with higher dimensions, and so easy for humans to write about higher-dimensional phenomena, yet impossible for humans to visualize the things they write about? Before the 20th Century our universe was obviously three- dimensional. All we had to do was look at it. Then along came relativity, which made the universe four-dimensional. Next up was Kaluza Klein theory, which required a five-dimensional universe. When string theory burst upon the scene, it needed 26 dimensions, which were somehow compressed into ten dimensions, with six of them rolled up into infinitesimal hyper-loops. The last I heard, M-theory has upped this number to eleven dimensions, with seven of them curled-up invisibly, and who knows where we will go from here. It is beginning to appear, at least to me, (not at all the rational skeptic,) that the concept of dimensions is a human- invented mental construct, and what we know as visualized dimensions are actually manifested levels of consciousness. Humanity is at the three-dimensional level of consciousness. Yes, I know this sounds mystical, but I am no apologist for the hopelessly inadequate, common-sense Newtonian view of the universe, which I now see as a sub-set of a far broader reality, which is probably a sub-set of a still broader reality, and so on to infinity. But why worry about theoretical infinities when we have actual infinities in the world of fractals. Today's image came about when I subtracted 1/2 part of Z^4 from one part of Z^3 and added C to produce a parent fractal that resembles nothing as much as an angel lying on its side with its head facing east and a tongue of fire over its head. (This Sunday is Pentecost.) Today's image is located on the southern shore of this tongue of fire, and indeed has eight tongues of fire circling the central minibrot. I named the finished work "Tongues of Fire" and rated it at a 6-1/2. The calculation time of 3-1/2 minutes is bordering on slowness, but still brief enough to make running the included parameter file almost a joy. For those with over-qualified computers, the finished image is posted for viewing on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Perfect spring weather prevailed all day Wednesday here at Fractal Central. The sky was clear, the wind was light, the humidity was low and the temperature reached 81F 27C. The fractal cats were more concerned with the pigeons pecking for scraps on the sidewalk. My day was slow enough to leave time for both a fractal and a philosophical discussion. And better yet, it looks like tomorrow will be the same. Until next time, take care and you can't get a universe from absolutely nothing, which means there always was something rather than nothing. (Don't ask why that something has always been there.) Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Tongues_of_Fire { ; time=0:03:32.62-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=+1.396812017323909/-0.0389524851568373/\ 3.840418e+011/1/-27.5/0 params=1/3/-0.5/4/0/0/0/0 float=y maxiter=3200 inside=0 logmap=400 periodicity=10 mathtolerance=0.05/1 colors=000FARGARHAQIAPJAOKANKAMKALKAKKAKKBKKCKKDLK\ ENKFNKGOKHPKIRKJSMKTOLUQMUSNVUOWWPXYQX_RYaSZbT_bU_\ cV`cTabRbaQbbP_dOXeOUgNRhNOf`BfYAfU9fQ8AA7pS6zm5zd\ 4zY3yS2tL1p66_BBXGFTLKQQONUTKZXGcaDheAmj7qn`qZ_o__\ m`ZlaZjbZhcYgdYeeYcfXbgX`hX_iWWmVTpUQsTNvWQuYSu_Vu\ aXtc_teathcsjfslhsnkrpmrrorqmoqklqijphgpfepdboc_oa\ Yo_VoZTnXRmVQmTOlRNlPLkNKjLJjJHiHGiFEhDDhBCQFW8Io9\ KmALkBMjCNhDOgEPeFQcGRbHS`IT_JUYKVWLWVMXTNYSSWQXTO\ aRMfOKTvTbcNTzlVwhXseZob`l_bhXdbUfXRCRSBVUBYXA`_Ac\ aAfd9jg9mi8pl8so8vqWierYUTNfVMdWMbYM`ZMZ_MYaMWaMUa\ MSaMX`Mc_Mc_Mc`Mc1Wm5Vm8UmBUmETmHSmKSmNRRRQQUQPXPO\ _OMbOLeNKhMJJn8Mk9PhASeBVbCY_D`XEcUFfRGiOHkRskQnkP\ ikPdkO`kNWkNRkMMGchJceMccOcaRd_UeXWfVZgTahRciOfjMi\ kKRlQamM8nvCqrFtoIwkMzhPzdSzazzZzzVzzSzzOzzLzzTzzN\ zz2zz8zzDzzQzzOzzNzzMzzLzzKhzzizzjzzjzzjzzjzzjzzjz\ zjzzkzzkzzkzzUzzSzzQzeLzz } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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Re: [Fractint] Fractint Issue for the developers?
by JackOfTradeZ＠comcast.net 07 May '08

07 May '08

. Those of you that have seen my deep zoom videos may have noticed that at a few points along the way the sequence "jerks" or stutters with distortion. This has nagged at me for years and I have pulled my hair out trying to figure it out. Turns out to be rather simple, and I have been kicking myself constantly for not having realized it sooner. I have been in communication with Michael Condron, who runs the new http://www.hpdz.net/ web site (you all should check out), and he has been comparing his home-grown software (which is apparently quite good) with fractint; we may collaborate on animations in the future if we can get our codes to match. He pointed out that fractint may not be jumping to a high enough level of precision soon enough when in arbitrary precision math mode. I re-rendered a couple of the jerky sequences using the "BFDIGITS" command to force a higher precision, and yes - it works! They render perfectly smooth. So now I am re-doing the famous Universe-3 and the current Universe-6 with this correction. Since fractint doesn't "know" I am rendering thousands of images for an animation, it has to be assumed that this problem can occur unpredictably at any point or time when a deep image is being rendered. Thus people rendering deep images may see a distorted oval where a circle should be etc., and would never know that it is a distortion - it would just look like another cool fractal! I wouldn't call this a "bug" or "software issue", it seems to me that a small change in the fractint SC should fix it, maybe the number of a single variable. It looks like a whole lot of tight "C" and "ASM" code, mostly way over my humble head, but a fix might be: I think correcting this in fractint may be as simple as changing a single variable in the code: IF (magnification = xxx) THEN (precision = xxx * c) END IF something like that. Of course, higher precision means longer render time, so a balance must be struck. My observation so far suggests that a single order increment should fix it. Stay Amazed! JoTz .

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FOTD 07-05-08 (Something Imaginary [5])
by Jim Muth 07 May '08

07 May '08

FOTD -- May 07, 2008 (Rating 5) Fractal visionaries and enthusiasts: Today, I'm in more of a philosophical mood than a fractal mood, so pardon me if I make a little diversion before getting to the Fractal of the Day. Those bored with opinionated philosophy may skip to the ninth paragraph. In the distant past, when I was just learning about the world, I read every book of popularized science that I could get my hands on. The books answered most of my childhood questions such as: how far away are the stars?, why does the wind blow?, how old is the earth?, what is the tallest mountain and the tallest water- fall?, (I found it was not Yosemite), where does lava come from?, where do meteors come from? My list of questions was nearly endless, and I found the answers to most of them in the 'science' books I read. But now that I am closer to the other end of life, my list of questions has changed, and I feel that the science I once almost worshipped has let me down. True, my questions are now more difficult. My head is filled by unanswered and perhaps unans- werable questions, such as: what is the meaning of life?, where did our unique individualities come from and where will we go from here? Answers such as: the meaning of life is 42, (ask a deaf person what 42 means), we came from oblivion and we will return to oblivion, are merely silly. Equally silly are attempts to avoid answering the questions by blaming our genes for programming us to invent such ultimately meaningless questions. But perhaps the most evasive and offensive thing I have heard is the standard Atheistic reply that men lack the courage to accept the harsh reality that deep inside they fear is actually true. This is perhaps the most destructive philosophy ever embraced by a thankfully small segment of humanity. Many years ago I tried and discarded such nihilistic Atheism, which like conventional dogmatic religion, raises more questions than it answers. (An Atheist once actually said to me that the physical universe is his god and science is his religion.) Perhaps it would be better for those running the oversized scien- tific corporation to stop wasting such immense sums of money in search of useless dream things such as 'higgs particles' and a 'theory of everything', and pause to find the courage to address the questions that people are really concerned about. Does all this mean that I believe in the supernatural? Maybe it does, or maybe not. But if things seem to be pointing in that direction, I will not curl into a ball and hide in the corner in fear of the unknown. I make no claims of having any answers, but of one thing I am certain. I have so far found even more unanswered questions in fractals than in the so-called 'real' world. Today's fractal image, by the way, lies in the parent that results when the formula Z^(2.01+0.03i)+C is iterated six levels up the complex logarithmic ladder. This parent fractal is basically a distorted Mandelbrot set rotated so that its main spike faces southwest. Today's scene showing an equally distorted minibrot is located in the much- broadened east branch of the valley setting off the large period-3 north bud. Since the image shows a minibrot surrounded by nothing much of interest, I could rate it at only a 5. The name "Something Imaginary" refers to the imaginary part of the exponent of Z. The calculation time of 4 minutes is a bit longer than I would have preferred, but still well within reason. The most reason- able way of all to view the image however is to visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and enjoy it as much as possible there. A day that could have been perfect was spoiled by a series of light showers in the early afternoon here at Fractal Central on Tuesday. But despite the rain, the temperature reached 72F 22C, earning the approval of the fractal cats. My day was slow enough to be satisfactory, but not good enough to be exceptional. The next FOTD will appear in 24 hours, when perhaps I can get out of this fractal rut. Until then, take care, and I once was sure, but now I'm puzzled. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= SomethingImaginary { ; time=0:04:04.96-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-0.54660864024034790/+0.989879191269876\ 70/126719.3/1/-117.5/0 params=2.01/0.03/6/0 float=y maxiter=2500 inside=0 logmap=200 periodicity=10 colors=000c3_d3Ze3Yf3Xg3Wg3Uh3Ti3Ri3Qk3Vl3_m3cn3ho\ 3mp3qn3ol3mj3kh4if6ge8ecAcaBb_D`YFZXHXVIVTKTRMRPOP\ OPOHWXAae4gm7fhAedEd`HcXLbTOaPR`KV_GYZCaY8dX4gW2m`\ DrdQwhbkbZ_YWOTTDOQ4NK4LL4JM4IN4GO4EP4DQ4BR49R48S4\ 6T44U43V43W43X43X43Y63Z94ZC6_E8_HA`KC`NEaQGaSIbVKb\ YMc`OccQdeSdgUchVcjWckXcmYcnZco_cq`cractbcuccwdcxe\ cyfcucdq`dnYejVegSecPf`MfXKgUHgQEgNBhJ8hG5iC3i93iC\ 5`E9SHEKJIBLM3JL5IL6HK7GK8FJ9Ge2Db2B_28X26U24R2BU2\ HW8OZFU`L_bSfeZlgeriknm2mi2lf2lb5k_8jWBjTEiPHhMKhI\ NgFQfBTf8Wg7Xg7Xg7Xg6Xg6Xg6Yg5Yg5Yh5Yh4Yh4Zh4Zh3Zh\ 3Zh3Zh3Ze8abCd_HgXLjUQmRUpOYsSXrVXrYXq`WqcWpfWpiVo\ lVooVoNW6OU6OT6OS6PR6PQ6PP6QO6QN6QM6RL6RK6RJ6TM9VP\ CWSFYVI_YL``ObbRceUehXgk_hnbjqekchkZMkZ2eZ2`Z2WZ2R\ Z2LZ2GZ2BZ26Z2BZ2GZ2LZ2Qh4Vs6Wu8`z9`zB`zC`zEgzFgzH\ lzIqzKvzLzzNzzOzzQzzRzzSzzJzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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FOTD 06-05-08 (Hidden Spiral [?])
by Jim Muth 05 May '08

05 May '08

FOTD -- May 06, 2008 (Rating ?) Fractal visionaries and enthusiasts: How should one rate an image that might not even be a fractal? I certainly don't know, which is why I consider the rating of today's image to be a question. The image exists in the same empty circle that held the most recent FOTD image of two days ago. But today, instead of butter- fly-like elements, we have a vague and hard to see spiral that exists in the near-chaos that fills the empty circle when the 'bof61' inside fill is applied to the emptiness. I named the image "Hidden Spiral" because, unless the function and parameters are set exactly right, the spiral vanishes. The calculation time of 1-2/3 minutes means that no great amount of time will have been wasted if the image fails to satisfy. One way of being sure of satisfaction however is to visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view the finished image, which is posted there. Ideal spring weather prevailed here at Fractal Central on Monday, with full sun and a temperature of 70F 21C. The fractal cats passed the day unconcerned with the weather, even growing bored with their catnip rats. My day was average; the next FOTD is due in 24 hours, and for all I know, it will probably appear as scheduled. Until then, take care, and what is the significance of the number 42? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Hidden_Spiral { ; time=0:01:38.98-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=Mystic2 function=tan passes=1 center-mag=-0.183903/0.273552/25.7373 params=4.28/1.3/5.12/-0.2/1.457/6.484 float=y maxiter=160 inside=bof61 periodicity=10 colors=000z00z00z00z00z00z00z00z00z60qG0lP0cZ0Uh0K\ q0Bz06z00z00z00z00z00z00z00z00z00z00z00z00z00z00z0\ 0z00i06q0Gi0Pm0GmBBhP2pc0zq0zz0zz0zz0zz0zz0zz0zz0z\ z0zz0zz0zz0zz0zz0zz0zzAzzKzzUzzZzzezzizzmzzozzqzzs\ zztzzszzqzzozzmzzjzzgzzczzZzzUzzPzz2hzPPzl2zzAzzKz\ zUzzZzzczzhzzmzzmzzmzzhzzczzZzzUzzPzzKz00000000000\ 000000000000000000000000000000000000000000000000h0\ Kz0hz0qz0vz0zz0zz0zz0zz0zq0xc0sP0jB0c00c00c00f00c0\ 0c00c00c00c00c00c00Z00P00K00B006002002000200600620\ B20B60GB0KB0KG0PK0UK0UP0ZU0UP0ZP0ZP0cP0cP0cP0hK0hK\ 0hK0lK0lP0qP0qP0qP0vP0vP0vK0zG0zB0zB0zB0zB0zB0zB0z\ 60z60z60z60z60z60z60z60z60z60z60z60z60z66z6Gz6Pz6Z\ z6hz6lz6vz6zz6zz6zz6zz6zz6zz6zz6zz6zz6zz6zzKzzUzzc\ zzlzzvzzzzzzzzzzzzqzzczzUlzGcz6Uz0Kz6PzGUzKZzUZzZc\ zhhqllcvlPzqGzv2zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0z\ z0zz0zz0zz0zz0zz0zz0zz0zz } frm:Mystic2 {; Jim Muth a=real(p1), b=imag(p1), c=real(p2), d=imag(p2), k=real(p3), f=imag(p3), g=pixel, z=(pixel)^a+(b*(pixel))^c: z=(fn1(z)+(d*(g)))^k+(f*(cos(g))) g=sqr(g), LastSqr <= 100 } END PARAMETER FILE=========================================

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No FOTD for May 5
by Jim Muth 05 May '08

05 May '08

Fractal visionaries and enthusiasts: There will be no FOTD for May 5. The FOTD for May 6 will appear on schedule. Jim Muth

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FOTD 04-05-08 (Where's the Fractal [What Rating?])
by Jim Muth 04 May '08

04 May '08

FOTD -- May 04, 2008 (What Rating?) Fractal visionaries and enthusiasts: To create today's image, I dredged up an old formula that I have not worked with for quite a while. I forget what the formula was originally supposed to do, but that doesn't matter. As today's image shows, the formula creates some strikingly unusual scenes, fractal or not. The parent fractal of today's image is not a fractal. It's only an empty circle. Regardless of how the parameters and function are tweaked, the Mystic2 formula draws nothing but flat black empty circles. But when those circles are rendered with an active inside fill and the parameters are set just right, all kinds of strange things happen. Today's image is but a tiny part of the unexpected things that can happen invisibly inside an empty circle. I named today's image "Where's the Fractal?". Actually I'm not sure that it is technically a fractal, consisting entirely as it does of 'inside' stuff. But it has enough fractal characteris- tics to pass muster as the FOTD for May 4. Since I'm not sure that the image actually is a fractal, how could I rate it? If I were pressed to give it a rating however, I would choose something around an 8. The 1-2/3 minute calculation time should cause no grief out there in fractal land. And with the finished image posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> satisfaction is virtually guaranteed. The sky was cloudy here at Fractal Central on Saturday, and the temperature never rose above 61F 16C, but the rain held off until 7pm, when all the outside stiff had been completed. The fractal cats, never ones to be worried about weather, spent the day guarding their chosen catnip rats. My day was uneventful. If tomorrow is the same, I'll consider the week-end a success. The next FOTD will appear in 24 hours. Until then, take care, and to be considered the greatest thinker in history, find the answer to the riddle of the universe. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Where's_theFractal { ; time=0:01:41.23-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=Mystic2 function=tan passes=1 center-mag=0.6817/0.318939/21/1/160/0 params=4.28/1.3/5.12/-0.2/1.457/6.484 float=y maxiter=160 inside=bof61 periodicity=10 colors=000UUUKUXUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUU\ UU000JF4000PQpQSoSTnTVmVXlWYkY_j_`i`bhbdgcegegffie\ hjdilckmbmoanq`pr_qtZsvYtwXvyWwzWmqRciMUaIT`HS`GR`\ GQ`FP`EO`DN`CM`BL`AK`AImYHytJusLrsaCAbBBbABc9Cd7Ce\ 6Df5Df4Da8GYCIUGKQKNMOPISREVTEUSETSESSESSERREQREQR\ EPREOQEOQENQEMQEMPELPEKPEKPGMNINMKOLLPKNRJPSIRTHSU\ GUVFWXEYYDZZC`_Bb`Adb9ec8gd7ze6jf5gc7da8a_9ZYBWVCT\ TDQRFNPGLNHMOGMOGMOFNOFNOENOENOEOODOODOOCPPCPPCPPB\ PPBQPAQPAQPARP9RP9RP8RP8SQ8SQ7SQ7TQ6TQ6TQ6TQ5UQ5UQ\ 4UQ4UQ4VN7VLAVIDVGGWDIWBLW8OW6RW4TV6UV7VU8WU9XTBYT\ CYSDZSE_RG`RHaQIbQJbPLcPMdONeOOfOPfQQgRRgTRhUShWSi\ XTiZTj_UjaUkbVkdVleWlfXmhXmiYnkYnlZonZoo_pq_pr`qt`\ quarvaru_stZstYssWssVtrUtqStqRtpQupOuoNunMunKvmJvm\ IvlGvkFwkEwjCwjBwiAxh8xh7xg6xg5xVHhJTUKSXLRZLRaMQc\ NQfNPhOPkPOmPOoSPpUQpWRqYSq_TqbUrdVrfWrhXsjYslZso_\ tq`tsatubuwcuyduIJtKLsMNr } frm:Mystic2 {; Jim Muth a=real(p1), b=imag(p1), c=real(p2), d=imag(p2), k=real(p3), f=imag(p3), g=pixel, z=(pixel)^a+(b*(pixel))^c: z=(fn1(z)+(d*(g)))^k+(f*(cos(g))) g=sqr(g), LastSqr <= 100 } END PARAMETER FILE=========================================

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FOTD 03-05-08 (Flying Staghorns [No Rating])
by Jim Muth 02 May '08

02 May '08

FOTD -- May 03, 2008 (No Rating) Fractal visionaries and enthusiasts: Today's parent fractal, which was found when 3/4 part of Z^(1.33) is subtracted from 3/4 part of Z^(1.13), resembles nothing as much as a monstrous waddling duck turned on its side, with today's image located on the southwest shore line of the main bay, near one of the duck's webbed feet. I named the image "Flying Staghorns". At one time I thought I saw antlers in the image, but now I'm not so sure. (At least there were no antlers in the tree tops.) Since today's image is almost a repeat of yesterday's image, I could give it no rating. The calculation time of 1-3/4 minutes is just about right for such a casually crafted image. And as always, the finished image is posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where it may be viewed instantly and near-effortlessly. Friday turned out unexpectedly pleasant here at Fractal Central, with hazy skies and a temperature of 73F 13C. The fractal cats ignored the weather and got into another spat over their catnip rat. Late in the day, we finally setlled the ongoing dispute by getting a second catnip rat. Now both cats have their own rat. My day was fairly busy; tomorrow promises to be slower. The next FOTD will appear in 24 hours. Until then, take care, and I lost my mind this morning, but after a short search I found it lying behind the waste basket. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Flying_Staghorns { ; time=0:01:47.50-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-5.11542429/-12.1715054/899.9603/1/-90/0 params=0.75/1.13/-0.75/1.33/0/1500/0/0 float=y maxiter=800 inside=0 logmap=66 periodicity=10 colors=000OFOPFMQGJRHHSIFTJCUJAWJ8YI6_I5_G4YE4UB3Q\ 72M42P76SA9VDDYGG`JKcMNePRhSUkVYnY`q`dtcgwfkyhnqem\ jbmb_lWTlOUkHPkLOiPPhSPfWPeZPdbObeOaiN_lNZpNYsMWwM\ VzMUnO`bQfRSlGUrFWsFYsFZsE`sEasEcsDdsDfsDgsCisCjsC\ lsCmsEkqFipHgoIfmKdlLbkM`iO_hPYgRWeSUdTTcRVdQWePYf\ OZfN`gLahKchJdiIfjHgjKamNXoQSqTNsWIuYDwdgScdQcaOc_\ NcXLbVKbSIbQHbNFbLEgSOlYXpceuinyowrnplnifnc_nXUnQO\ nKRlNTjPVhRXfTZeV`cXbaZe_agYciXekVgmTioRkqPzsOzoNz\ kMzgMzcLz_LzWKzSKzOJzLJzJGzHEzFCzDAzB8zB7zB7zC8zC9\ zC9zDAzDBzDBzECzEDzEDzFEzFFzFFzGGzGHzGHzHIzHJzHJzV\ 9zIIzIIzJHzJHzKHzKGzLGzLGzLFzMFzMFzNEzNEzOEzODzODz\ PDzPCzQCzQCzRBzRBzSBzSAzSAzTAzT9zUAzUFzVMzVSzDUzFZ\ zGczIczJczLczMczOczPczRczSczUczMczNczNczNczNczNczN\ czNczNczNczNczOmzOmzOmzOmzOmzOtzOtzOtzOtzOtzPtzPtz\ PtzPtzPtzPtzPtzPtzPtzPtzQtzQzzQzzQzzQzzQzzQzzQzzQz\ zQzzRzzRzzRzzRzzRzzRzzzzz } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 02-05-08 (Even More Spirals [7])
by Jim Muth 01 May '08

01 May '08

FOTD -- May 02, 2008 (Rating 7) Fractal visionaries and enthusiasts: Today's image lies in the parent fractal that appears when 3/4 part of Z^(1.6) is subtracted from 3/4 part of Z^(1.4) and (C) is added. Once again this parent is an oversized monstrosity closely resembling a Mandelbrot set rotated 180 degrees, but with no main spike and a spiral-filled East Valley that lies on the west side and is beginning to be swallowed up. Today's scene is located in a spiral in the East Valley area of its parent. I named the image "Even More Spirals" in recognition of the abundance of spirals favored by fractal artists. Actually, there's nothing wrong with spirals, just like there's nothing wrong with the crew of the star-ship Enterprise being possessed by alien spirits from space. After giving the image its name, I rated it at a 7, which is good enough, though far from outstanding. If I had put a bit more effort into the coloring, I might have raised the rating to a 7-1/2, but I decided to browse through some old Scientific American magazines from 1963 instead. (I find the 45-year-old issues more interesting than the current over-designed and some- what pretentious ones.) The included parameter file runs on my 2000mhz fireball in 1-1/4 minutes -- not too bad for an image that rates a 7. And for those who cannot, or prefer not, to run parameter files, the completed image is posted to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Morning sun on Thursday gave way to afternoon clouds and evening sprinkles here at Fractal Central, while the temperature reached 59F 15C and the fractal cats argued over their catnip rat. My day was slow enough. Tomorrow is likely to be the same. The next fractal will be posted in 24 hours. Until then, take care, and what ever happened to all those wonderful hi-tech products, which the promoters told us that the space shuttle program and space station were going to make possible? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Even_More_Spirals { ; time=0:01:17.76-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-2.352816253126894/-0.5553738233918362/\ 2.85e+008/1/87.5/0 params=0.75/1.4/-0.75/1.6/0/525\ /0/0 float=y maxiter=1500 inside=0 logmap=134 periodicity=10 colors=000bMKaLK`KKZJKXIKVHKTGKRFKPEKNDKMCKLBKKAKJ\ 9KI8KQ8MWHOUKPUNRUOTUOUUQWUSXZWV`YTc_SiaQmbOm_NmZL\ nXKo_NobQodUogZojcpnhsqmvurzzvzzzzzznrzlmyjgxhbwdd\ v`fvXhvTjvPlvLmvHovDqv9sv5uv2vv4su5pu7nu8ktAhtBftD\ ctE`uGZvHWwJTxKRyMOzNMzUMz`MzgMznMztMzpOzmQzjSzfUz\ cWz`YzX_zUazRczNezKgzHizEjzDhzDfzCezCczBbzB`zAZzAY\ z9Wz9Vz8Tz8SzENzJIzPEzU9z_4zd0zb4za7z`AzZEzYHzXKzW\ OzURzTUzSYzR`zPczOgzNjzMmzSkzYizcgziezoczuazz_zxYz\ wXzvWzuVztTzsSzrRzqQzpPzoNznMzmLzlKzkJzlKzlLzlMzmN\ zmOzmPzmPznQznRznSzoTzoUzoVzoVzrFzmHzhJzcLzZNzUPzP\ RzKTzFVzAXz6Zz8YzAYzBXzDXzFWzGWzIVzJVzMSzPPzRMzUJz\ XGzZDzaAzd7zf5zg8zhBziDziGzjIzkLzlNzlQzmSznVzoXzo_\ zpazqdzqfzqczq`zqZzqWzqUzqRzqOzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzhzz1zz6zzBzzGzzLzzQzz\ Vzz_zzdzzzzzwzzXzzWzzVzzb } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 01-05-08 (Oodles of Spirals [7])
by Jim Muth 01 May '08

01 May '08

FOTD -- May 01, 2008 (Rating 7) Fractal visionaries and enthusiasts: The parent fractal of today's image resembles a crinkled knockwurst with a squashed bud on the west side of its V-shaped main bay. Today's scene is located on the inside of the north branch of the valley that encloses this bud. Rarely have I seen a fractal with so many spirals. The name "Oodles of Spirals" came almost automatically. I could have named it 'A Slew of Spirals' but I'm not sure how many a slew is. At first glance the coloring impressed me as having too many blues and greens, and not enough reds, but the longer I looked at the colors, the better they appeared to me. When the time came to rate the image, I pulled a 7 out of the fractal basket, and the rating stuck. The calculation time of only 1-1/2 minutes will make life a joy for even the busiest fractalist. And if even 99.86 seconds is too much to spare, the finished image may be accessed in its full glory on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Unusually brisk weather prevailed here at Fractal Central on Wednesday. The sun was strong, but a biting north wind and morning temperature of 36F 2C made it feel more like February. The fractal cats agreed as they fought for possession of their catnip rat. My day was about as routine as a day can be. The next FOTD will be posted in its full glory only 24 hours from now. Until then, take care, and if ghosts exist only in the minds of the super- stitious, they do in fact exist, but exactly where are these ghosts located? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Oodles_of_Spirals { ; time=0:01:39.86-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-0.5598091849845/+0.0619018865197/\ 6.05367e+007/1/-44/0 params=1/1.997/1/4.003/0/0/0/0 float=y maxiter=975 inside=0 logmap=97 periodicity=10 colors=000LpzLmwLltLjqKinKgkKehLdeMdbMd_NdXOeUOeTP\ eTPeSQeSSgUUiWWkYYm__oaaqccseergepidnlclnbjo_hoYel\ VbiT_fQXcOV`LTYJRVHPSENRCMP9JN7HK4EG2BC08928A4BC5D\ E7GF9IHALJCOLEQMFTOHVQJYSKZTM_UOZUQZUSYTUZUWZUXZUX\ _UW_UW_UW_UW`VV`VV`VV`VVaVVaVUaVUaVUbWUbWTbWTbWTcW\ TcWScWScWSdXSdXSdXRdXReXReXReXQeXQfYQfYQfYPfYQgYUi\ WZkUcmShoQmoOrsNvtNztNzsOzsOzrOzrPzrPwqPtqQqpQnpQk\ pRhoReoRbnSanS_nSZmTZmTYlTXlUXlUWkUVkVVjVUjVUkWTlY\ Sm_SmaRncQneQogPoi3ok5nj6ni7mh9mgAlfBlfDkeEkdFjcGj\ bIiaJiaKh`Mh_NgZOeZOcZOcYNcXMcWLaVNdUs2yr3xq4wq5wp\ 6vo7vo7un8un9tmAtlBslCrkCrkDqjEqiFpiGphGohHogInfJn\ fKmeLleLldMkcNkcOjbPjaQiaQi`Rh`Sg_TgZUfZUfYVeYWeXX\ dWYdWZcVZcV_bU`aTaaTb`Sc`Sc_Rd_QeZQfZPgYzzFzzGzzGz\ zHzzHzzHzzIzzIzzIzzJzzJzzKzzKzzKzzLzzLzzLzzMzzMzzN\ zzNzzNzzOzzOzzOzzPzzPzzQzzQzzQzzRzzRzzRzzSzzSzzTzz\ TzzTzzUzzUzzUzzVzzVzzkzzn } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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<Jim Muth> I really enjoyed creating your FoTD for 08/4/26 & /27
by Hal Lane 30 Apr '08

30 Apr '08

########################################################### Jim, I really enjoyed creating your FoTD for 08/4/26 & /27 in high resolution. They are really very aesthetically pleasing. Thanks for making them quick to compute! ;-) I appreciate your mentioning the parent fractals, also. Its always rewarding and instructive to see these. Zooming around a bit in them revealed lots of interesting stuff. I also had fun trying and rotating different color maps. I would like to remind people who calculate the parent fractals that they need to set the Log Palette (on the 'X' Basic Options screen) to "No" or zero. Otherwise, the logarithmic palette optimized for Jim's zoomed FoTD image will be used for the parent fractal, to the great detriment of the appearance of the parent fractal. - Hal Lane ######################### # hallane(a)earthlink.net # ######################### ###########################################################

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FOTD 30-04-08 (Red Rampage Riot [7])
by Jim Muth 30 Apr '08

30 Apr '08

FOTD -- April 30, 2008 (Rating 7) Fractal visionaries and enthusiasts: I named today's fractal "Red Rampage Riot". After all, it does have a good bit of red in it. The parent fractal is another variation on the square roots of 2 and 3, which appears as a near-Mandelbrot set rotated 180 degrees. Its most unusual feature is the two infinitely divided main stems along the positive X-axis, which instead of spreading apart as they move farther from the origin, move together and ultimately join. Today's image lies very deep in the area where the stems merge and vanish. The mathtolerance entry assures that the parameter file will run at the correct magnitude. I rated the image at a 7, which is close to the FOTD norm. The calculation time of 46 seconds is unusually fast, so running the included parameter file will be no problem. But if unexpected problems do arise, the finished image may be seen on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Just before I sent off yesterday's FOTD, fractal lady happened to glance at the end of the FOTD discussion, where I wrote that I wonder if intelligent design and evolution may both be right. She told me the sentence was silly, that only one could possibly be right. But I replied, "what's the big deal?" Photons can be either waves or particles, depending on what we want them to be, and this, which is equally as silly, can easily be proved scientifically. Chilly but otherwise fair weather with a temperature of 55F 13C prevailed here at Fractal Central on Tuesday. The fractal cat duo enjoyed the conditions from the less-chilly indoors. I observed the conditions from the local garden center, where we spent the afternoon planning for a better yard to come. I actually enjoyed it a little. The next FOTD, maybe better than today's, maybe not, will be posted in 24 hours. Until then, take care, and if it's not one, it must be the other. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Red_Rampage_Riot { ; time=0:03:58.98-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=+3.533592786414534/-0.00138674232240322\ /9.796122e+010/1/-40/0 params=1.6/1.414/-1.6/1.732\ /0/0/0/0 float=y maxiter=1800 inside=0 logmap=77 periodicity=10 mathtolerance=0.05/1 colors=000zHKzWKzTKzPKzKKzAKx5Hs4En4Bi49d46_43V41R\ 75O98LCBHEEEHHBJK8XD5i72v1Uf1uR1sO3qL5oJ7mG8kDAiBC\ g8Ee6FcFNbOUaW``dg_ln`jiahdaf_bdVcbQc`LdZGdYBZPOUH\ `O8mJ0zN6rRCjVIbYOWaUOe_Ghd9dh8ak7Yo6Vr6RmEOhMLdTI\ _`FVhCRoPYhadbnjXhjVbjTXjRSjQMjOGjMAjK5jJWgCue5qfC\ mgJihPeiWajbYkhUloQmuVfv_`wdVwiPxnJysDygRiXcUPbVHb\ W9bX2bY9dXFfWMhVSjVZlUdnTjpTheUgWVfMWeCXd2Xi7WnCVs\ HUlMQfRN`WJV`GOeCIj9Co56s29TJB3_jI6NS50`53bC6dJ9eQ\ CgWFhbIjiLkoIjhGiaEhVBgO9fH7fAAkCCoELqSUseausewohx\ llyiozfZzoJzxKvwKswKovKlvKhuKeu7LA9KFBJKDIPEIUGHZI\ GcKFhLFmOJiQNeTRaVVYXZU_bQafMcjJb_QaPXbM_bKabIdbGf\ cEhcCkcAmc8oZBmVEkRGjMJhIMfEOeCQZARS9SM7UF5V84W29X\ 9DXFIXLMXSRXYVXc_MTdBIi17XSXLqvNjqPclQXgSQcTJZVCUW\ 5QVCVUJ_TQcSXhRclQjqQpuPnrOlpNjmMhkLgi`RWpAIdpvaoc\ ZoMWo4_RHc3TY4SS5RN5QH6PB7O67NE6LL6KS6IZ5He5Fl5Es5\ DmPMggUbzaewZgtW2RHHQUWPe } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 29-04-08 (Incomprehensible-2 [Indeterminate])
by Jim Muth 29 Apr '08

29 Apr '08

FOTD -- April 29, 2008 (Rating Indeterminate) Fractal visionaries and enthusiasts: Maybe I'm just imagining it, but things seem to be getting a bit dull on the two fractal lists lately. Whatever happened to the controversial fractal philosophy? Maybe it's time for someone to start the philosophical ball rolling. If I do wax philosophi- cal, science, religion, new-ageism, paranormalism and philosophy of all kinds will all be fair game. But today, the much more conservative discussion is about fractals. To create today's image I increased the portion of Z^sqrt(2) in yesterday's parent fractal to 1.5 parts, which greatly increases the fractal's size. Then I checked to see what was happening far out on the positive X-axis. What I found is revealed in today's image. I named today's fractal "Incomprehensible-2", though I can not comprehend why I did so. The image seemed to have no definite value, so I gave it an indeterminate rating, which, like divid- ing zero by zero, is equal to anything the viewer wants it to be. The calculation time of 3-1/4 minutes, while not the shortest of all time, is much better than yesterday's time. And as always, the finished image is posted to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where it may be viewed instantly and at leisure. Clouds and rain describe the day Monday here at Fractal Central. The chilly temperature of 52F 11C was of no help. The fractal cats, disgusted by the miserable outside conditions, spent most of the day sleeping and playing with their fresh catnip rat. My day was average. Tomorrow will likely be similar. The next FOTD will appear in 24 hours. Until then, take care, and some believe that the universe was intelligently designed to support life. Others believe that the evolution of life is an extremely lucky but perfectly natural accident. I believe that both sides are half right. But of course, I have no proof. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Incomprehensible-2 { ; time=0:03:14.86-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=+11.13581279223/-0.03806984753/9489579/\ 1/144/0 params=1.5/1.414/-0.8/1.732/0/525/0/0 float=y maxiter=32767 inside=0 logmap=144 periodicity=10 colors=000UUkUUiUUhUUfUUeUUcUUcUUaUV`UXZUZYU_XW`VY\ aU_bT`bSbcRddPeeOgeNifMjgLlhJnhIoiHqjGskFtmEuoSvqe\ wsaccc000000zUQzRNzOKzKHxHEvDBwA8v75r87o89k8Ah8Cd9\ Ea9FY9HV9JR9KOAFKAAHAADAAAAACDADFAEIAFKAHMFIPKJROK\ TNMWMNYMO`LPbLRdKSgKTiJUkJSnKQqLOtMNsPMsRLrTLrVKqX\ JqZJp`IpbHodGofGnhFnjEmlEmn7X`0HN4IR8JVCKZGLbKMfON\ cRNYQLUQKQPIOPHM84K93KA3KA2KB1KC0KC0Ki5ek8dlBdmDcn\ GcoJbpLbqOasRatT`uW`vZ_w`_xcZyfZzhZz`czThzLmzDrHBx\ JMwKXwLgwKtzMqwNntOkqPhoQelRbiS_fTXdUUaVUzWUzXUzYU\ zZUz_Xze_z`bzWezRhzMkzHnzCqz7tz0wz3zz6zz9zzCzzEzzH\ zzKzzNzzQzzNzzSzzXzzazzdzzfzzgzzhzzizXjzTpzNkzPfzR\ azTYzVTzXOzZKz`FzbAzdxzv6zfMzc`zaazdbzfczhdzjdzlez\ nfzpgzrjzvgztdzsazqZzpXznUzmRzkOzjMziLzkMzhNzeNzbO\ z`PzYPzVQzSRzQRzNSzKTzHTzFUzCVz9Vz7Xz9ZzB`zCbzEdzF\ fzHhzJjzKlzMnzNlzOkzOizPhzPgzQezQdzRbzRazS`zSZzTYz\ TXzTRzWMzZHzaCzd7zg0z0kzk } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 28-04-08 (A Strange Seahorse [No Rating])
by Jim Muth 28 Apr '08

28 Apr '08

FOTD -- April 28, 2008 (No Rating) Fractal visionaries and enthusiasts: I think this is the first FOTD where I have chosen the first spot I zoomed in on to be the FOTD for the day. I confess, I was just not in the mood on Sunday to search for a better fractal. Is this the beginning of the end of my fascination with these incredible images? I think not, but only time will tell. As for today's image, it lies in the Seahorse Valley area of the same parent fractal that gave us yesterday's image. I didn't even feel like calculating a new parent fractal. Of course, I gave the image no rating. It deserves none. But I did give it a name -- "A Strange Seahorse". The name indicates that the Seahorse Valley in which today's image lies is quite strange when compared to the Seahorse Valley of the classic Mandelbrot set. And the calculation time of almost 10 minutes is notably slower than I would have liked, but relief is at hand on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the image is posted for instant happiness. Sunday at Fractal Central was partly cloudy with a temperature of 63F 17C, while the fractal cats were on their better behavior. My day was lazy, but not depressingly so. The next FOTD will be posted for all the world to enjoy in 24 hours. Until then, take care, and spread the word of fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Strange_Seahorse { ; time=0:09:56.33-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=+3.68754563329/-0.14920767621/2050486/\ 1/165/0 params=0.7/1.414/-0.9/1.732/0/0/0/0 float=y maxiter=6800 inside=0 logmap=726 periodicity=10 colors=0008ZK9_L9aMAcOAePBgRBiSCjTClVDnWDpYErZEs_J\ qYNpXSoWWmV_lUdkShiRmhQqgPufOtbQtZRtVStRUtNVtJWtFY\ tBZt7_t4`s7arAaqCapFaoIbnKbmNblQbkSckVcjYci_chbdge\ dfgdejddmecoebrebteVpfNlfFhf8ef9bg9`h9Yi9Wj9UkARlA\ PmAMnAKoAIpBFqBDrBAsB8tB6uD8tFAtHCtIEsKGsMIsOKsPMr\ ROrTQrVSrWUqYWq_Yqa_qbapdcpfepggpehlchibhe`hb_hZYh\ WXhTVhPThMShIQhFPhBNh8Mh5Nf7Oe8Od9PcBPbCQaDQ`ERZGR\ YHSXISWJTVLTUMUTNUSOPQSKOWFM_AKc5Ig0Gj3Jg6LddAOd9P\ c8Qc7Rb7Sb6Ta5Ua5UZ6OW6JT6DQ68O63WEFcLQkT`r_knYhkX\ fhWceVabTZ_SXXRUUQSRPPONNLMKILIFKFCID9HA6G83F50E31\ G51I62J72L83M93OA3PB4RD4TE5UF5WG6XH6ZI6_J7aL7cM8dN\ 8fO9gP9mQ9`R6eI4a92Y1KJ7`5Dc4De4Dh4Cj3Cm3Co3Cr2Bt2\ Bw2By2BvBFsKJpSMmTOkTPhTRfUScUUaUV_UXXVYVV_SV`QWbN\ WcLWeJWfIXdIYcHYbHZaGZ`G__F_ZFaYEcWEeVDgUDiTCkSFmR\ KoQPqPUsNZuMcvLhwKmxJryIvzHzzGzzKzzNzzQzzTzzWzz_zz\ bzzezzhzzkzzCzzEzzFzzHzzI } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 27-04-08 (Web of Darkness [9])
by Jim Muth 27 Apr '08

27 Apr '08

FOTD -- April 27, 2008 (Rating 9) Fractal visionaries and enthusiasts: For today's image I took yesterday's parent fractal, but subtracted a little more Z^sqrt(3) from a little less Z^sqrt(2), resulting in a fractal that is somewhat larger than yesterday's parent, with different oddities located mostly along the X-axis. I found today's image along the positive X-axis, which is where a main spike would normally be expected in a Mandeloid rotated 180 degrees. But in today's parent, a spike is nowhere in sight. Instead of a spike, we find a maze of twisting pathways, infinitely divided, with countless minibrots scattered about. Today's image shows one of these minibrots. I named the image "Web of Darkness". The unusual amount of darkness surrounding the windmill-like spider-web pattern inspired the name. The rating of a 9 indicates that I consider the image to be much better than the everyday FOTD fare. The calculation time of a mere minute should leave every fractalist iterating with joy. And the finished image is also joyously posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The unusually fine spring weather continued here at Fractal Central on Saturday. Mostly sunny skies with a temperature of 73F 23C can hardly be beat. At nightfall a mild thunder-shower moved in, but by that time the day had ended and the rain merely watered the flowers. The fractal cats must have agreed, for they were on their best behavior all day. My day was as slow as I had hoped it would be, which is the way I like days to be. The next FOTD will be posted in 24 hours. Until then, take care, and look for the light admidst the gloom. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Web_of_Darkness { ; time=0:01:02.82-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident center-mag=+4.089540127691547/-0.0001022448756743/\ 1.324527e+008/1/90/0 params=0.7/1.414/-0.9/1.732/0\ /0/0/0 float=y maxiter=500 inside=0 logmap=108 periodicity=10 colors=000GHgFIiFJkEKmELoDMqDNsCOuCPvDOtDMrEKoEIkE\ GgFEcFCZFAUG8QG6MG4IH3JH4JH5JI6JI7JI7KJ8KJ8KJ9KKAK\ KALKBLLCLLCLLDLLDLQENUFOYGPaHQfISjJTnKUrLVvMWsQXqT\ YnWZlZ_ia`gdadgbbjc_mdYpeVsfUvgZuccu_huXmuTmuPmuMm\ tIhtEctBZt7Ut3Ut0OqEImSChe7crBZmEUhHPcKK_OFVRAQUAL\ XAHWALWAOVARVAUUAXUA_TAbTAeSAhSAkRAnR7qR3tTCsUKrVT\ rX`qYiqZqp_ypWwkSugOscLr_HtUEuPBvK8xE5y92z4AjCHVJP\ FQW0XU4YS7YQAZODZMG_KJ_IM`GP`ESaCVaAYb8`b6cc4fc3ic\ 6fZ8cUA`PCZKEWFGTAIR6HP5FM5EK5sYdsXesWfsVhrUirTjrS\ lrRmrQnrQooSnmUnkVniXmfYmd_mb`l`blYclWelUfkShkPikN\ kjLljJnjHojKmhNlfPkeSicUhbXg`Ze_adYdcWfaVi`Tk_SnYQ\ pXPsWNuVMrUOpTPnTQkSSiRTgRUdQWbPX`PYZO_WN`UNaSMcPP\ dNUeLZgJchGhiEmkCrl9vm7zo5zp3zqzznzzkzzizzfzzczzaz\ z`zz`zz_zz_zzZzzZzzYzzYzzKzz7zzTzzOzzKzzGzzBzz7zz3\ zz4zz5zz6zz7zz8zz9zzAzzBzzCzzDzzEzzFzzGzzHzzIzzJzz\ KzzLzzMzzNzzGzzFzzEzzDzzS } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 26-04-08 (Mix and Match Them [8.5])
by Jim Muth 25 Apr '08

25 Apr '08

FOTD -- April 26, 2008 (Rating 8.5) Fractal visionaries and enthusiasts: In today's paper I saw a column about a comedian who made fun of the pope on his recent visit to america. The columnist thought it was an inappropriate thing to do, and commented that such mockery could weaken or destroy someone's faith in the existence of God, a belief that makes life endurable, and without which we would face the specter of meaninglessness and oblivion. When I read this, I smiled and thought, "if one's faith is so weak that it could be thrown into doubt by a second-rate comedian, that doubter should already be considered an Atheist." (Atheists get along well enough without faith in a supernatural God, BTW, but they substitute faith in science and reason for faith in God.) I am promoting neither Atheism nor Theism. I am merely telling my thoughts about a newspaper column. IMO, the evidence, or lack thereof, is equally unconvincing on both sides. But what I am promoting is fractals. And today we have one that came about when 0.8 parts of Z^sqrt(3) was subtracted from 0.8 parts of Z^sqrt(2) and C was added. The parent fractal closely resembles a Mandelbrot set rotated 180 degrees. But a closer examination shows that both the east and west sides along the X-axis of this parent are much changed. The main stem has degenerated into little more than a tiny nub, and East Valley has broadened into a wedge. Today's scene lies near the northern edge of this eastern (western) wedge. I named the image "Mix and Match Them". I had a reason when I gave it this name, but I have since lost track of the reason. Regardless, it's a very unusual image, especially for one that calculates in only 46-3/4 seconds, and well worth the small bit of effort needed to see it. The rating of 8.5 is well-earned. Almost no effort will be needed to visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and enjoy the completed image there. A thin veil of clouds made Friday less than perfect at Fractal Central, but the temperature of 77F 25C and blossoming trees gave compensation for the weaker sun. The fractal cats agreed. My day was appropriately busy. The next wonderful FOTD is due in 24 hours. Until then, take care and prepare. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Mix_and_Match_Them { ; time=0:01:15.85-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident inside=0 center-mag=-0.3488069853915473/+0.123787083556466/\ 57322/1/42.5/0 params=0.8/1.414/-0.8/1.732/0/0/0/0 float=y maxiter=2100 logmap=75 periodicity=10 colors=000878A78C78E78G78LDDPJHUOLYUPbZTfdYljapoev\ uizzmysgxlbveYuZTsSNjLIbEDX78T13Y14b15g16l17p18tK9\ xPAzUBzPCvKDrFEmAFm5Gm1Gh3Hd4Ie6Jf7Jf8KgALhBUiCcjE\ mjPzkGzlImmJcmKUlQSlWTlaVlgWdZSXROQIKIAGB2CD3DF4EH\ 5EJ5FL6GN7GP8HR8IT9IVAJXBKZBK`CLbDMdDMbGKaII_KHZMF\ XOEWQCUSBTU9RW8QY6P_5N_CM_JK_QJ_WI_bG_iF_pE_vIXuLV\ tOSsSQrVNqYLpaIodGngDmkBln8kq6jhFi`OiTXhLehDnhBofA\ pe9pd8qb7qa6r`5r_4sY3sX2tW1tV5pW9mWDjXGgXKdXO`YRYY\ VVYZSZaPZeL_iI_lF_pC`t9`w6`tBbrFdpJenNglSijWjh_lfc\ mdhoblq`prZttXxuYuqYrnZojZlgZic_f`_cX_`U`YR`VNaSKa\ PGaMDbJ9bG6bE3_H8XJDULIRNMOPRLRWIT`FVeOfgWriZskatm\ dtnguoiupfrqdorbls_itYfuWcvU`wRYxPVzNSzLQzNRzORzQU\ zRXzS_zUbzVezXhzYkzZnz`qzatzbwzczzdzzezzfzzgzzhzzi\ zzjzzkzzlzzmzznzzozzpzzqzzAzzCzzDzzEzzFzzGzzHzzIzz\ JzzKzzLzzMzzNzzLzzKzzIzzHzzFzzEzzDzzBzzAzz8zz7zz5z\ z4zz3zzczz_zzWzzTzzRzzPzz } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 25-04-08 (Total Confusion [No Rating])
by Jim Muth 25 Apr '08

25 Apr '08

FOTD -- April 25, 2008 (No Rating) Fractal visionaries and enthusiasts: Today's image takes us to the fractal that is created when the formula Z^sqrt(3)+C is calculated 2 levels up the logarithmic hyper-something when no function is applied. The parent fractal resembles a half-deflated beach ball draped over the edge of a cliff. The not-too-attractive and under- iterated minibrot in today's scene resembles its parent beach ball rather well. The scene is located a short distance to the west of the main bay of the parent fractal, where a zigzag filament is being squeezed between two heavy discontinuities. I named the image "Total Confusion" after a quick glance showed very little orderliness in it. Then I let it go without a rating. I didn't like the image enough to rate it. The calculation time of 2-2/3 minutes will try the patience of not even the most impatient fractalist. And last but not least, the finished image is posted for instant viewing on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Absolutely perfect weather prevailed Thursday here at Fractal Central. The sunny skies and temperature of 75F 24C made time spent outdoors a pleasure. The fractal cats, who never get outside to enjoy the weather, were unimpressed. My day was slow -- once I got the G.D. (graphic design) work out of the way that is. And better yet, tomorrow is due to be the same. The next FOTD will be posted in 24 hours. Until then, take care, and what color is the number 8? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Total_Confusion { ; time=0:02:40.92-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-1.679007675579299/+0.0786582104032291/\ 1.345969e+008/1/-145/0 params=1.732/0/2/0 float=y maxiter=5000 inside=0 logmap=155 periodicity=10 colors=0001AM19N18O17P17Q16R15S14T14U35V55V75W95WB\ 5XD5XF6XH6YJ6YL6ZN6ZO6ZN7XM8VM9TLARLBPKCNJDLJEJIFH\ IGFJHHJIJKJKKKMLLNLMPMNRMNSNOUNPVOQXORZPS_PTaMPaPT\ bSXbV`bXdb_hbblbdpbbnc`ldZkeXifVhgTfhRdiPcjNakL`lJ\ ZmHYmjyMfsKbmJZhHVbGRXFNSDJMCG99FHBEOCDVDCaEBhFAoG\ 9vHDsGGpFKnENkDRhCUfBXcA``9cZ8gW7jT6mR6hQ7dP7`O7WN\ 7SM7OL7JK7FJ7BI77I7CL7HN7MP7RR7WT7`W7eY7j_7oa7tc7Y\ bZBbzFazJazNazR`zV`zZ`zb_zf_zj_znZzrZzvZzqWvmTsiQp\ dNm`KjXIgTFdOCaK9ZG6WD1RC4TB6UA9V9BW8EX8GY7I_6L`5N\ a4Qb3Sc1Ml3Ud5`X7gP9nHAuAAqBAnCAjCAgDAcEA`EAXFAUGA\ QGANH8GGAKHCNIEQJGTKIXKK_LLbMNeNPiNRlOToPVrQWuQZqN\ anKdkIggFjdClaAgcFceK_gPViURkYNmbIogEql9rtAspAslBs\ hEosBsd5xO8wRAvTCuVEtXGsZIr`KqbMpdOogQniSmkUlmWkoY\ jq_is`kvahuaeuaguaiubkubmuboubqubsucuucwucwucwufzt\ czu`zuZwuWwuUwuRuuPsuMquKouHouFquHsrIupJvmKwkMxhNy\ fOzcPzaTzbQz_1z61z81zA1zC } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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FOTD 24-04-08 (Minibrot in Violet [6])
by Jim Muth 24 Apr '08

24 Apr '08

FOTD -- April 24, 2008 (Rating 6) Fractal visionaries and enthusiasts: Everyone knows that quadratic minibrots are surrounded by a symmetrical pattern of elements in the 2,4,8... series. Well, today's image shows that this is not always true. The minibrot at the center of today's image lies in an area devoid of any trace of symmetry. I named the image "Minibrot in Violet" after the irregular violet area surrounding the minibrot. And then I rated it at a 6. The image lies in the same area of the same parent fractal as yesterday's image, in the East Valley area of a different but still anomalous minibrot. The calculation time of just under 3 minutes is within reason. The finished image is posted for instant viewing on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A mostly sunny and warm day here at Fractal central on Wednesday, with a temperature of 77F 25C, was not spoiled when a shower passed over at 6pm. The fractal cats missed the weather. They got into the catnip this afternoon and were several hours sobering up. Except for the goofy cats, my day was normal. The next FOTD image will be posted at the usual time in 24 hours. Until then, take care, and be patient. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Minibrot_in_Violet { ; time=0:02:58.51-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=conj passes=1 center-mag=-0.6494432062863946/+0.032501227941523/\ 34194.97/1/87.5/0 params=2.005/0/1/0 float=y maxiter=2750 inside=0 logmap=174 periodicity=10 colors=00041S31T11V01W63_C4bI5eO6hU8k_9neAqkBtAUp9\ To9Sn9Rm8Ql8Pk8Pj7Oi7Ni7Mh6Lg6Kf6Ke6Jd5Ic5Hb5Gb4Fa\ 4F`4E_3DZ3CY3BX3BX5CW6DW8EW9FVBGVCHVEIUFJUGKUILTJM\ TUNTcOSmPSzQSzzRzzRzzRvzbowZiuWcsSXpPRnLLlIKmJJmJI\ mKImKHmLGmLFmMFmMEnNDnNCnOCnOBnPAnP9nQ9nQAoRBoRCpR\ DpREpRFqRGqRHrSIrSJrSKsSLsSMtSNtSOtSPuTQuTRvTSvTTv\ TUwTVwTWxUXxUYxUZyU_yU`zUazUazUDjcCkcCldArgCmdDibF\ e`G`YHXWJTUKPSLKPNGNOCLP8JU8LZ8Mc8Nh8Ok7Ql8Pl9PlAP\ mBPmCPmDOnEOnFOnGOoHOoHNoINpJNpKNpLNqMMqNMqOMrPMrQ\ MrQMnOLkNKgMKdLJ`KIYJIUIHRHHNGGKFFGEFDDE8BBACECDGE\ DJGELHFOJFQLGTNHVPHYQI_SJaUJdWKfYLiZLk`MnbNpdNsfOu\ hPygOwfNueMsdLqcKobKmaJk`Ii_HgZGeYGcXFaWE_VDYUCWTB\ USBSRAQQ9OP8MO7KN7IM6GL5EK4CJ3AJ38K57K77K97KA7KC7K\ E7KF7KH7KJ7KL6KM6KO6KQ6LR6LT6LV6LW6LY6L_5La5Lb5Ld5\ Lf5Lg5Li5Lk5Mm3Lo5Lq6Ks7Ku8Jw9JxBIyCIzDIzEHzFHzHGz\ IGzJFzKFzLFzMEzOEzPDzQDzR } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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FOTD 23-04-08 (Very Dark Shadows [7])
by Jim Muth 22 Apr '08

22 Apr '08

FOTD -- April 23, 2008 (Rating 7) Fractal visionaries and enthusiasts: Today's lively fractal is infested with dark shadows, which is why I named it "Very Dark Shadows". The name has nothing to do with an old TV series, which is the only soap-operaish program I ever actually got interested in. It merely refers to the gloomy appearance of the image, which is entirely of my making. The parent fractal came about when I iterated the formula Z^(2.005)+C at a level one step up the infinitely-valued loga- rithmic ladder, with the 'conj' function applied. This function is probably totally wrong, but what the heck, it makes an inter- esting image, consisting of a near-normal Mandelbrot set rotated so that the period-4 bud on the southern shore of the main bay intersects the negative X-axis, which is where all the action lies. There is an anomalously large minibrot in this area, and today's scene is located in the East Valley of this minibrot. I might have made the image a lot brighter, but being in a kind of down mood despite the bright weather, I let it go with the depressed feeling created by the dark areas. At the end, I rated it at a 7. The calculation time of 13 minutes is slow, but nothing that any fractalist has never seen before. And the wait may be elimina- ted by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the finished image there. They say that Pennsylvania had the best weather in the nation for our election on Tuesday. Being located in the center of the state, Fractal Central enjoyed the best day so far this spring. The blue skies, puffy white clouds, temperature of 73F 23C and lack of airplane contrails could hardly be beat. Being uninter- ested in politics, the fractal cats merely enjoyed the sun. My day was average; tomorrow looks to be the same. The next FOTD will be posted right here in 24 hours. Until then, take care, and even the most rational-thinking scientists admit that miracles are real. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Very_Dark_Shadows { ; time=0:13:18.46-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=conj passes=1 center-mag=-0.659994386833905/-0.0400706991520263/\ 4.475544e+011/1/-58.3/0 params=2.005/0/1/0 float=y maxiter=7500 inside=0 logmap=1270 periodicity=10 mathtolerance=0.05/1 colors=000TKUTKUTKUTKUTKUTKUTKUTKUTKUTKUTKUTJUTIUT\ IUTJUTJUTJUTJUTKUTLUTMUTNUTNUSOSPPRMQQJQPGROESNCTM\ BTLCUMCVNCVOCWPCXQCXRCYSCZTCZUC_VC`WC`XDaXDaYDbZDc\ _Dc`DdaDebDecDfdDgeGgfKhgPewUhzZkzcnzhqzmtzrwzvzzz\ rzvrzrrzmrvhrrcrmZrhWrcUrZWrUZrV`rWcrXfvVetWerXeqY\ eoZen_dl`dk`diadhbdfccddccecafc`fcZgbYhbWibVjbTkbS\ k_QiYPhWOfUMeSLdQKbOIaMH`JGZHFYFDXDCVBBU99T78R57Q1\ 3Q36P49P5CP7FP8HP9KPBNPCQPDTPEVPFVQFVQFVRFVRGVSGVS\ GVSGVTHVTHVUHVUHVUGUTGTSGSRGSRFRQFQP000FKOFONEOMEN\ M84C8CFEGKDKJDKIDEHDIHCIGCHFCGFCGECFDBECBECBDBBCAE\ 68C99BCAAFB8IC7KC6ND4QE3TFKUFHUF2VF3WE3XDzXCzrB5ZB\ 5UA5U96U86U77U77Q68_58b49b08c48d78eB7fE7gI7hL6rP6i\ S6jW5kZ5lb5me5mh6mi7mj8mk9mlAmmBmnCmoDmpEnqForGpsH\ qtIruJsvJtvIuuIvuHwvLxwPyxUzyZzzczzhzzmzzrzzvzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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FOTD 22-04-08 (Deep Three [No Rating])
by Jim Muth 22 Apr '08

22 Apr '08

FOTD -- April 22, 2008 (No Rating) Fractal visionaries and enthusiasts: Yesterday's FOTD took us deep into Scepter Valley, the next valley beyond Seahorse Valley of the Mandelbrot set. Today's image takes us deep into the third valley out the negative X-axis, located around -1.368. I think this valley is named Double Scepter Valley. Unlimited intricate detail characterizes the scene. In fact, there is actually so much small detail that it becomes overwhelm- ing. Some of this excess detail is due to rendering the image with the 'outside' set to 'summ', which works best with this difficult-to-color fractal. Due to the unusually large maxiter of over 3-million, all variations of the logmap coloring method spread the bands much too wide, resulting in large areas of a single flat color. And shutting off the logmap gives an image of near total chaos. The 'summ' option is far from perfect, but it is about as good as can be done with this image. The 'real' and 'imag' options work almost exactly the same I named the image "Deep Three" because it lies deep in the third valley out the negative X-axis. I declined to give it a rating because I feel that if I had really worked on the raw image, I could have done notably better. But I have good news! The calculation time is a sizzling 1/100 of one second under 3 minutes. And even better news is that the finished image is posted for instant gratification on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Partly cloudy and mild conditions prevailed here at Fractal Central on Monday. A high temperature of 70F 21C was very close to normal. The fractal cats enjoyed the sun while it was out, and chased each other around F.C. when it was not. In my department, the work was finished on schedule, leaving the remainder of the afternoon free for a fractal search. The next FOTD will appear in 24 hours. Until then, take care, and be a big-time thinker. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Deep_Three { ; time=0:02:59.99-SF5 on P4-2000 reset=2004 type=mandel passes=1 float=y center-mag=-1.368099862408421/+0.000169327019037/\ 7.392152e+009/1/-74/0 params=0/0 maxiter=3200000 bailout=9 inside=0 outside=summ periodicity=10 colors=00090zB0yC0uE0sG0qH0oH0kJ0iK0gN1dP3bQ4`S6ZS\ 7WU9UWBSXCPZEN`GKbHJbKGdNEfPCgQBiS7kU6mW4mX1oZ0q`0\ sb0ud0wf0yg0yi0zk0zm0zo0zq0zs0zu0zy0zw0zu0zu0zs0zs\ 0zq0zo0zo0zm0zm0zk0zk0zi0zg0zg0zf0zf0zd0zd0zb0z`0z\ `0zZ0zZ0zX0zX0zW0zU0yU0yS0yS0yQ0wQ0wP0wN0wN0wK0uK0\ uJ1uJ1uH3uG3sG4sE4sE6sC6uE4sC6sC6qC7qC7oC9oB9mBBmB\ BkBBkBCiBCi9Eg9Eg9Gf9Gf9Hd9Hd7Hb7Jb7J`7K`7KZ7NZ6NX\ 6NX6PW6PW6QU6QU4SS4SS4UQ4UQ4UP4WP3WN3XN3XK3ZK3ZK3Z\ P0SS0NW0GZ0Bb04f00i00m00q00w00u00s00s00q00q00o00m0\ 0m00k00k00i00g00g00f00f01d03b04b06`07`09Z0CX0EX1GW\ 1HW3JU4KQ6QS4PU4NW3NX3KZ1K`1Jb0Hd0Hf0Gg0Gi0Ek0Cm0C\ o0Bq5BsA9uF7wK7yP6zU6zU4zU3zU4zU6zU7zU9zU9zUBzKCzA\ Ez4Ez6Gz7Hz9JzBJzCKzENzGPzHPzKQzNSzPUzQWzSWzUXzWZz\ X`z``zbbzddzffzgfzigzkizmkzokumgmmffkdZkbUi`NiZGgX\ 9gW3fU0dW0fU0fS0gS1gQ1iQ3iP4kP6kN7kN7mK9mKBoJCoJEq\ HEqHGsGHsGJsEKuEKuCNwCPwB } END PARAMETER FILE=========================================

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FOTD 21-04-08 (FOTD for April 21, 2008 [No Rating])
by Jim Muth 21 Apr '08

21 Apr '08

FOTD -- April 21, 2008 (No Rating) Fractal visionaries and enthusiasts: I'm still a bit down about losing Tippy on Saturday, so my usual fractal enthusiasm might be a bit suppressed. But there is a fractal for today nonetheless, and not a bad one at that. Today's image takes us back to that most famous of all parent fractals, the Mandelbrot set, where we check a scene deep in Scepter Valley, which is the valley at -1.25 on the X-axis. I could not honestly give a rating or a name to the image, which I found almost without effort. The slow calculation time of 30 minutes can be cut to 18 seconds by rendering the scene with the outside set to 'iter' instead of 'tdis'. But doing this misses the best part of the image. An alternative way to save time is to view the calculated image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A partly cloudy, rather pleasant morning here at Fractal Central on Sunday gave way to a heavily overcast afternoon, with a temperature of 63F 17C and intermittent heavy showers. The fractal cats ignored the rain as they took the day off. With the rain saving me from an afternoon of yard work, my day was slow enough. The next FOTD fractal image will be posted in 24 hours. Until then, take care, and give yourself at least a ghost of a chance. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= FOTD_For_Apr_21_08 { ; time=0:29:57.34-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-1.25000687812826500/+0.001998204548718\ 07/2.730733e+010/1/15/0 params=0/0 float=y maxiter=100000 bailout=9 inside=0 outside=tdis periodicity=10 mathtolerance=0.05/1 colors=000LVpPUqUTrZSsbSsZMqVHoRCmN7kK2jM6fNAcOE`P\ IYQMVSQRTUOUYLVaIWdFUbLTaQS_VRZ_QXdPWiOUnNTsMSxPOV\ SK1VI5XH8_GBaFEdEIfDLhCOkBRmAVp9Yr8`t7cq9aoA`mBZkD\ YiEXgFVeGUcITaJR_KQYMPWNNUOMSPLUOOWNQXMTZLV`KXaJ_c\ IaeIdfHfhGhjFkkEmmDpoCrpCtiAqc9nY7kS6hM5eLDfKKgJRh\ JYhIdiHkjHrjMmgRieVec_`adX_hTYmOWrKUvGSxwUvqTulTtg\ SrbSqYRpTRnOQmJQlEPk9PdGXZNdTUlVXiW_gXbdYeb_h_`kYa\ nVbqTctReqRfoRhmRikRkiRlfRndRobRq`RrZRpYPoYOnYNmYM\ lYKkYJjYIiYHgXFfXEeXDdXCcXAbX9aX8`X7SOJJFVB6fFBhJG\ jNLlQQmUVoY_qadsdit_mjVpaRtTMwKIzBGtGFnKEiODcTCZXA\ T`9Ne8Ii7Cm67q98oB8nD8mF8lI8kK8jM8iO8hR8gT8fV8eX8d\ _8ca8bc8ae8`_BQUEFPH4SVRVhlXdkZak`YkbVkcRkeOjgKjiH\ jkDjlAjhPgdcdbbeabe`be_afZafYafW`gV`gU`gT_hS_hR_hQ\ _hNcgKggIkgFofDsfAwf8zfAuhBpjCllDgnEcpDdqDerCfrCgs\ BhtBitChsDgsEfsEesFdsGcrHbrHarI`rJ_rJZrIYqHXpGWoFV\ oEUnDTmCSmR``LZeGYjBXnGWo } END PARAMETER FILE=========================================

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FOTD 20-04-08 (Fractal Journey [6.5])
by Jim Muth 19 Apr '08

19 Apr '08

FOTD -- April 20, 2008 (Rating 6.5) Fractal visionaries and enthusiasts: It's a rather gloomy discussion today. At 8 this morning I got a call from my sister back at old Fractal Central. She told me that Tippy, one of the old fractal cats, died peacefully during the night, just two weeks short of his 19th birthday, probably from a heart attack. There was no long period of sickness; he was in pretty good health to the end. It's kind of sad to lose a friend of 19 years. He was already 8 years old when I started the FOTD in April of 1997. But that's the way it goes sometimes. Thomas, Tippy's litter-mate, is declining, and will probably soon go to join his brother. And then I assume my sister will go to the local SPCA and choose fractal cats 5 and 6. Today's image keeps us in the same parent fractal, this time taking us to a cut-off bit of debris just east of the fan. I named the image "Fractal Journey". After all, that's what the search for a fractal is. Then I rated the result at a 6.5. The image is only average. The calculation time is a speedy 2 minutes. It is even more convenient to view the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> With lots of sun and a temperature of 86F 30C, Saturday was a repeat of Friday here at Fractal Central. But heavy clouds moved in around sunset, and the forecast for Sunday is for showers. The new fractal cats, numbers 3 and 4, still in their prime years, were more interested in the birds than the weather. My day was about average. Sunday will likely be the same. The next in the series of FOTD's will be posted in 24 hours or so. Until then, take care, and look on the bright side. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Fractal_Journey { ; time=0:01:53.96-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+5.992943482504987/+0.0360478707784354/\ 1.636003e+009/1/-92.5/0 params=-10/-1.1/-1/-11/0/\ 525/0/0 float=y maxiter=1800 inside=0 logmap=135 symmetry=none periodicity=10 colors=000MUlOVjQViSWgVXeXXdZYb`YacZ_eYZg`XiX`kX_m\ UboPfqOisIluHpwAsy7vpFnhNg`V`TbUUjNcrGmy9mt8cp8Wl8\ Kg7Mc7G_7IV6JR6LN6MJ6OG9PECQBFR9IS6LT4OU2QV3SW3UW4\ WX4YX5_Y5aZ6cZ6e_7g_7i`8k`8lYBjVDiSFhPIgNKeKMdHPcE\ RbCT`9W_6YZ3_Y1aX2`Y3`Y3_Y4_Z4_Z5ZZ5ZZ6Z_6Y_7Y_7Y_\ CXXHXUMWSRWPVWN_VKdVHiUFnUCrUAqSDqQFqOIqMKqKNqIPpH\ SpFUpDXpBZp9ap7cp6elAghDheGiaKjYNkVQlRUnOXoK_pGcqD\ fr9is6lt9kpBkmDkjFkgHkdJjaLjZNjWPjTRjQTiNViKXiHZiE\ `iBbi8ciAdiBeiDfiEgiGhiHiiJjiKkiMliNmiPniQoiRphPph\ OqhMqgLrgJrgIrgH_TEHEBIHCIJDILEJNFJPGJSHJUIKWJKYKK\ _LKaMGiZCpj9wvCurFtnIrkLqgOpcRn`UmXXlT_jQbiMehIhfF\ keBnd8h_BcWEYSHTNKNJMIFPCAS76V22X46Z5A`7Ea8IcAMeBQ\ fDUhEYiGakHemJinKmpLqqPtpSwpWzpZzpbzpezoizolzopzos\ zovzopzijzcezZ_zTUzOPzIJzDDz78z2Gz9OzFWzMczSkzZszd\ rzerzerzerzerzerzfrzfrzfrzfrzfrzgrzgrzgrzgrzgpzenz\ cmzakz_izYhzWfzUdzTHzoJzm } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD April 19, 2008 -- (Most Unexpected [8])
by JimMuth＠aol.com 19 Apr '08

19 Apr '08

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Re: [Fractint] HELP !!!
by JackOfTradeZ＠comcast.net 17 Apr '08

17 Apr '08

. Hey - someone give me a good formula(s) to try to animate? Universe #6 is at E+87, soon to be posted. The trip out to E+112 may take another 6 months. In the mean time I am getting seriously bored. I may start drinking again. Need some good idears ... .

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FOTD 17-04-08 (Gone and Returned [6.5])
by Jim Muth 17 Apr '08

17 Apr '08

FOTD -- April 17, 2008 (Rating 6.5) Fractal visionaries and enthusiasts: Note: there will be no FOTD for one day only -- April 18. Today we have another image from the same parent fractal, and it's another image that rates a 6.5. 6-1/2 images seem to be all this parent fractal has in it. The scene is located on the eastern edge of the parent's fan, in the Seahorse Valley of a large but ill-defined minibrot there. But once again the final result falls short of the expectation. Then again, maybe my expectation was a bit too much. The image really is rather interesting. In an effort to make something of nothing, I evaporated the image and brought it back to life with the bof61 inside fill, but nothing times something always equals nothing, so the rating remained at a 6.5, but almost a 7. The name "Gone and Returned" refers to this evaporation and reconstitution. Let's face it, the calculation time of 11-1/2 minutes is slow, so my advice is to view the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> An absolutely perfect day here at Fractal Central on Wednesday was fully appreciated by all concerned, the fractal cats included. With me, the work was moderate. But due to a big job expected tomorrow, there will be no FOTD for April 18. The next FOTD will appear on schedule on April 19. Until then, take care, and they say that life is a learning experience. This seems fair enough, but when do we get to put to use the all the lessons we work so hard to learn in the 80-year school of life? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Gone_and_Returned { ; time=0:11:34.04-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+5.309042814869086/-2.049162804283094/\ 769420.9/1/40/0 params=-10/-1.1/-1/-11/0/1e+100/0/0 float=y maxiter=20000 inside=bof61 periodicity=10 colors=0006Kq5Ks4KuX_i3KwtKNoLLkLKgMIcJH_HFVDER8CJ\ 3BJ99e91FE8ELFDPLCQSBUYAWd9YjWEaYD`ZDZ_CYaBXbBVdAU\ e9Tg8Sh8Qj7Pk6Om5Nn5Lp4Kq3Jr3In4Kk5Lg6Md7N`8PY9QUA\ RRBSNCTKDVGEWDFX9GY6HZTVLnh7ldEk`KjXQhTWgPafMgdLeb\ KcaJb_I`ZI_XHYVGXUFVSEURESPDROCPMBNKAMJAKH9JG8HE7G\ C6EB6D95B84A6385376786B97E97IA7LA8PB8SC9WC9ZD9bDAe\ EAiFBlFBpGArFBsGCsmDsGzmGEtHmtHGtHHncHuIIuIJuIKumK\ uIEhU8Xe1Ks2Lq3Lp3Ln4Lm4Lk5Lj6Lh6Lg7Le7Ld8Lb9La9L_\ ALZALXBLWCLUCLTDLRDLQELOFLNFLLGLKGLIHLHILFILEJLCJL\ BKL9FA7KL8PV9UdAWw0ZnB`fLbZWeQfdRecRebSebSeaTe`Te_\ Ud_UdZVdYVdXVdXWdWWdVXcUXcUYcTYcSZcRZcP_dRZcSYcTXc\ UWbVVbWUbXTbYSaZRa_Qa`QabP`cO`dN`eM_fL_gK_hJ_iIZjH\ ZkGZmFYlGZlGZlGZkHZkHZkHZkHZjIZjIZjI_iJ_iJ_iJ_iJ_h\ K_hK_hK_iLahK_gKYfJWeJVdITcIRbHPbHOaGM`GK_FIZFHYEF\ XEDWDBYC8WDAVDCUDETEGSEIQEKPFMOFONFQMGSKGUJGWIGYHH\ _GHaEHcDIeCIgBIiAJa8JmUKU } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 16-04-08 (Most Indeterminate [6.5])
by Jim Muth 15 Apr '08

15 Apr '08

FOTD -- April 16, 2008 (Rating 6.5) Fractal visionaries and enthusiasts: On Tuesday morning fractal lady made a remark about the comments I so frequently insert at the close of the FOTD discussions. She said that any psychologist who reads the FOTD could do a pretty good psychological analysis of me. I agreed with her. And why not? "After all, that's their job," I reminded her. Analysis or not, I certainly do enjoy fractals. It's not that I'm trying to show that I'm an artist, it's simply that I enjoy exploration, and discovering the abstract things that happen when numbers start doing their thing. In today's FOTD for example, I found a minibrot in a most unlike- ly place in yesterday's parent fractal -- in the rudimentary East Valley of a larger but decaying minibrot at the edge of the great fan. Unfortunately, today's minibrot failed to live up to the enthusiasm I felt when I first realized that it was there, so I was forced to rate the scene at a third consecutive 6.5. I named the image "Most Indeterminate" when I failed to find what I expected. To complicate matters even more, the calcula- tion time proved to be an unwieldy 8 minutes. But eternal salvation is at hand in the form of the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the completely calculated image is or soon will be posted for immediate gratification and possible celestial enjoyment. Perfect spring weather made Tuesday a near perfect day here at Fractal Central, and the fractal cats agreed by spotting a pair of squirrels scampering about the yard. The dynamic duo made sure the squirrels stayed out of trouble, while I finished the nominal work. The next FOTD is scheduled to appear in 24 hours. And I would not be surprised if it actually does appear. Until then, take care, and who cares what the world is made of? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Most_Indeterminate { ; time=0:08:04.55-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+2.7845333264158/-2.7122381527887/1.118\ 171e+007/1/-150/0 params=-10/-1.1/-1/-11/0/525/0/0 float=y maxiter=10000 inside=0 periodicity=10 colors=000cOmfQjiSgkUdbajUipMpuOnqPlnRjkShgUgdVeaX\ cYYaV_`S`ZObXLcVIdUFeTHeTIeTKeTLeTNeTOeTQeTReTTeTU\ eTWeTXeTZeT_cQXbOUaLR_JOZGMYEJWBGV9DU6AT48U79V99WC\ 9XE9YH9ZJ9ZL9_OA`QAaTAbVAcYAd_AdaAc`Bb_Bb_BaZCaYC`\ YC`XC_WDZWDZVDYUEYUEXTEXTEVPCUJASJ9FA7QD6TF5VG5YH5\ _I4bJ4dK4gL4iM3lN3nO3qP3sQ2vR2xS2zT2xY3w`4vf5ug6to\ 7sm8rx9oqDmrHkpLimPgjTehXce`agjY`dUYeQVeMSfIPgEMgA\ Jh7GhCO_HVRMaIRhAbNCr1Em8GgEI`KJcQLVWNTaORgQPmRRkT\ TiVVgXXeZYd_Joe5yj4qd3i_4NR41I94KD7LIAMMDNQFOVIPZL\ RcOSgQTkTUzcVzcWzcXzcYzcZnR_kN`gKadHbaDcZAdW7eU6fS\ 6fQ6gP6gN6hL5hJ5iI5iG5jE5jD5jFCgHJeIQbKX`McYNjWPqT\ QwRSsQToQVlPWhPYeOZaO`ZNaVNcRMdOMfKLgHLiDKjAKl6Jm3\ Jj5Mg7Od9RaBTZDVXFYUH_RJaOLdLNfJPiGRkDTmAVp7Xr5YtB\ WsGUrLTqQRpVPo_OndMmiLmhOcgRUfULeXBd_2`Z5XY8TXBPWE\ LVHHUKDUMGTNISOKRONRPPQPRPQUPQWORYNR`NSbMSdLTfLTgI\ WhFYiD_jAak8cl5el3gg6fc8e } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 15-04-08 (On the Brink of the End [6.5])
by Jim Muth 15 Apr '08

15 Apr '08

FOTD -- April 15, 2008 (Rating 6.5) Fractal visionaries and enthusiasts: Today's scene lies in the same parent fractal that gave us yesterday's image. But unlike yesterday's image, which was all there, today's scene is half evaporated, with the evaporated half on the right and the unevaporated half on the left. The scene is located very near the positive X-axis, in a detached area of debris just east of the great 'fan'. Both the bailout and the proximity are critical. In my opinion, the evaporated half gives the better impression, though it is up to the individual viewer to make the final judgement. Unfortunately, even with all its fancy technical stuff, the image can not honestly, again IMO, be rated higher than a 6.5. The name "On the Brink of the End" refers to the edge of the area of total evaporation, which neatly bisects the minibrot as well as the entire frame. The 'inside' part of the image was rendered with the 'fmod' option. The calculation time of 1-1/2 minutes is quite reasonable, and will cause no one any impatience. The fastest and easiest way to see the image, as almost always, is to make a virtual trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view it in completed form there. Chilly but bright weather was the rule here at Fractal Central on Monday. The high temperature of 48F 9C was more typical of early March than mid April, but the strong sun and lower winds kept the feeling of spring alive. The dynamic cats spent the day in as much sun as they could find. My day was fairly busy; tomorrow will probably be the same. The next FOTD will be posted in 24 hours. Until then, take care, and take a step on the bright side. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= OnTheBrinkOfTheEnd { ; time=0:01:26.02-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+6.150456348458149/+0.0026827408035873/\ 1.483275e+010/1/172.5/0 params=-10/-1.1/-1/-11/0/\ 2.26966821394e+017/0/0 float=y maxiter=875 inside=fmod proximity=0.02643535 logmap=104 periodicity=10 mathtolerance=0.05/1 colors=000DBKHCMKCONDQQDSTEUWEWZFYaFZeG`hGbkHdnHfq\ IhtIjwJlzJmvMlmOfpRjmPiiVhhcgg_ffffddeUUwaic_kbXma\ VU`Tr_zt_Ns`mzazqbChczzd5nezze3mb3m`4mZ4mX5lV5lT5l\ Q6lO6kM7kK7kIzkG6fC5b94Z54V23X63Y93ZD3_G2`K2aN2bR2\ cU1`U1YU1VU1SU1PU1MU1JU1GU1DU1AU17U15U9ATGETOISVMS\ UNQTNPSONROMQPKPPJOQINQGMRFLRDKSCJSAIT9HT8KR9NPAQO\ BTMCWLDZJE`IFcGGfFHiDIlCJoAKq9LiEQaJVVOZNTcGYg8bl1\ fp5cn8amC_lFXkJVjMTiQQgTOfXMe_JdcHcfFbiDafCbdBcbAc\ _9dY8dW7eT6fR5fP4gM3gK2hI2hL4jN6kP8lS9mUBoWDpZFq`G\ rbIteKugMviNwgMufMseMqcMobMmaMk`MjZMhYMfXMdVMbUM`T\ MZSMYUPVWRTYTQ_VOaXMcZJd`HfbFhdCjfAlh8nj5pl3qn1nk5\ lh8jeBhcEf`IdYLbWO`TRZQVXOYVL`TIcRGfSEeTDeUCdUBdVA\ cW8cX7bX6bY5aZ4aZ3a_8b`CbaGbaKbbObcTbdXbd`bedbfhbf\ lbbb`ZUZVKXRBVN2UO9RPGPQNMQTKR_HSfFSlDRiHPfLOcON`S\ LYWKWZJTbHQfGNjFKmDHqCEuBCx9Tg7iS6yC7u88q49m0XMFVL\ KTLPRLTPLYNLaaTkWOdPKYJFR } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 14-04-08 (Wiggly Squiggly [6.5])
by Jim Muth 14 Apr '08

14 Apr '08

FOTD -- April 14, 2008 (Rating 6.5) Fractal visionaries and enthusiasts: A fractal like a little child deserves a childish name, such as "Wiggly Squiggly", so that's what I named today's image, which lies in the parent fractal that results when 10 negative parts of Z^(-1.1) are combined with one negative part of Z^(-11) and (1/C) is added. This parent fractal is a grossly oversized thing with quite a spectacular 'fan'. Today's scene is located near the southern edge of this fan. The parent fractal appears promising, so I might stick with it for a few more days to see what I can find. I'm certain it holds images that will rate better than today's 6-1/2. The calculation time of just under 4 minutes is a bit longer than I would have preferred, but still short enough to make calculation almost a pleasure. For total pleasure however, go to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view the completed image there. While I am working with fractals, my thoughts often drift to dis- tractions such as the nature of reality. By this time I am no longer certain that such a thing as an absolute reality even exists. The whole idea of an objectively real world out there and apart from us may be just another concept invented by our overly fertile imagination. Then, once we had invented our reality, we designed a method of science that would be compat- ible with our invention. And then again, I sometimes wonder whether it is myself that is doing the dreaming . . . Heavy clouds, chilly temperatures and occasional light rain spoiled things here at Fractal Central on Sunday. The fractal cats agreed and passed most of the day sleeping and chasing each other around. My day was reasonably calm, which left ample time for the fractal hunt, but as today's image shows, I bagged only a mediocre one. The next FOTD will appear in 24 hours. Most likely it will be an improvement. Until then, take care, and endure in the big search. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Wiggly_Squiggly { ; time=0:03:55.47-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+2.62230097131821/-2.780963225811715/\ 1.866183e+008/1/-170/0 params=-10/-1.1/-1/-11/0/\ 525/0/0 float=y maxiter=3200 inside=0 logmap=383 periodicity=10 mathtolerance=0.05/1 colors=000RFKRFLRFLQFLOFLMFMKFMGFMJFIGFNGFNGFNFFLE\ FJDFHCFFDFDEFBFF9GF7HF5IF3JF1KF0LF4MF8MFCLFGJFKHFO\ FFSEFUCG_BHX9Ic8JZ6Kc6K`3Kc7KcAKcCKcFKcIKcKKcNKbQK\ _SKWVLTWLQWMSWMUWNVWNXVOZWO_YPa_OcaNdbMfdLhfJigIkh\ GmgBrhEnhGkhJhhLehObiPZiRWiSTiTQiVNjXJj_GjaDjdAjg7\ lh3jj4hk4fm4em5co5ap5`q6Zr6Xs6Ws7Ut7Su7Ru8Pv8Nw8Jz\ 4Mw8OtCQrGSoKUmOWjRYgV_eZabbc`feYjfTsgWmhYgi_ajaWk\ cQkgJleLldMmcOmbPmaQn`Sn_ToZVoYWoXXpWZpV_pUzoVznVz\ nVzmVzpWzmVzkUzhTzfSzdRzaQz_PzXOzVNzTMzQLzOKzLJzJI\ zHIzIMzJQzKUzLYzMazMezK_zJUzHOzGIzECzD6zC0zE4zF7zH\ BzIEzJHzLLzMOzOSzPVzQYzT_zWazZbzadzdezggzjhzmjzpkz\ ofzoazoYzoTzoPznPzmQzlQzlRzkSzjTzjUKiVJhWJgXIgYIfZ\ He_Hd`GdaGcbFbcFbdFaeE`fE_gD_hDZiCYjCXkBVlBXmBWnAV\ oAQp5Rq6Rr6Rs6St7Su7Sv7Tw8Tx8Ty8Tz8Uz9Uz9Uz9VzAVzA\ VzA0znBz`LzNGzSHzRHzRHzQIzQIzQIzPJzPJzPJzOKzOKzNKz\ NLzNIzJIzJIzJIzJIzJJzKJzK } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 13-04-08 (Minibrot [No Rating])
by Jim Muth 13 Apr '08

13 Apr '08

FOTD -- April 13, 2008 (No Rating) Fractal visionaries and enthusiasts: Today's image is named "Minibrot", and that's all it is. After spending the entire afternoon clearing the winter debris from the yard, I had almost no time for a proper fractal search. So I took the first minibrot I could find in the Z^(1.75)+C Mandeloid as it appears 6 levels up the logarithmic ladder when the cosine function is applied, and declared it Fractal of the Day for April 13. The parent fractal is a distortion of the classic Mandelbrot set, with today's scene located in its Seahorse Valley area. With no effort involved in its creation, the image could not be given a rating. The calculation time of 4-3/4 minutes is within reason. But it is equally reasonable to completely avoid the effort of calcula- tion and view the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Saturday was the best day so far this spring here at Fractal Central. A heavy thunder-shower around 5am cleared out the murk, and by 9am the day was sunny with a temperature of 68F 20C. Things got even better in the afternoon when it reached 73F 23F. The fractal cats watched from the back window with amusement as I started work in the yard. The next FOTD is due and will likely appear in 24 hours. Until then, take care, and don't waste energy on a heroic but futile effort to create true meaning in a meaningless universe. This is what born-again skeptics and Atheists do, and I have never yet seen one succeed. But above all else, think positive. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Minibrot { ; time=0:04:43.24-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=cos passes=1 center-mag=-0.643729366910521/+0.3961159852470334/\ 95347.75/1/97.5/0 params=1.75/0/6/0 float=y maxiter=7500 inside=0 logmap=212 periodicity=10 colors=0002G83G94GA6GB7GC8FDAFEBFFCFGDFGKJKRMOYPSd\ TWkW_rZbo`alaajbagc`ed`be`_f`Yg_Vh_Ti_Qj_NkZLlZImZ\ GnZEfdDZiCSnBKsADxGLwMTvS`uYhtcpt`nsYlsVksTisQhsNf\ sLesKctJatI_tIYtHXtGVtFTtFRuEPuDOuCMuCKuBIuAGuAFu9\ Gr9Ho9Im9Jj9Kh9Le9Mb8M`8NY8OW8PT8QQ8RO8SL8SJ9RK9RL\ 9RL9RM9QN9QN9QO9QP9QPUZKnfGmdImcKlbLlaNk`Pk_QjYSjX\ TiWViVXhUYhT_hS`fXad`acdbahb_mcZqcXudWydTzeRzePzeN\ zeLzeJzeHzeFzeDzeBzeEvcGrbIoaLk`Nh_PdZRaYUYWWUVYRU\ `NTbKSdGRfDQcPR``RZkR_jT_jU`jW`iX`iZai_ahabhbbhdbh\ e`ggZfhXeiWdjUckSclRbmPanN`oM_pK_qIZrHYsFXtDWuCWvD\ UvDSvDRvDPvDOvDMvEKvEJvEHvEGvEEvEDvIKoMRiPYcTdYXkS\ _rM`pOanPblQcjRdhSefTfdUgbVh`XiZYjXZkV_lT`mRanPboO\ c_WVKbM5iE5jG4kI4lK4mM4nO3oQ3pS3qU3rW2sY2t_2ua2vb3\ wa4xa5ya5za6z`7z`8z`8z`9z`Az_Bz_Bz_Cz_Dz_EzZEzZFzZ\ GzZGzZKz`NzaQzbTzcWzdZzeazfezghzhkzinzjqzktzlwzmtz\ oqzpozqlzrizsgzt2z81z70z7 } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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FOTD 12-04-08 (Fragmentary Vision [6.5])
by Jim Muth 12 Apr '08

12 Apr '08

FOTD -- April 12, 2008 (Rating 6.5) Fractal visionaries and enthusiasts: Today's image lies in the Z^(sqrt(2))+C Mandeloid as it appears 1/2 level up the logarithmic ladder when calculated by the MandelbrotBC2 formula. I took a step backward when choosing this formula. The scene is located in a valley on the east side of the main bay, which might or might not be an East-type valley. Whatever the nature of the parent valley, there are no elephants or even pieces of elephants in the image. What we do have is a moderately attractive but well broken-up scene with a near-shape- less minibrot at the center. This minibrot might become better defined if calculated at a larger maxiter, but I feel that the current maxiter of 12500 is plenty large enough. The name "Fragmentary Vision" describes the image. The rating of a 6.5 includes an extra half-point for the bit of extra effort I put into the coloring. The calculation time of 10-1/4 minutes is slow, but the time can be speeded up by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Mild but overcast weather prevailed here at Fractal Central on Friday, with the temperature around 66F 19C. The cats slept through most of it. My day was moderately busy. Hopefully, tomorrow will be slower. The next FOTD, whatever it may be, will be posted in 24 hours. Until then, take care, and be calm in a fractal crisis. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Fragmentary_Vision { ; time=0:10:14.12-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 passes=1 periodicity=10 center-mag=+0.15332371912302240/-0.010277132064488\ 32/5.053782e+009/1/-167.5/0 params=1.41421/0/0.5/0 float=y maxiter=12500 inside=0 logmap=1050 colors=000MC4NC1PE2PE2QF2QG2RH3RH3SJ3SJ3TK3UL4UL4U\ L4UM4UM4UM5UN5UN5UN5VO6VO6VO6VP6VP6VP7VP7VQ7VQ7VQ7\ WR8WR8WR8WS8WS9WS9WT9WT9WT9XUAXUAXUAXVAXVAXVBXWBXW\ BXWBYX9XWBXVCWUDWTEVSFVRGUQHUPITOJTNKSMLSLMRKNRJOQ\ IPQHQPGRPFSOETODUNCVNBWMAXM9YL8ZL7_K6`K5aJ4bG0bJAc\ LFdNKdPPeRUfUZhWcjYhk_mmdnpamn_jlYgjVdhTafRZdPWbMT\ `KQ_INZFKYDHXBEW8AW9AVABVACUBCUCDUCETDETDFTEGSFGSF\ HRGIRHIRHJQIKQIKQJLPKMPKNOLNOMOOMPNNPNNKNOOMPPMPNL\ QTLRNLRUKSVKLZLSVKZRKdNKkJJrFJyAKzBJzRJyDIwEIvEHuF\ HsGGrHGpIFoIFmJEbKEeLDeMDkMDmMCzUBwN9qP9pRAoUBmWCk\ VDiZEfcFdcGTUH`ZIYZJWZKUZLRdMVcKUcKThKVhJXhJZaJ_hI\ `hIahIbqHcqHdlHeqGfqGgrGhrFjsFltFpuEtuHxuLzuPzuSzu\ Wzu_zubzufzujzunzuizuhzufzuezuczubzv`zw_zxmzymzzmz\ zmzzmzzmzzmzzmzzmzzmzzmzzmzzmzznzznzzozzpzzpzzqzzr\ zzrzzszzszztzzuzzuzzvzzwzzwzzxzzyzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100, p=real(p2)+PI q=2*PI*floor(p/(2*PI)), r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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FOTD 11-04-08 (Renormalization [Rating Normal])
by Jim Muth 10 Apr '08

10 Apr '08

FOTD -- April 11, 2008 (Rating Normal) Fractal visionaries and enthusiasts: Today's image is yet a third view of the scene that appeared two days ago on April 9. But whereas in yesterday's reimage we tore the original image to shreds, in today's view we 'renormalize' it into a reasonably symmetrical object. I named today's image "Renormalization". As far as I know, renormalization is something physicists do when the numbers behind their theories add up to infinity or zero, or something else absurd. They simply insert arbitrary terms into their formulas, which result in the formulas accurately describing the ideas they are trying to prove. I'm not sure if this band-aid approach actually proves anything, but it sure eliminates a lot of headaches for the theorists, especially those still searching for that elusive theory of (almost) everything. In today's image I renormalized things by simplifying the orientation parameters to 90,0,0,90, which conveniently draws the 'Rectangular' direction, defined by the imag(c) and imag(z) axes. After much stretching and skewing, this simplification produced a near-symmetrical pattern around the hole at the center, which once was a perfect minibrot. Since the scene was renormalized, the rating could be nothing but 'normal'. But things in the image are not quite as normal as they first appear. Today's orangish pattern has only two rounded points, whereas the Mandelbrot version of the same scene has four points. Where did the other two points go? Most likely, they rolled off into the fourth dimension. The calculation time of today's image is a blessedly brief 34 seconds, fast enough to bring joy even to the hearts of those who don't get the point of fractals. The trip to view the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> is equally fast. With a high temperature of 72F 22C, gentle winds, and brilliant sun, Thursday was the best day so far this spring. The fractal cats must have agreed. They got into a spat over who should sit in the sunniest window. My day was moderately active. Tomorrow will probably be the same. The next FOTD image will be created sometime during the next 18 hours and posted in 24 hours. Until that semi-glorious moment breaks upon the waiting world, take care, and renormalize yourself. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Renormalization { ; time=0:00:34.74-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot4 center-mag=+0.000000003\ 13126323/-0.0000000643364187/2.29769e+007/1.4265/\ -86.5334566310032614/83.7362695773166621 logmap=181 params=90/0/0/90/-1.749446905449293/6.834887985e-0\ 07/-1.749446905449293/6.834887985e-007/2.0000001/0 float=y maxiter=1800 inside=0 periodicity=10 colors=0000850966A79B8BC9ED9HEAKFBOFBRGCWHD`IDeNEl\ TFoaOuiYvrVzxSzxQzyNzyXzzgzzpzzzI00GA0EK0BUT9_O6_K\ 4_F2_B7XCCVDHTDMQEOXCROEWMFewcdoZcgUb_PaSKfEsdGjcH\ bbIVaJNI`RKZQLYPNXOOWNPUMRTLSSLTRKVQJWOIzzzzzztwso\ rnkieg`XkSOzXLvVLqSHjOFeMF_ic``V`SNo_9lXAjUBgSCePD\ bMELhzNevOcrPanR_jSYfTWbVUZWSVXQRZON_MJiF0hG2gG3fH\ 4fH5eH6dI7dI9cJAbJBbJCaKD`KEL5kTDVxy9vvAtsArpBqmBo\ jCmgCldCjaDhZDfWEeTEcQFaNF`7l`9h`Ad`C``DX`FU`GQ`IM\ `JIsSNoQLkOJgNIcLGjzJgoIedHbUGYtjZqgZoeZlcZjaZg__e\ Y_bW_`T_YR_WP`TN`RL`OJ`MHLk9MiANgAOeBPdBQbBR`CSZCT\ YCUWDVUDWSEXREYPEZNF_LFkmzjjuigqhdlgbhf_deX_dUWcSS\ bPNaMJlVFjTFhRFfQFeOFcNFaLF0OR4NP7NOBMNEMMHMLLLKOL\ JRLIVKHYKGxQ0vP1uP2sO3rO4pP5oQ6mS7lU8jW9iYAg_BfaCd\ cDceEagFiicgk_fmWeoTcqPbsMauIUwIWxHXyHYzGZzG_zFQzf\ UzXYzORzuSzqTzmUzjVzfWzcWz_XzWYzTZzP_zM`zICzzPzbtz\ rozhjzZezPDzrHzkLzdPzZTzS } frm:SliceJulibrot4 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 10-04-08 (All Hell Breaks Loose [!!])
by Jim Muth 10 Apr '08

10 Apr '08

FOTD -- April 10, 2008 (Rating !!) Fractal visionaries and enthusiasts: Look at what has happened to the perfect minibrot of yesterday's image. Not only has it stretched beyond recognition, it has come apart. But this is what happens in the four-dimensional Julibrot when the Mandelbrot scene is double-rotated and sliced at a critical angle. In this case, the angle defined by the real(p1) parameter is the critical one. A change as little as 0.1 degree makes a world of difference. I was so surprised at the result that I rated the image at a !! This is a most unusual rating indeed. And I must apologize for the name "All Hell Breaks Loose". The image is not really that violent, and I doubt that any fractalists believe in the literal existence of that legendary hot place down below. As for a description of the motion known as double rotation, I am working on it, but at the same time I am finding it extremely difficult to put into words. Those in a hurry will find the calculation time of 34 seconds quite reasonable. Those even more hurried may view the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> With a temperature of 63F 17C, Wednesday was mild enough here at Fractal Central in central Pennsylvania, but the clouds kept it from being ideal. The fractal cats live in an ideal world, so they were not disturbed by the grayness. My day was moderately busy, but we were irritated by an irate customer who claims he didn't get what he wanted and refuses to pay his bill. Thankfully, fractals do not incur bills, and even if they did, they would never refuse to pay. The next FOTD will be posted in 24 hours. Until then, take care, and keep going in hypercircles, whatever they are. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= AllHellBreaksLoose { ; time=0:00:34.64-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot4 center-mag=+0.000000006\ 15716237/+0.00000013555853479/1.861013e+008/0.0130\ 8/92.6807800722809247/-33.0516955361447415 params=-92.5/162/147/-42/-1.749446905449293/6.8348\ 87985e-007/-1.749446905449293/6.834887985e-007/\ 2.0000001/0 float=y maxiter=1800 inside=0 logmap=181 periodicity=10 colors=0003966A79B8BC9ED9HEAKFBOFBRGCWHD`IDdNEkTFl\ aOikYftVmzSrzQvzNzzK_PHNYnLYjIYeGZaEZXBZT9_O6_K4_F\ 2_B7XCCVDHTDMQEOXCROEWMFewcdoZcgUb_PaSKfEsdGjcHbbI\ VaJNI`RKZQLYPNXOOWNPUMRTLSSLTRKVQJWOIXNHzzztwsornk\ ieg`XcSOzXLvVLqSHjOFeMF_ic``V`SNo_9lXAjUBgSCePDbME\ LhzNevOcrPanR_jSYfTWbVUZWSVXQRZON_MJiF0hG2gG3fH4fH\ 5eH6dI7dI9cJAbJBbJCaKD`KEL5kTDVxy9vvAtsArpBqmBojCm\ gCldCjaDhZDfWEeTEcQFaNF`7l`9h`Ad`C``DX`FU`GQ`IM`JI\ sSNoQLkOJgNIcLGjzJgoIedHbUGYtjZqgZoeZlcZjaZg__eY_b\ W_`T_YR_WP`TN`RL`OJ`MHLk9MiANgAOeBPdBQbBR`CSZCTYCU\ WDVUDWSEXREYPEZNF_LFkmzjjuigqhdlgbhf_deX_dUWcSSbPN\ aMJlVFjTFhRFfQFeOFcNFaLF0OR4NP7NOBMNEMMHMLLLKOLJRL\ IVKHYKGxQ0vP1uP2sO3rO4pP5oQ6mS7lU8jW9iYAg_BfaCdcDc\ eEagFiicgk_fmWeoTcqPbsMauIUwIWxHXyHYzGZzG_zFQzfUzX\ YzORzuSzqTzmUzjVzfWzcWz_XzWYzTZzP_zM`zICzzPzbtzroz\ hjzZezPDzrHzkLzdPzZTzSXzL } frm:SliceJulibrot4 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 09-04-08 (Perfect Proportions [6.5])
by Jim Muth 09 Apr '08

09 Apr '08

FOTD -- April 09, 2008 (Rating 6.5) Fractal visionaries and enthusiasts: Although the minibrot at the center of today's image looks like a quadratic one, it is not. The parent fractal was generated by the formula Z^2.0000001+C rather than the classic Z^2+C. On the surface, the parent cannot be distinguished from a perfect clas- sic Mandelbrot set, but down deep, especially along the negative X-axis, things are quite different. The little minibrot in today's image lies at the edge of the infinitely divided X-axis in the vicinity of East Valley of the large minibrot at -2.475 on the X-axis. Yes, I know that the large minibrot is centered at -1.75 of the negative X-axis, and not -2.475, but today's parent is not the standard Mandelbrot set. It is the fractal I call the shadow Mandelbrot set, which lies in the same Julibrot figure as the classic M-set but is double rotated 45 and 45 degrees toward the Julia orientation. This less-familiar shadow set has twice the area of the classic set, and the linear dimensions are therefore 1.414 times those of the classic set. As for double rotation, don't waste mental energy trying to picture it. It's a four-dimensional thing im- possible to visualize in three dimensions except in a projection. With its near-perfect square pattern, the minibrot in today's image is quite striking in its own right. Enjoy it while you have it, for we will see another view of it in tomorrow's FOTD, when we see what a difference a little rotation can make. The image rates a not-too-bad 6-1/2. The name "Perfect Propor- tions" refers to the strikingly perfect square pattern, which will not remain perfect for long however. The calculation time of only 35 seconds makes running the included parameter file a pleasure. Equally pleasurable is the trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the finished image is posted for instant viewing. A dull, dreary morning gave way to a brilliant blue sky at noon, followed by a balmy sunny afternoon with a temperature of 63F 17C. The cats enjoyed the balminess from their shelf in the front window. My day was busy, but still well under control. The next FOTD, a shocking scene indeed, is already in the bag and will be posted in 24 hours. Until then, take care, and be ready for the big change. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= PerfectProportions { ; time=0:00:34.89-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot4 center-mag=0/0/\ 2.154207e+008/1/-179.25/0 params=45/0/45/0/-1.749\ 446905449293/6.834887985e-007/-1.749446905449293/\ 6.834887985e-007/2.0000001/0 float=y maxiter=1800 inside=0 logmap=181 periodicity=10 colors=0003966A79B8BC9ED9HEAKFBOFBRGCWHD`IDdNEkTFl\ aOikYftVmzSrzQvzNzzK_PHNYnLYjIYeGZaEZXBZT9_O6_K4_F\ 2_B7XCCVDHTDMQEOXCROEWMFewcdoZcgUb_PaSKfEsdGjcHbbI\ VaJNI`RKZQLYPNXOOWNPUMRTLSSLTRKVQJWOIXNHzzztwsornk\ ieg`XcSOzXLvVLqSHjOFeMF_ic``V`SNo_9lXAjUBgSCePDbME\ LhzNevOcrPanR_jSYfTWbVUZWSVXQRZON_MJiF0hG2gG3fH4fH\ 5eH6dI7dI9cJAbJBbJCaKD`KEL5kTDVxy9vvAtsArpBqmBojCm\ gCldCjaDhZDfWEeTEcQFaNF`7l`9h`Ad`C``DX`FU`GQ`IM`JI\ sSNoQLkOJgNIcLGjzJgoIedHbUGYtjZqgZoeZlcZjaZg__eY_b\ W_`T_YR_WP`TN`RL`OJ`MHLk9MiANgAOeBPdBQbBR`CSZCTYCU\ WDVUDWSEXREYPEZNF_LFkmzjjuigqhdlgbhf_deX_dUWcSSbPN\ aMJlVFjTFhRFfQFeOFcNFaLF0OR4NP7NOBMNEMMHMLLLKOLJRL\ IVKHYKGxQ0vP1uP2sO3rO4pP5oQ6mS7lU8jW9iYAg_BfaCdcDc\ eEagFiicgk_fmWeoTcqPbsMauIUwIWxHXyHYzGZzG_zFQzfUzX\ YzORzuSzqTzmUzjVzfWzcWz_XzWYzTZzP_zM`zICzzPzbtzroz\ hjzZezPDzrHzkLzdPzZTzSXzL } frm:SliceJulibrot4 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 08-04-08 (Fierce Fiery Scene [7])
by Jim Muth 07 Apr '08

07 Apr '08

FOTD -- April 08, 2008 (Rating 7) Fractal visionaries and enthusiasts: Today's fractal came about purely by accident as I was using the 'fmod' outside option to search for a minibrot in the Z^(sqrt(2))+C fractal as it appears 4 levels up the logarithmic ladder when no function is applied. I never found a minibrot, though many are certainly nearby, but I did find a strikingly colored scene that consists entirely of 'outside' stuff rendered, of course, with the 'fmod' option. The image uses only a small part of the 256 available colors. In this case however, the lack of the full color palette is hardly noticeable. After a brief moment of indecision, I rated the image at a 7. The name "Fierce Fiery Scene" kind of describes the image, though I could find no signs of flames in the picture. The calculation time of 7-1/2 minutes is a bit slower than I would have preferred, but the image is different enough to be worth the effort. And as always, the finished image is posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The weather was dry all day Monday here at Fractal Central, but the heavy clouds and temperature of 48F 9C hardly felt spring- like. The fractal cats spent the day keeping warm by the warmest radiator. I spent the day being busy with work and reading about a certain cat in a quantum box. The fiery fractal ended the day with a moment's satisfaction. The next FOTD, not so fiery, will appear in 24 hours. Until then, take care, and is Schrodinger's cat dead, alive, sick, or none of the above? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Fierce_Fiery_Scene { ; time=0:07:37.14-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-0.6634403428163981/-1.406626216391897/\ 1.641796e+009/1/100/0 params=1.41421/0/4/0 float=y maxiter=1500 inside=0 proximity=0.002 outside=fmod periodicity=10 colors=0003B`3B`3Ba3Ba4Ba4Ba4Bb4Bb4Bb4Bb4Ac4Ac4Ac5\ Ac5Ad5Ad5Ad5Ad5Ae5Ae5Ae5Ae36h48f5Ae5Bd6Dc6Eb7Ga7H`\ 8JZ9LY9MXAOWAPVBRUBSTCURDWQDXPEZOE_NFaMFbLGdJHfIHg\ HIiGIjFJlEIoCJnDJmDJmDKlDKlDKkDLkDLjDLjDMiDMiDMhEN\ hENgENgEOfEOfEOeEPeEPdEPdEQcEQcFQbFRbFRaFRaFS`FS`F\ S_FT_FTZFTZFTZFU`GVaHWbHXcIYeJZfJ_gK`hKaiLbkMclMdm\ NenNfpOgqPhrPisQjtQkvRlwSmxSnyTmzUnzTnySnxSnwRnvQn\ uQntPnsOnrOnqNnpMnoMnnLnmKnlKnkJnjIniInhHngGnfGneF\ ndEncEnbDt_6r`9paBnaDlbGkcIicKgdNedPdeRbfU`fWZgY_j\ Z_l`Yg_WbYUYXSTVQOUOJSLFQMERMERMESNESNESNDTNDTODUO\ DUODUODVPCVPCWPCWPCWQCXQCXQBYQBYRBYRBZRBZRBZRA_RA_\ RBZSCYTDXVDWWEVXFUYFT_GS`HRaHQbIPdJOeJNfKMhLLiMKjM\ JkNImOHnPGpQFrREtSDvTCxUBzUBzUAxTAvSAtRAsQAqQApPAo\ OAnOAmNAkMAjMAiLAhKAgKAeJ9dI9cI9bH9aG9`G9ZF9XE9VE9\ TD9RC9PC9NB9LAAJ9BIACHADGAEIAFKAGMAHNAIOAJPBKQBLRB\ MSBNTBOUBPVBQWBRWCSXCTXCU } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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FOTD 07-04-08 (Fractal Mark of Doom [6])
by Jim Muth 07 Apr '08

07 Apr '08

FOTD -- April 07, 2008 (Rating 6) Fractal visionaries and enthusiasts: One of the most accessible interpretations of the quantum weirdness is the idea of multiple universes with multiple versions of everything and everyone. But this raises a question that I have never been able to answer. Are those other versions of myself (and everyone else) really conscious, and if they are, who are they? Are they identical twins who are constantly popping into existence complete with my stored memories, and if so, how do I know that I am not merely a twin that popped into existence a second or so ago, complete with a brain filled with the memories of the original me, who or what ever that might be? And at the other extreme, if those other versions of myself are not conscious, then what is the difference? Also, if some supposedly conscious people in alternate worlds are not in fact conscious, how many assumed conscious people in this world are not actually conscious? Finally, perhaps I am the only con- scious being in this entire universe. (Solipsism?) It is pathetically laughable to see intelligent and rational scientists twisting themselves into such knots as multiple universes to explain something that simply does not and can not fit into the classical world-view. I find the concept of a near- infinity of different versions of myself and everyone else in multiple universes a prime example of 'clutching at straws'. And IMO, when reason and logic lead to such an absurdity, it is a sure sign that something monumentally important has been wrong right from the start of the scientific method. It seems as though science is determined to self-destruct. If so, I wish it a pleasant journey. As for today's fractal, it was rendered with the outside set to 'fmod', and the initials of the name, "Fractal Mark of Doom", spell out that option. The scene lies in the Z^(1.99)+C Mandeloid as it appears 0.9 levels up the logarithmic ladder, where it is rotated about 100 degrees, so that the large period-3 north bud intersects the positive X-axis, which in this case is a line of discontinuity. Today's scene is located in the area of this intersection. The bailout radius of 1.79 is critical. The rating of a 6 seems about right. The picture really isn't all that great. The calculation time of just over 1 minute will give no one impatience. And the finished image is posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Sunday turned into the best day so far this spring here at Fractal Central, as full sun, gentle breezes and a temperature of 61F 16C combined to bring pleasure to all, including the fractal cats, who spent an unusually long time in the afternoon sun. As for me, I did as little work as possible, trying to ignore the grass, which is starting to turn green, but is still a couple weeks from trimming stage. The next FOTD will appear in 24 hours, give or take a few. Until then, take care, and would the real me please stand up. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= FractalMarkOf_Doom { ; time=0:01:06.42-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident center-mag=+0.93654970565216/+0.0000009491899/\ 9.489796e+008/1/112.5/0 params=1.99/0/0.9/-98.31 float=y maxiter=1500 inside=0 proximity=0.1412 outside=fmod periodicity=10 colors=000cIQeJQgKQiLRkMRmNRoOSpPSrQStRTvSTxTTzUUz\ VUzWUzXVzYVzZTzYVzXXzWZzW_xVauUcrTeoTflShjRjgQldQm\ aPoZOqXNsUNtRMvOLxLKzHJzJKzLLzMMzONzQOzRPyTQyVQyWR\ xYSxZTw`UwbVwcWveWvgXvhYujZul_um`toatpbsrbstcsudrw\ eryfrzgqzhqzlszhqzeozamzZkzWizSgzPfzLdzIbzF`zBZz8X\ z5Wz6Vz7Vz8Vy9Vy9VyAVxBVxCVxCUwDUwEUwFUvFUvGUvHUuI\ UuITuJTtKTtLTtLTsMTsNTsOTyIPsOTnUXi__dec_kgTqkVpjX\ oiYnh_mgalfbkedjefidghcigbkfale`nd_k`Xoc_sfawhdzkf\ zmhzjfzgezdczabzpWz_azJfz3ky5jw7iv9htBgrCfqEeoGdmI\ clJcjLbhNagP`eQ_dSZbUY`WX_XXYZWW`VVbUTcTReSQbROdQM\ fPNeQNdQNcRObRObROcSPcSPbTPaTDeVP`T`XRlTPxPNzLLzOM\ zQNzSNyUOwWOuZPr`QpbQndRkfRiiSgkTdmTboU_rT`qUaqVbq\ WcqWdqXeqYfqYgqZhp_ip_jp`kpalpampbnpcopcpodqoerofs\ oftoguohvohwoixnjynjznkznlznlznmznnzqqznnzllxjiugg\ reepcbm``jZYgXWdUUaSR_QPXNMULKRJIOGFLEDHE9MHBOJCQL\ DSMEPPGQTHSXIT`JVdKWgMYkN } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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FOTD 06-04-08 (Frankenfractal [7.5])
by Jim Muth 06 Apr '08

06 Apr '08

FOTD -- April 06, 2008 (Rating 7.5) Fractal visionaries and enthusiasts: Today's evaporated quickie surprised me when it turned out to rate a 7-1/2 on the Jamth scale of fractal worth. I don't have much to say about it except that it is spectacularly colorful, mostly due to the program, but partly to my efforts. The parent fractal is the same one that gave us yesterday's image, though instead of being located in the snowman's head, today's image is located in a spiral lying beyond his left foot. The name Frankenfractal is a bit of an exaggeration. The fractal is nowhere near as impressive as its namesake monster. With a calculation time of under 2 minutes, today's parameter file should be no problem to run. But in case the unexpected happens, the completed image may be seen on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Variable clouds and a temperature of 52F 11C made Saturday fairly harmless here at Fractal Central. The cats, being of a fractal nature, ignored the outside conditions to find their action inside. My day was fairly lazy. The next FOTD will be posted in 24 hours. Until then, take care, and keep watching that paradigm. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Frankenfractal { ; time=0:01:55.66-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-23.11035411865113/-22.10717055110748/\ 135535/1/156/0 params=-3/-1.3/-1/-3.3/0/1e+050/0/0 float=y maxiter=950 inside=bof61 periodicity=10 colors=000_H0WE0VA0S71P31L01I01H018000000000000015\ 0G30I30K30L10N13P16Q0AS0DT0HV0KW0PY0S_0_Q0eI0lA0s3\ 0q60q80qC0qE0oH0oK0oN0oP0mS0mV0mY0m`0ld0lg0lj0ll0W\ b0IV05N00G00C007103300500600700700C00G00K00P03S07W\ 0C`1Ge5Lj7QmAVsD_xGdzIhzLmzNsz0zt0zo5zhAzdGzYLzTSx\ NYtIdsDjo8qmCjhDeeE_`GVYIQVKKQLGNNCKHHLDLN8QN5VP0_\ Q0dQ0hS0mS0lP5jLDlILmGKoHIqIIsIHtKHvKGxLGzNNzNVzPb\ zPjzQszSzzSzzTzzTzzWzzYzz`zzbzzezzgzzjzzlzzgzzbzz_\ zzVzzSzzNzzKzzGzzDzz8Kz60q10t00q00m00j00g00d00`00Y\ 00T00Q00N00K00H00E00C00800H00Q01_05g0Yz3Vz3Sz1Px1N\ z1czcczczX0zO0z00q00h00`00T00L00I80GI7DVIAdW7qj6wz\ 7wz7wz7wz7wz7mz7mz7bj7_h7Wg7Te7Sd7Pb7L`7K_CIVEHSIG\ PLELQEHTDEWCC`A8d86h81l70q60t50x50tA0sE0oK0mP0lV0h\ _0ge0ej0_e0V`0QY0KT0GQ0CL07I01E00C0070050EL0sd0zv0\ zx0zz0zz0zz0zz0sz0jz0Yz0Tz0Qz0Lz0Iz0Ez1Cz1Gz0Iz0Nt\ 0Qo0Vj0Ye0b`0eW0hT0eP0bL0 } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 05-04-08 (Angelic Snowman [7])
by Jim Muth 05 Apr '08

05 Apr '08

FOTD -- April 05, 2008 (Rating 7) Fractal visionaries and enthusiasts: Today's semi-glorious image lies in the parent fractal that results when 3 negative parts of Z^(-1.3) are combined with one negative part of Z^(-3.3) and (1/C) is added. To make things more interesting the bailout radius was increased to 780,100, which partially evaporated the scene, and the image was rendered with the inside set to 'fmod', which created the excessive sharp angular detail. Both values are critical to the effect. The above-mentioned parent fractal reminds me of an angelic snowman with a halo around his head, which is what I named the image. But do not expect to see a snowman in the image. The oversized parent fractal is the snowman. Today's scene is located on top of the snowman's head. The rating of a 7 might be a bit excessive. The image is too hectic for my taste, but it's still worth a look. That look may be had by running the included parameter file and waiting 1-2/3 minutes, or by visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Steady rain and a temperature of 43F 6C here at Fractal Central on Friday made it a day that rated a pathetic 2. The fractal cats gave it a 1. The other aspects of Friday were notably average. The next FOTD will appear in 24 hours. Until then, take care, and don't ask questions that demand too much thought. You might be told to sit down and shut up. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Angelic_Snowman { ; time=0:01:41.67-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+5.84307665577121/+5.123185232569579/\ 3964884/1/165/0 params=-3/-1.3/-1/-3.3/0/780000.0/\ 0/0 float=y maxiter=750 inside=fmod proximity=0.016581 periodicity=10 colors=000pkmpanpSopIpjHmdGj_GgUFePFbJE_EEYBCO9AE7\ 959G4AM4CS4DZ4Fd4Gj4Hp4Lr3Os3Su2Vv2RqUOmuMjsKhqIfo\ HdnFalD_jBYhAWgB_kCcoDgrIZpNRoSJmXBla3kd4dg4Yj5Rl5\ KeFL_PLTZMNhMHrMPnGXjBdf6lb1ic6gdAeeFcfJagN_hSYiWW\ i_RjaMkcIleDmg9ni4ok0olX0Sd9QlIOtRMeP`ROnPOkNOhLOe\ JObHO_FOXDOUBOS_3M`7SaBXbFacJfdNkeRpfVunozgozapzVn\ zPmzIjzCqz9hy7jz5Us3cz1QiFTbTYYebTzhagmiwwqbqovpQS\ olMnjGmhBmgT`miOsdWq_coWknRslNzkJsfGlbDeYA_UJYTRWS\ ZUSfSRnQRgSP`UNUWLNYJGZIMWNSURYSWcP_iNdoLhr7St6Sv4\ Tw3Tr6Qm8OhBLcDJZFHXEVVDhUCuLKnxTgyKYyBOqFNjINcLNX\ ONPSNIVNBYN4`NBSWIKdOCl_agoHAeL5XO1qzqtldw_SyNGySJ\ yXMy`PyeSyiVynYyr_phYh_W_QUSHTldNnYLoSJpLHrFFs8Dt2\ BrJDp_FooHfrGZtFRvEOoFLhGIaHFWICPJ9IK6CKFLHOTEW`CQ\ bIKdNEfT8gYvScsP_qMWnJTlHPiEMgBIe9FI2iQ5bX8XdBRkEL\ sHFzJ9qNGhRM_VSRZZIbdAejLhaVkTenKoqByt3xuBwuJvuRvu\ YuuetumtutmvdgwQawBesAhcA } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 04-04-08 (Fighting the Blues [Fluid Rating])
by Jim Muth 04 Apr '08

04 Apr '08

FOTD -- April 04, 2008 (Fluid Rating) Fractal visionaries and enthusiasts: I recently came upon an article somewhere on the internet that claims we need a new scientific paradigm. Apparently the modern theories of physics are very difficult to fit into the classic Newtonian paradigm, which assumes that there actually is an 'ultimate reality' 'out there', and measuring physical material and energies is as close as we can come to knowing it. All this is very interesting, but if this is not true, I wonder what science would turn to for an ultimate reality if it were forced by its discoveries to admit that the physical universe might not be as real as it appears to us through the indirect means of our senses. Perhaps we would need to turn to numbers and fractals for the ground of our being. Sometimes all this philosophical pondering gets wearisome. I'm no closer to an answer that I was when I read that book about the philosophy of science 40 or 50 years ago. But some things never grows wearisome, and at least for me, one of those things is the universe of fractals. Today's fractal image is named "Fighting the Blues". Its parent fractal came to be when I checked the formula Z^(2.01)+C as it appears 1.5 levels up the logarithmic ladder when no function is applied. At this level the almost-Mandelbrot set is rotated 180 degrees, so that East Valley falls on the negative X-axis, where all the fractal splitting is found. Today's scene is located in this shattered version of East Valley. The image looks as though it were very near the cut-off point of the bailout radius, but this is not so. I raised the bailout to 2100 and it made no difference. The increased bailout does make a difference in the appearance of the image however. I rendered the scene with the outside set to 'tdis', which colors the bands of the image according to the distance the points travel before finally escaping for good. Obviously, a larger area in which to skip about will affect the total distance a point covers before finally escaping. I gave the image a fluid rating. This means I was so uncertain about the quality of the image that I decided to leave it to the viewer to rate the image as he sees fit. I kind of like the moody overall blueness, but at the same time I feel that the image is too flat. One opinion cancels the other and leaves me totally undecided. One thing certain is the calculation time, which on a reasonably fast almost SOTA 2000mhz machine is about 2-1/2 minutes. Or, instead of waiting, the impatient fractalist may speed to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and enjoy the finished image posted there. Morning sun gave way to afternoon clouds and evening rain here at Fractal Central on Thursday, while the temperature of 52F 11C kept things relatively pleasant. The local fractal cats consi- dered the situation, stretched and went back to sleep. In my department, the day was average. If tomorrow is the same, I'll call it a success. Until then, take care, and watch your paradigms. Whatever they are, they're getting trendy. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Fighting_the_Blues { ; time=0:03:33.34-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-0.254450031265811/-0.0000447770940377/\ 2101678/1/45/0 params=2.01/0/1.5/2000 float=y maxiter=1500 inside=0 outside=tdis logmap=old periodicity=10 colors=000cuAguDguDguDguDjuFjuFjuFjuFnuInuInuInuIr\ uKruKruKruKuimuDuu0uu0un0uj0ug0uc0u`0uY5uUDuPKuLTu\ JbuGmuEuuBuu8uuvK0uF0nD0gA0`50U30L20G00B0060030000\ 0000000000000000650PO7gfIvuTvufwwwvuuvuuvtujOuL0u3\ 0uG0uU0uj0qv5XvFFvO20uuv0uv0uv0uv0uv0uv0uv5uuAunIu\ jOucTuYbuUitPtqJumGuiBub6u_3uX0uQ0tO0qK0mI0mD0iA0f\ 70f50OA07F00K00Q00I60DU35vA2vI0vF2vF5vFArFFjFK0Wu0\ WuJFbEFfzzzzzzzzzzzzzpzyfxyXzuPzrIunAuj5uj3ug5uc7u\ `AuYHuWKuROuJRuETu8Vu4Xu0Zu0`u0bu0cu0cu0cu0bu0au0`\ t0Zt0Wy0Vs0Sp0Qn0FW00W00W00WB0W`0tv0uv2uvAuvIivXKv\ _2vb0vf0vi0vt0vu0vu0vu0vu0vu0vu0vu0vu0vuuvuuvuuvuu\ vuuvuuvuuvuuvuuvuuvuuvuuvuuvuuvuu6iu4iu1iu0iu0iu0i\ u0iu0iu0iu0qu0tu0uu0uu0uu0uu0uu0uu0uu0uu0uu0ut0uq0\ ui0uf0ub0uX0uT0uO0uK0uI0uD0uA0u70u50u50u51u56u3Bu3\ Gu3Lu3vuivqKjT3YD0L00J00J00G00G00G00E00E00E00B00B0\ 0B000700720Q30i54u5Eu7RuA } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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FOTD 03-04-08 (The Rest in Pieces [6])
by Jim Muth 03 Apr '08

03 Apr '08

FOTD -- April 03, 2008 (Rating 6) Fractal visionaries and enthusiasts: The formula behind today's mischief combines 5 negative parts of Z^(-1.25) with one negative part of Z^(-5.5) then adds (1/C). The resulting parent fractal is a string of three vertically stacked bays, with the largest bay on the southern end of the string. Today's scene lies deep in the eastern branch of the valley separating the large southern bay from the smaller one above it. I tried many tricks to bring the image to a better life, but achieved nothing more than a kind of fractal zombie, appearing to be in a kind of trance. Rendering the scene with the outside set to 'tdis' helped a little, but brought the image nowhere near the potential I at first thought it held. The rating of a 6 is about FOTD average. The name "The Rest in Pieces" has no connection to a chain-saw type movie. It rather indicates that the image is infinitely broken into ever smaller pieces. The calculation time of 8-1/2 minutes is a bit slow for a merely average image, so why not view the image in completed form at leisure on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Bright sun but a chilly 50F 10C temperature made Wednesday notably average here at Fractal Central. I kept busy while the dynamic cats took it easy. The next FOTD will be ready in 24 hours. Until then, take care, and be ready for anything. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Rest_in_Pieces { ; time=0:08:28.22-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=t center-mag=+0.6775879162089047/-2.051238510923745/\ 1.930465e+009/1/67.5/0 params=-5/-1.25/-1/-5.5/0/\ 0/0/0 float=y maxiter=4200 inside=0 outside=tdis periodicity=10 colors=000zzHnUJnVJnVInVInWHnWHnWGnXGnXGnXFnYFnYEn\ YEnZDnZDnZCn_Cn_Cn_Bn`Bn`An`Ana9na9na9o`Ao`Bo`Co`D\ o`Eo`Eo`Fo_Go_Ho_Io_Io_Jo_Ko_LoZMpZMpZNpZOpZPpZQpZ\ QpYRpYSpYTpYUpYVpYVpYWpXXpXYpXZqXZqX_qX`qXaqWbqWbq\ WcqWdqWeqWfqWfqVgqVhqViqVjqVkrVkrVlrUmrUnrUorUorUp\ rUqrUrrTsrTsrTtrTurTvrTwrSxrTwrUwrUwrVvrVvrWvrWurX\ urYurYurZtrZtr_tr_sr`srasrarrbrrbrrcrrcqrdqreqrepr\ fprfprgorgorhorhorinrjnrjnrkmrkmrlmrllrmlrnlrnlrok\ rokrpkrpjrqjrrjrrirsirsirtirthruhrvhrvgrwgrwgrxfrx\ fryfszeryfryfrygrygrygrxhrxhqxhqxiqxiqxiqwjqwjqwjp\ wkpwkpwkpvlpvlpvlpvmovmovmounounounouoouonuontpntp\ ntpntqntqntqmsplrplqpkqokpojoojnninnimnhlnhlmgkmgj\ mfilfilehldgkdgkcfkcekbdjbdjacjabi`bi`ai_`h__hZ_hZ\ ZhYYgYYgXXgWWfWVfVVfVUfUTeUSeTSeTRdSQdSQdRPcROcQNc\ QNcPMbOLbOLbNKaNJaMIaMI`LH`LG`KG`KF_JE_JD_IDZICZHB\ ZHBZIEXJHWKKVKNULQTMTSMWQ } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 01-04-08 (Flowery Failure [5])
by Jim Muth 02 Apr '08

02 Apr '08

FOTD -- April 01, 2008 (Rating 5) Fractal visionaries and enthusiasts: Today's image is the second consecutive merely average one. Good fractals seem to come in clusters. I named today's evapo- rated image "Flowery Failure" because it just doesn't have that certain something that causes me to feel that 'this is a very good one'. And I can't say what the image lacks. It has enough sparkling emerald detail, and certainly enough contrast. The parent fractal seems promising enough, so why then could I give today's image a rating of only a very average 5? It must be that there have been too many similar fractals in the long history of the FOTD. Regardless, the parent fractal, which was created when I com- bined one negative part of Z^(-1.5) with 0.3 negative part of Z^(-3.3) and added (1/C), is one of those rambling things that cannot be described. basically, it consists of a series of circular bays and smaller sub-bays, with today's scene located in a skeletal valley on the southeast shoreline of a large eastern sub-bay. As I mentioned earlier, the image was evaporated by raising the escape radius to 10^50, which is not one-half of 10^100, but 1/(10^50)th of it. The resulting blank screen was restored to life by rendering the scene with the inside set to 'bof61'. Finally, the calculation time of 2-2/3 minutes may be bypassed by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The weather absolutely stank here at Fractal Central on Monday. Heavy clouds, drizzle and a temperature of 41F 5C prevailed all day. The local fractal cats checked the outside conditions once, then decided to spend their day, as they do every day -- inside. My day was about as busy as expected, though I was a bit disap- pointed by the gaudy but somehow humdrum fractal. I'll try again for fractal excellence in 24 hours. Until then, take care, and if it is true that nothing is real, what just wrote that nothing is real? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Flowery_Failure { ; time=0:02:41.31-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+2.32327651312/-1.28247104496/2849086/1\ /-140/0 params=-1/-1.5/-0.3/-3.3/0/1e+050/0/0 float=y maxiter=2500 inside=bof61 periodicity=10 colors=000TNCUNBVNBWNBXPCYQCYRDZSDZTD_UE_VE`WF`XFa\ YF430b_G9w_OkQb`GgL8qO7gQ7qS7pU6pW6pZ6p`6ob5od5of5\ oh5ng7ng8ng9nfBnfCmfDmeFmeGmeHmdIldKldLlcMlcOlcPkb\ QkbSkbTkaUkaVjaXj`Yj`Zj``j_ai_bi_diZeiZfiZghZfgZff\ ZffZeeZz430dZdcZzbZdbZdafc`Zz_Zc_ZzZZbYZbYZaXZaWZa\ X_cWZaWZ`Wf_VZZVZYVZWUZVUZUUZTUZSTZQTfPTfOSZNSZMSZ\ KSfJRZIRZHRZGQZEQZDQZCQZBPfAPZ8PZ7OZ6OZ5OZ4OZ3P_4Q\ _5Q_5R_6R_6S_7430T_8T_9U_9V_AV_BW_BWfCX_CX_DY_EY_E\ Z_F__F__G`_H`_Ha_Ia_IbfJb_J_`KTUKWXKUULSXLQULSXNTU\ OUXPVURWXSXUTYVUYTWYTXYSYYRZYQ`YPaYObYNcYMeYLfYKgY\ MkYKiYJhYIgYGfYFeYEdODQVBaSA_Q9YN7WK6UH5SF4QE5OE6N\ E7ME8LE9KEAJEBIECHEDGEDFEEEEFDEGCEHBEIAFI9GI8HI7IJ\ 6JK5KL4LM3MN2NO1OP0PQ1QR2RS3ST4TU4UV4VW5WX5XY5Y_6Z\ `6_a6`b6ad7be7cf7dh8ei8fj8gl9hm9in9ko9mp8oq8qrAssB\ utBvuCwvDxwDyxEzyFzzFztGznHziHzbIzXJzXIqPIgPHYPHOP\ GLOGMOFNOFOOEPOEQODRNDSNC } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 02-04-08 (FOTD for 02-04-08 [Unrated])
by Jim Muth 02 Apr '08

02 Apr '08

FOTD -- April 02, 2008 (Unrated) Fractal visionaries and enthusiasts: Today's image is unworthy of either name or rating, and I gave it neither. Curiously, the day was quite slow and I spent more time than usual searching for a worthy FOTD. But the more I searched, the less attractive the fractals became. I finally gave up the search, took the best I had found, livened it with an fmod outside and bof61 inside, and called it fractal of the day for April 02. The parent fractal came into being when I combined 0.8 negative part of Z^(-11) with 8.8 negative parts of (1/Z) and added (1/C). The parent fractal reminds me of a splitting atom, with today's scene located on the nucleon that shot out to the northwest. The calculation time of over 15 minutes is inexcusably slow, so why not go straight to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view the finished image there. Record warmth arrived at Fractal Central on Tuesday afternoon, with lots of sun and a temperature of 73F 23C. A mild thunder- shower at sunset did not spoil a near-perfect day. The dynamic cats agreed. My day was not very busy, but for some reason fractal inspira- tion eluded me. I'll try again tomorrow. Until next time, take care, and as the parent fractal of today's image shows, even sub-atomic reactions are fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= FOTD_for_02-04-08 { ; time=0:15:17.47-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=t center-mag=-32.0121141386194/+85.1819914889908/\ 11115.91 params=-0.8/-11/-8.8/-1/0/10000/0/0 float=y maxiter=4500 inside=bof61 proximity=0.5 outside=fmod periodicity=10 colors=000fcBgcBgcBhbBhbBibBiaBiaBjaBjaBk`Bk`Bl`Cl\ _Cm_Cm_Cm_CnZCnZCoZCoYCpYCpYCr_BpYCoXCmWDlVDjUEiTE\ hSEfRFeQFcOGbNGaMG_LHZKHXJIWIIUHJTGJSFJQDKPCKNBLMA\ LL9LJ8MI7MG6NF5NF2NE3NE4NE5NE6NE7NE8NE9NEANEBNECNE\ DNEENEFNEGNDHNDINDJNDKNDLNDMNDMNDNNDONDPNDQNDRNDSN\ DTNCUNCVNCWNCXNCYNCZNC_NC`NCaNCbNCcNCdNCeNEfODeNCe\ NCdNBdNAdNAcN9cM9bM8bM7bM7aM6aM5bL6aM6aN6`N7`O7`O7\ _P7_Q8ZQ8ZR8ZR9YS9YT9YT9XUAXUAWVAWWBWWBVXBVXBVYCUY\ CUZCT_CT_DT`DS`DSaESbERbERcEQcFQdFQeFPeGPfGPfGOgGO\ hHNhHNiHNiHMjIMjIMkILlJLlJKmJKmJKnKJoKJoKJpLIpLIqL\ HrLHrMHsMGsMGtMGtLHtLItLJtKJtKKtKLtJLtJMtJNtJNtIOt\ IPtIPtHQtHRtHRtGStGTtGTtGUtFVtFVtFWtEXtEYtEYtEZtD_\ tD_tD`tCatCatCbtBctBctBdtBetAetAftAgt9gt9ht9it0gs3\ ht5ht7ht9itBitDitFitHjtJjtLjtNkuPkuRkuTkuVluXluZlu\ `mubmudmuglvfmuemtdmscmscnrbnqanp`np_oo_onZomYomXp\ lWpkWpjdeAdeAedAedAedAfcA } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 31-03-08 (Time for Flatworms [7])
by Jim Muth 31 Mar '08

31 Mar '08

FOTD -- March 31, 2008 (Rating 7) Fractal visionaries and enthusiasts: Something is wrong with the following scenario, which I read many years ago, but I have never found the apparent flaw in the reasoning. In a certain town lying on the border between Mexico and the United States, a peculiar currency situation exists. In Mexico, ten U.S. dollars are worth only nine Mexican dollars, while in the U.S., the value of ten Mexican dollars is only nine U.S. dollars. One day a cowhand strolls into a Mexican cantina and orders a one-dollar beer. He pays for it with a Mexican ten- dollar bill and receives in change a ten-dollar U.S. bill, which is worth only nine dollars in Mexico. After drinking his beer he strolls across the border to an American saloon and orders another beer. This he pays for with the American ten-dollar bill, receiving a Mexican ten-dollar bill for change. He takes this back to the Mexican cantina and repeats the process, drink- ing beer merrily all day and ending up as rich as he started, with a ten-dollar bill. The question: Who paid for the beer. The moral: Forget about working and visit sunny Mexico. The conclusion: You can't get something for nothing . . . maybe. The solution: (IMO) Such an exchange rate is irrational. (But what if it actually existed?) And speaking of something for nothing, the same is true of fractals. The cost of today's image is 10 minutes calculation on a fast machine. The result is an image that must be seen rather than described. The holes in the diagonal blue background 'object' remind me of flatworms, which is why I named the image "Time for Flatworms". The rating of a 7 is close to correct. And don't be deceived by the apparent X-axis symmetry of the parent fractal. It breaks down on closer examination. Finally, if fractal calculation is not your cup of tea, visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and see the finished image posted there. Sunday dawned clear but unusually cold here at Fractal Central, with a temperature of 23F -5C. But by afternoon the strong sun warmed it to 50F 10C, making things quite pleasant. The fractal cats spent most of the time by the heat. My day was slow and lazy, which leads to weird thinking, but things are due to perk up tomorrow. The next FOTD will be posted in 24 hours. Until then, take care, and where are those multiple universes when you need one? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Time_for_Flatworms { ; time=0:09:59.62-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-1.01019/0.00203573/18.69511/1/35/0 params=-0.5/-1.1/-0.5/-1.9/0/0/0/0 float=y maxiter=25000 inside=0 logmap=8 periodicity=10 colors=000wkYwjYviYvhYugYufYteYteYsdYscYsbYraYr`Yq\ _YqZYpZYpYYoXYoWYnVYnUYnTYmSYmSYlRYlQYkPYkOYjNYjMY\ jMYgOZdPZbQZ_SZYTZVUZTVZQXZOYZLZZG`XJ_ZMZ`OYaRXcTW\ eWWfYVh`UjbTkeSmhQpgRogSngSmfTmfTlfUkeUkeVjeVidWid\ WhdXgcXgcYfcZebZeb_db_ca`ba`baaa`a``b``b__cZ_cZ_dY\ ZeXZeXZfWYfVYgVYgUXhTXhTXiSWiRWjQWjQVkPVlOVlOUmNUm\ MUnMTnLToKToKSpJSpISqIRqHRrGSsERrFRrGRrHQqIQqJQqKP\ pLPpMPpMPoNOoOOoPOnQNnRNnSNmTMmTMmUMlVMlWLlXLkYLkZ\ Kk_Kk_Kj`JjaJjbJicJidIieIhfIhgHhgHghHgiGgjGfkGflGf\ mFenFenFeoEdpEdqEdrDcsDctDcuDcuDbvDavD`vD_vDZvDYwD\ XwDWwDVw8YyBWxDVwFUvHSuJRuMQtOOsQNrSMqVKqULqULqUMq\ UMqUNqUNqUOqTOqTOqTPqTPqTQqTQqTRqSRqSRqSSqSSqSTqST\ qSUqSUqRUqRVqRVqRWqRWqRXqRXqQXqQYqQYqQZqQZqQ_qQ_qQ\ _qR_rR_sS_tSauTcvUewUgxViyVkzWmzWmzXmzYmzYmzZmzZmz\ _mz_mz`mzamzamzbmzbmzcmzdmzdmzemzemzfmzfmzgmzhmzhm\ zimzimzjmzjmzkmzlmzlmzmmz } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 30-03-08 (On The Trail [7])
by Jim Muth 30 Mar '08

30 Mar '08

FOTD -- March 30, 2008 (Rating 7) Fractal visionaries and enthusiasts: Today's scene lies in the fractal that results when 0.5 part of Z^(-1.9) is subtracted from 0.5 part of Z^(-1.1) and (1/C) is added. I'll not try to describe this parent fractal, which is quite typical of this family of fractals and is easily created by the MandAutoCritInZ formula. The scene is located in a small valley on the shore line of one of the circular bays of the parent. If the fractal is evapora- ted and the 'bof61' inside fill applied to the resulting blank screen, the result is an image virtually identical to the actual image. The rating of a 7 indicates average satisfaction. The name "On The Trail" can imply anything the viewer wishes. The calcula- tion time of 4 minutes is average. The next FOTD will be posted in a near-average time of 24 hours. The finished image is posted for viewing on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Sunny but unseasonably cold weather made Saturday a mixed blessing here at Fractal Central. A sunrise temperature of 25F -4C was anything but springlike, but when the strong sun raised the temperature to 50F 10C in the afternoon, it felt almost like spring. The fractal cats ignored the weather outside, and spent the day by the heat, My day was notably average, and I made the most of it by being notably lazy. The next FOTD will be posted in 24 hours. Until then, take care, and did you hear about the ship carrying a cargo of yoyos? It got caught in a storm and sank 27 times. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= On_The_Trail { ; time=0:04:04.32-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip center-mag=-0.2886299468294951/+1.132653355152376/\ 1.150575e+008/1/-107/0 params=0.5/-1.1/-0.5/-1.9/\ 0/0/0/0 float=y maxiter=5000 inside=0 logmap=-430 periodicity=10 colors=000MMJOPIQRGSUFUXEWZCXaBYdAPP9Xc7Wa6W_5VY4V\ W3UU2US1WW6X_AZcE_fIajNbmRdrVquZtwVzwRtwNmmJccFWUB\ UK7S93R30QEAQOK605A19D2CG3FJ3IM4LPXOSsRVsUYpX`m_Nj\ g9gnBbkDaiFYgGVdISbKP`LNZJK`KGXAAS00N00NZX_ikcdYi`\ LobKncJmdIleHlgGkhFjiEijDiiChiBghAfh9eg8dg7cXI`MTZ\ NRVOQQQOMRNHSLDTK9SSIRZRRe_VfbZfebggfgjjhmnhorirui\ tnekhabaYUWULxkXxjWxiVxhUwgTwfSweRwdQwcPwbOwaOxQPu\ STrTWoU_lVbiWffYicZm`_pY`tVawTcxRdyPezOgzMhzKizIkz\ HlzFmzDozBpzAqz8sz6tz4uz3vz5uz7tz8tzAszBs_DtaEucGv\ eIwgJxjLylMznzzpzzrzzozzlzzjzzgzzezzazzZzzWzzTzzQz\ zMzzJzzGzzDzzAzz7zz5zz4zz2zz1zz0zzDzzQzzbzz4zzJzzJ\ zzJzzJzzJzzJzzJzzJzzJzzJzzJzzJzzJbzJczJdzJdzJczScz\ `cziczqgzkkzeoz_rzUqz`pzfozlnzrmzxkzwizwhzvfzvdzuc\ zuazt_ztZzsXzsVzrUzrSzqQzqPzqVzj_zddzYizSZzaOzkEzu\ FztGzsHzrIzqJzpKzoKznLzmMzlNzkOzjPziPzhNziMzjLzjJz\ kIzlGzmFzmWzUUzRRzOPzMQzK } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 29-03-08 (Not Quite There [6])
by Jim Muth 28 Mar '08

28 Mar '08

FOTD -- March 29, 2008 (Rating 6) Fractal visionaries and enthusiasts: Today's fractal began with great promise, but by the time the finished product was ready, the promise had all but vanished. I'm not quite sure what's wrong with the image. Maybe it's the colors, of perhaps the overly busy appearance. Maybe it's that the minibrot too closely resembles those in the more remote valleys of the classic M-set. But whatever it is, I could rate the image no higher than a 6. The name "Not Quite There" shows my disappointment. The formula of the parent fractal subtracts 1/2 part of Z^(-2) from 1/2 part of Z^2 and adds C. The parent itself consists of a scattering of Mandeloids, with today's scene located in a valley on the south side of the largest bud of the largest Mandeloid. In an attempt to add interest, I rendered the image with the outside set to 'tdis', which is the setting I use almost as frequently as the standard equal-iteration bands. The result was not all that I had hoped. The calculation time of 9 minutes could be faster, but it also could be slower. All calculation problems may be bypassed however by visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the finished image there. Friday started rainy here at Fractal Central, but by mid-morning the rain ended and by mid-afternoon the sun appeared. When the temperature reached 48F 9C, the day actually became quite pleasant. The fractal cats enjoyed the sun when it finally broke through. My day was notably average. The next FOTD will make its initial appearance in 24 hours more or less. Until then, take care, and be true to your fractals or they'll be false to you. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Not_Quite_There { ; time=0:09:20.96-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-1.56188992602/-1.56422169664/5.5e+007/\ 1/-37.5/0 params=0.5/2/-0.5/-2/0/0/0/0 float=y maxiter=5500 inside=0 outside=tdis periodicity=10 colors=000wnuwmuwktwitvhsvfsvdrvcrvaqv`qx`nqWhkSbd\ NXZJSSFMMAGF6A925B36D46F47G57I58K68M69N79P8AR8AT9B\ U9BWACYAC_BD`BDaAFb9Hb8Jc8Kc7Md6Oe5Qe5Rf4Tf3Vg2Xh2\ Yh1_i0ai0bb3eX6hQ9jKCmDFK7IK1LKU0`cezEGAGGFIGKKFPK\ FULFULFUIIUGKUENWCPYAR_9Sa8Ud7Vg6Xj5Yl8WmBVnEUoHSp\ JRqMQrPOsSNtVMuXLvVOrUQoTSlSVhRXeQZbPaZOcWMeTLhPKj\ MJlJIoFHqCGs9Fu6It9LsBNsDQrGTrIVqKYqM`pPbpReoTgoVd\ lYai_ZfaWccU`fRYhOWjLTlIQnGNqDKsAHu7Ew5Cy9DtDEoHEj\ KFeOF`SGWVHRZHMbIHeIDYEOQBZJ8hOBiSDiWGi_IicKigNikP\ ioSisUiwWipZdja`cdXYgTRjOLmKEpG8rCCqFFpHJpJMoMQoOT\ nQXnT_mVcmXfl_jlamkcqkftjhwjjvkkulltlltmmsmmrnnqon\ qooppooppnqpnrqmrqlsrlsrhqndpk`nhYmeUkaQjZMhWJgTZf\ _meekfbig`ghYzzWzzTzzRmzPmzMmzKUnHSoFRoDTjEUeFW`FX\ WGZRG_MHaHIbCId7Je2Jb5I`7IY9HWCHUEG_7_f5gd7hc8hbAh\ `Bh_DhZEhXGhWHhVJhUKhXOj_SkaVmdZngapieqliroltqputs\ wzzzyzyxxxxvxxuwxswxqvwpv } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 28-03-08 (In a Soiled M-brot [8.5])
by Jim Muth 27 Mar '08

27 Mar '08

FOTD -- March 28, 2008 (Rating 8.5) Fractal visionaries and enthusiasts: One of the reasons I am fascinated with fractals is because they are four-dimensional things, and I waste no end of time futilely trying to visualize a four-dimensional anything. Many phenomena in 4-D hyperspace have similar things in our familiar 3-D space, which help us to understand hyperspace. But there is at least one thing in 4-D space (I am sure many others exist.) that is totally unlike anything in our 3-D space. That thing is the motion called double rotation. In 3-D space an object rotates about a line as its axis, and due to the gyroscopic effect, that line will retain its orientation. But in 4-D space a 4-D object rotates about a plane as its axis, which makes the situation more complex. In a simple 3-D type of rotation, the points of a 4-D object describe a circle, while an entire plane of the object remains fixed in place as its points turn on themselves. And just as in 3-D space, the gyroscopic effect will keep the object rotating in the same direction. But what of that axis plane, where the points remain stationary, while turning in place? This is the weird thing. Since the axis-points are not moving, they are not subject to the gyrosco- pic effect, and the entire axis-plane can turn on itself around its center point, carrying the entire 4-D object with it, while the entire object continues to rotate in the first direction. The object is now in a state of double rotation, a motion totally alien to our familiar 3-D objects. While fantasizing a walk on a 4-D hyperplanet recently, and trying to imagine the apparent motion of the heavenly bodies, I realized that I was perilously close to visualizing double rotation, (as projected into 3-D space of course.) What I imagined is extremely difficult to put into words, but I'll give it a try in a near-future FOTD discussion. As for today's image, it lies in the parent fractal that results when 0.01 part of Z^(-2) is subtracted from the classic Mandelbrot set. This fractal is a distorted M-set, filled with debris. Today's image is located in the East Valley area of the remains of the large minibrot on the negative X-axis of the M-set. I named the image "In a Soiled M-brot", which the parent fractal most certainly is. I rated it at an 8-1/2 -- 8 points for the underlying fractal, 1/2 point for my coloring work. The calculation time of only 49 seconds means that no one will be disappointed with the result. Some may prefer to avoid the calculation however, so for convenience, the finished image is or soon will be posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Good weather in early spring never lasts long in Central Pennsylvania, so we were not too disappointed here at Fractal Central when Thursday turned out cloudy, chilly and drizzly. The temperature of 45F 7C kept people well wrapped, while the drizzly mist kept the rain gear handy. The fractal cats kept cozy near the heat. My day was on the busy side, though not too busy to affect the fractal. The next FOTD will appear in 24 hours. Until then, take care, and there is more to empty space than meets the eye. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= In_a_Soiled_M-brot { ; time=0:00:49.43-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident float=y center-mag=-1.230634995848692/-0.488602834129332/\ 1.201185e+011/1/140/0 params=1/2/-0.01/-2/0/0/0/0 maxiter=1500 inside=0 symmetry=none periodicity=10 colors=000WJLVIJUHITFGSEFRDDQtCPrAMp9Mn7MlkMjhMheM\ fbMd_MaYMZVMWSMSPMPMMMKMJHMGEMDBMA8aEKZDIXCGVBESAC\ Q9AO88dhkjGbgF_eEXcDU`CRZBOXBLVAIS9FQ8CO799aiAZeoo\ rmiskcsjYthStfMueHucPsbWracq`jp_roZynHWXJYVL_UNaTP\ cRQdQSfPUhNWjMXkLZmJ`oIbqHcrGanF`kEM87_hEZeDYbCWZC\ VWBUTATQASN9QJ8PG8OD7NA6nsA`dh_aeZ_cYY`XWZWUWVSUUQ\ RTOPSLNRJKQHIPFFODDNBAM98qrcoo`mlZkiXifVgcTe`RcYPa\ VN_SKYPIWMGUJESGCQDAOA8NKTMIQMHOMGMMEJMDHMCFMACM9A\ M88f3mb4e_5Z4c`4c`4aZ4_X6YV7WT8URASPBQNCOLDMJFJHGH\ FHFDJDBKB9L97zzzwwwsssooohfhc`aZXYXUUVSSTQQQOOOMMM\ KKKDCKA9z6gw7cs7`o7Yk7Vg7Td7Rb7P`7NZ7KX7IV7GT7ER7C\ M7AJ78zUKrOAgI9XC7sTHnQFjNEfKCbIBYFAUC8Q97Lr_MnYMk\ WMhUMeSMbQMZOMWMMTKMQIMNGMJEMGCMDAMA8bmz`hzZdzX`zW\ WzUSzSOzRJzPFHNBBDxNErLFlJGfHH`FIVDJPBKJ9LD7zyKwwK\ rrVmhYhcUbYQ_TMWNITIEPCAzqHmaD_M9TVESTDRRCRPCQNBQL\ APJAPI9OG9OE8NC7NA7M86YLN } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 27-03-08 (Going Ever Deeper [8.5])
by Jim Muth 26 Mar '08

26 Mar '08

FOTD -- March 27, 2008 (Rating 8.5) Fractal visionaries and enthusiasts: A rating of 8-1/2 for a fractal that takes 16 minutes to calculate is pretty unusual, but today's image is unusual enough to earn it. The name "Going Ever Deeper" refers to the magnitude of today's image, which at close to 3*10^13 goes beyond the limit of perfect resolution. The mathtolerance entry assures that the image will be calculated at the correct magnitude. The scene of today's action lies in the same area of the same parent fractal that gave us yesterday's image. The tiny minibrot at the center, which is beyond resolution, was most difficult to find. Nothing but pure instinct led me to it. To see the difficulty, reset the logmap to zero and return to the parent fractal. There is almost no clue at all that the minibrot exists. The calculation time of 16 minutes is admittedly slow, so I recommend visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and enjoying the fully rendered image there. With bright sun, puffy clouds and temperature of 61F 16C, Wednesday turned out to be the best day so far this spring here at Fractal Central. The local fractal cats must have agreed, for they spent the better part of the afternoon gazing at the outdoors that they never get to visit. My day was busy but made satisfying by the better-than-average fractal of the day. Tomorrow will likely be less busy. I have no comment about the next FOTD fractal, which will be posted in 24 hours. Until that semi-glorious moment, take care, and stop to wonder why fractals exist at all. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Going_Ever_Deeper { ; time=0:16:03.45-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=+0.23410086762640360/+0.069182405395851\ 56/2.761998e+013/1.0001/-85/0.026873983727 inside=0 params=2/1.25/1/2.5/0/0/0/0 float=y maxiter=5000 logmap=2030 periodicity=10 mathtolerance=0.05/1 colors=000JAJy2Lz0Lo9ilEfiJefNbbQa_UZXZXUbUQeTNiQK\ nOCsJHpNKnQOkTRhWWeZZbaaadeZfhWilTloQosNrvLtyJwzFz\ zCzz9zz5zz4zz2zz2zz2zz2yz1vz1sw1pv1ns0kp0hn0el0bi0\ _f0Xe0Ub0R_0OX0Lk0Jv0Fk0Cf09L05JH2ZE0b00X00X00N40R\ 90WE0_J0dN0hR0lW0p_0td0yh0zl0zi0zh0zf0zd0zb0ya0yZ0\ yX0yW0yT0yR0zQ0zN0zL0zK0zH0wF0uE0sA0q90o70m40l21k1\ 1j01i01h01g00f00d01c02c05c07c09c1Ac2Ec4Fb5HX7Kf9Le\ ANdCObERaFT_HUZJXXKZWL_UNaTOdRQeQRfTLkORhLXeJbbFha\ ClZ9rW5wU2zR0zO0zN1zR5zW9z_EzbHyfLvkOsoTprWnv_kzdk\ zbhzbfzaezadzabz_az__zZZzZXzZUzXTzXRzWQzWOzWNzULzU\ KzXHzUJzTJzRKyQKsOLnNLhKNbJNXHORFOLEQFER7CQ9CQACQC\ CQCCkzCQzCkzAkzAOzAOJAOKAOLAONAONAOO9NQ9NQ9NR9NT9N\ T9NU9NW5JK7LQ9NW9OaAQfARlCTrFZzCUwAQr9Ll7Jf5Ea29U1\ 5O01J00C005007207427757997CC7FF7HJ7KL7LO7OR7RU7TW9\ WZ9Xa9_d9bf9di9fl9ho9kr9nt9ow9rz9rz5sz7sz9tz9tzAtz\ CvzCvzEvzFwzFwzHwzJyzJyzK } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 26-03-08 (Only a Minibrot [7.5])
by Jim Muth 25 Mar '08

25 Mar '08

FOTD -- March 26, 2008 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image takes the same parent fractal that held yesterday's image and doubles the portions of both Z^1.25 and Z^2.5. In the resulting fractal, the two M-sets are no longer partially merged, but are now well separated, connected by only a narrow 'inside' N-S band centered symmetrically on the X-axis. Today's scene is located very near the point where this band intersects the X-axis. When rendered in the usual manner, the scene is rather dull and lifeless. So to add some life I rendered the image with the outside set to 'tdis' and the inside set to 'fmod'. The proximity factor of 11 was a mistake, but it worked so well that I decided to keep it. When the time came to rate the day's effort, I found enough pizazz in the image to rate it at a 7.5, giving myself a generous half-point for the coloring. The name "Only a Minibrot" refers back to yesterday's image, which held a gaping hole and an impressive spiral in addition to the minibrot, while today's image has only the minibrot. With a calculation time of just under 6 minutes, the parameter file borders on the slow side, but IMO, the small effort is worth it. And for instant gratification, the finished image may be accessed on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Near perfect 50F 10C early spring weather continued at Fractal Central on Tuesday, and the fractal cats continued to enjoy the sun. My day was unusually busy, but never beyond control. The next in the near-endless string of FOTD fractal images will be posted in 24 hours. Until then, take care, and dwell in peace in hyperspace, where I might soon take a tour of a hypersphere. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Only_a_Minibrot { ; time=0:05:54.49-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=mandautocritinz function=ident passes=1 center-mag=+0.233227944685145/+0.0082092285206308/\ 1.051e+007/1/-148.75/0 params=2/1.25/1/2.5/0/0/0/0 float=y maxiter=10000 inside=fmod proximity=11 outside=tdis symmetry=none periodicity=10 colors=000CszHkzNezT`uZVodPigTdkXZo`TsbPveJziEzr0z\ o4PH00000040CAUPPHdLRsR`zX000qzguzbvzXxzTzzNzzJzzE\ zzAzz4zz0zz0zz0zz6meL`H`P0oN8uLJxLXzJgzHuzHzzCzz8z\ z4zv0zq0zi0zd0zZ0zN0zE2z46z0Az0Cz0Cu0Em0Ee0EZ0GR0G\ J0GC0H40H00H00A602N00b00X20R80LG0GL0AR04Z00d00k00q\ 00v00q40m80iC0eG0`J0XN0TR0PV0JZ0Gb0Cd08e0Ae0Ce0Ee2\ Ge6He8JeALgH6gN0eL0dL6bLC`LJZLPXJXVJbTJiRJqPJvNHzL\ HzJHzHHzGHzGHzLNzRTqXZV`bAid8qe6xg4zi4zk2zm0zo0ze0\ zW0zO0z00u00e00T20GA080200020460AA0EE0JH0PL0TP0ZT0\ dX0g`0md0sx0ke0vP2z86z00z08z0Ez0Lz0Rz0Zz0dz0kz0qz0\ xz0zy0zx0zw0zv0zuAzuJzuRzu_uqfolnihkddibbl`bqZbpZb\ qXbpV`oT`pT`oR`oP`mN_kN_kL_iJ_vNjiJdZHTNGHC82CE8CJ\ CCPGCVLCZPCcTCcZCcbCceCckCcoCcsCcxCczCcz6cq0cd0cR0\ cE0c00c04cm8cmAcmCcmEcmGcmHcmLcmNcmPcmRcmTcmUcmVcm\ Zci`cebcbdc`ebXgZTiTR`czZcvZsqXqkXoeVm`VkVTiPTgJTe\ ERgLPiTNk`LmgJmmHouGqzEsz } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 25-03-08 (Hole-Spiral-Midget [6.5])
by Jim Muth 25 Mar '08

25 Mar '08

FOTD -- March 25, 2008 (Rating 6.5) Fractal visionaries and enthusiasts: Holes, spirals and minibrots -- today's image has them all. And there are layers also -- not artificial human-created layers, but real layers, created by the numbers themselves. All this, and the result rates only a 6.5. I'm not quite sure what the image lacks, maybe it is a well- defined focus of attention, but despite all the fractal goodies, I could bring myself to rate the image no higher than a 6-1/2. The slightly oversized parent fractal was created by the formula Z^1.25+0.5(Z^2.5)+C, and is shaped like two M-sets, one facing NNW and the other facing SSW, loosely connected along their main bays. Smaller minibrots lie just beyond the main buds of the two M-sets. Today's scene lies between the northern minibrot and the main bud there. I named the image "Hole-Spiral-Midget", the three things vying for attention in the scene. The calculation time of 4 minutes could be faster, but it also could be slower. All calculation may be avoided however by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Near ideal early spring weather prevailed here at Fractal Central on Easter Saturday, Sunday and Monday, with lots of sun and a temperature near 50F 10C each day. The fractal cats enjoyed the sun in their sunny window. I managed to survive the holiday with only a little annoyance. But the work for tomorrow looks to be heavier than usual, which could affect the FOTD. Regardless of the work however, the next FOTD, in glorious RGB color, will be posted in 24 hours. Until then, take care, and wonder about the things worth wondering about. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Hole-Spiral-Midget { ; time=0:04:00.62-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-0.78157556/+1.91021611/363.0164/1/-85/\ 5.219991e-013 params=1/1.25/0.5/2.5/0/0/0/0 float=y maxiter=5000 inside=0 logmap=40 periodicity=10 colors=000nI0c00Z00c00m00tL0m00c00U00U00U00U00U00U\ 00z00Y00Y00z00Y00Y00z00Y00Y00zU0Z00Z00m00Z00Z00Z00\ Z00ZNmZJlYFlZGkZHjZHiZIiZJh_Jg_Kf_Kf_Le_Md`Mc`Nc`O\ b`Oa`P``P`aQ_aRZaQYaQYaQXbPWbPVbPVbTUgUTgUScVScTRc\ TQcUP`ULcUPfSThRXiP`jNdkQfjQgjRgiNgjOhiOhjQhjQijRi\ jRiiSiiSjhTjhTjhTkgTkhTkgUlgUlfUlgUlgUmfUmgUmfUnfU\ neUneUneUodUodUocUpcUpbUpbUqbUqaUqaUq`Ur`Ur_Ur_Us_\ UsZUsZUsYUtYUtXUtXUuXUuWUuWUvVUvVUvUUvUUwUUwTUwTUx\ SUxSUxSUxRUyRUyRUyRUyRUyRUyRUyRUzRUzRUzRUzRUzRUzRU\ zRUzRUzQUzQUzQUvQUzQUzQUzQUzQUzQUzQUzQTzQSzQRzQQzQ\ PzQOzPNzQMzRLzRKzSJzSIzTGzUFzUEzVFzVGzWHzWIzXJzYKz\ YLzZMzZNz_Oz_Pz`QzaRzaSzbTzbUzcVzdWzdXzeYzeZzf_zf`\ zgazhbzhczidziezjfzkgzkgzkhzkhzkizkizkjzkjzkkzkkzk\ lzllzlmzlmzlmzlmzlmzlmzlmzmmzmmzmmzmmzmmzmnzmozmpz\ nqznrznszntznuzovzpwzqxzryzszztzzuzzvzzwzzxzzyzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 22-03-08 (Satiny Satin [8])
by Jim Muth 21 Mar '08

21 Mar '08

FOTD -- March 22, 2008 (Rating 8) Fractal visionaries and enthusiasts: DUE TO THE SPRING HOLIDAYS THERE WILL BE NO FOTD ON MARCH 23 AND 24. THE NEXT FOTD WILL APPEAR ON MARCH 25. Today's image lies in the fractal created when 1/2 part of Z^3 is combined with Z^1.5 and C is added. The parent fractal consists of two Mandelbrot sets connected like siamese twins into a single N-S stretched fractal with X-axis symmetry. Smaller disconnected M-sets lie N and S of the main fractal. Today's scene lies in the East valley area of the disconnected M-set on the northern side of the main fractal. When I saw the image with its crumpled, satiny interior, I had no choice but to name it "Satiny Satin". I would have given myself an extra half point for producing the satin effect, but it was the program, not I, that created the colors. Still, the rating of an 8 makes the 1-3/4 minute calculation time almost a bargain. Another bargain may be found at the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the image can be seen already calculated. Except for late afternoon clouds, the Friday weather was near perfect here at Fractal Central. With little wind and full sun, the temperature of 46F 8C felt just about right for the start of spring. The fractal cats agreed. My day was quite busy; the next two days will be busy also. The next FOTD will be posted in 72 hours. Until then, take care, and have a happy fertility festival. (Eggs and rabbits, as well as resurrections, are symbols of fertility and new life.) Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Satiny_Satin { ; time=0:01:45.36-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=+0.2127364819281549/+2.181650197032898/\ 2.3169e+010/1/-45/0 params=1/1.5/0.5/3/0/0/0/0 float=y maxiter=1800 inside=0 outside=tdis periodicity=10 mathtolerance=0.05/1 colors=000zizzkzzlzzlztizfgkRfXBdI0b20a00f00i04n0B\ q2Jw6Qz9YzDdzGizInzIszIxzIzzJzzJzzJzzJzzIzzIwzIpzI\ izIbzIXzI_zQbzYfzfgtnknwngzpbzxLiz2Gz00z40wN0nd0fw\ 0Yz0dx2kiEqVQxGaz1lz0ws09x8NzXYzsizllzfpz_szTtzNxz\ Gzz9zQ98N06RENXXarzzmzzbzzdxzfxyfxx_xxTrxNnxGix9bx\ 2Yx0Rx0NxkILgDRf9Yd6da2i_0pY0wX0zR0zO2zL8zIBzEGzBL\ z8Qz4TzBVwIXlOYbV_TaaIgb8nd0sd0kV0dL0YD0R20L00E00L\ 01R09X6IbDQiJYnQftXnzbtqVkiObaIVTBNL4ED06400806B0D\ D0LG0RI0YQ1QXBIdL9kV1qb0kd4fdGafRXfbRgnNgzIgz9dp2a\ X0YD0V0OO0z00zE1zzBzzzzzTz0az0kw0ss0pp8nnJlkTkgdgf\ pfbzdazbf00iD0lY0ps0bD1YT9TiGOzNJzTOTGT04990QO1fb6\ wpBkb9_R9OG9D49109001000000000100600B00G00N00R10X1\ 0a20f20k20f40a60X80R80N90JzzOzwTzpXzkazdfz_kzTpzOt\ zIxzDszGpzIlxLgqNdiOabRYXTTOVQIYN9_I2aE0dB0f80gG0a\ N0VV6OaEJgNDpV6wb0zi0zg1zf6zdBzbGzbLTVROiDJx0Ot6Tq\ EYnNalTfiakfindpqfttgxxiz } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 21-03-08 (In a Secret Garden [5.5])
by Jim Muth 21 Mar '08

21 Mar '08

FOTD -- March 21, 2008 (Rating 5.5) Fractal visionaries and enthusiasts: Today's image rates only a 5.5, but that's how it goes when I have no time to work on the coloring, which turned out quite a bit too purplish for my taste. The name "In a Secret garden" sounds more like the title of a cheap bodice-busting romance novel than the name of a fractal. The image lies near the negative X-axis of the parent fractal that results when 0.5 part of Z^3 is combined with Z^1.5 and C is added. To try to make something from nothing, the image was rendered with the inside set to 'fmod'. The result is hardly worth the 8 minutes required to run the included parameter file. I recommend viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where it is or soon will be posted for instant viewing. The first day of spring turned out rather blustery and chilly here at Fractal Central, with more clouds than sun and a tempera- ture of only 39F 4C. The local cats took advantage of the few minutes of sun, and stayed by the heat the rest of the time. Due to the upcoming holiday, my day was unusually and unexpec- tedly busy. But holiday, holy day, or not, the next FOTD will be made public in 24 hours. Until then, take care, and what's it all about anyway? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= In_a_Secret_Garden { ; time=0:08:03.67-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-0.30956628123146/+0.03096772886562/\ 202890.6/1/7.5/0 params=1/1.5/0.5/3/0/0/0/0 float=y maxiter=5000 inside=fmod proximity=0.7 periodicity=10 colors=000poplPUdWYYcaQjeIriBymGroLlpQfqU`rS_mR_hQ\ _cP_ZO_UN_PM_KPYORXSUWVWVZZUb`TebNicImdCqe7uf2yd7o\ bCf`GYZLPXPGRUOMZVHbaCgi7lp2pwAauINs6jYamUboObqIbs\ Dbu7bv2_nBXgJVaGTWERRBPL9NF6LA4OH5RO6UU6X`7_g8bj8e\ k9gh9daJaST_JaXIYUJVRPRPUOP_KUdHZjDcoAhpFmqJrrOvrS\ zsXvt`mtdcmaXg_Q`XLVVGPTEIQCCOB6MGCPLHSQMVURXWOYYL\ Z_I_aG`cDaeAbg8cbDeZHfULhQPiTQgWQeYQd`QbbQaeQ_gQZk\ YYndYqkXtrXNScMO0GV6BaC6hI1oN6mJAkFEiBIg7Id8Ia9JYA\ JVBKRCvh2ll3bo4Us5Kv6By6HsJNnVThgYcsP_hHWZ9SO1PE5c\ R8rcFshMtlTuq_vuewydvpdugduZctQcsHcs9Q`PDIdrIYo_Yl\ qXem_ZicSdgL`jEXn7SrMRr`PrpNqmNrjOsgPtdQuaRvZSwZ9n\ _Cj`FfaHcaK_bMXcPTcRQi_LnhGtqByz6oqAeiDWaHMUKDMNGQ\ QIUSLXUN`WQdZSg`VkbXndUheRbfOXgLRgNSfOTePUdQVcRVbK\ ShEQn7Nt1Lz5Pt8TnBXiE`cHdYKhTNlNQpILfFGXCBN97D7FD7\ OD6XD5dD5mD4lZviUqfQmcMi`IeYEa`AYeJUlOKoVBu_2rX9nT\ GkPM000dF_aKedMhgOjjSjhRj } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 20-03-08 (Darkest Terraces [7])
by Jim Muth 20 Mar '08

20 Mar '08

FOTD -- March 20, 2008 (Rating 7) Fractal visionaries and enthusiasts: I often see TV shows about true-believing psychics who know that psychic powers do exist, and I see TV shows about true-disbelie- ving skeptics who know that such powers are not real, and both sides are adamant in their opposing convictions. My opinion is that both sides are correct. Psychic powers are not real but they do exist. (Don't ask for an explanation, just add this paradox to the long list of other paradoxes uncovered by our old friend, 'modern science'.) The dispute is as silly and meaning- less as debating whether fractals exist. Fractals are not real, but they do exist -- just like ghosts and bigfoots. Take today's fractal image for example. Run the included para- meter file and a minute later you will see the image on your screen. There is no doubt of it, fractals do exist, for you can see one with your own eyes, and what you see most certainly does not exist only in your mind (whatever that means). But now try to find the physical object that was photographed to produce the image on the screen. No matter where or how far you search, you will never find the actual physical object. No such object exists. When we imply the fullest meaning of the word 'real', fractals do not quite measure up. Today's image lies in the parent fractal that comes about when various portions of Z^3 and Z^5 are combined and 1.038i is added to initial Z. I think this is the first time I have used the ability of the MandAutoCritInZ formula to vary the automatically preset value of initial Z. The result appears a lot more like a critical fractal than the one the formula calculates automati- cally when imag(p4) is left at zero. But the resulting fractal is not exactly critical. Today's image shows a 'dry valley', which is a sure sign that a fractal is not exactly critical. To add interest I rendered the image with the outside set to 'tdis' and the inside set to 'fmod'. The result reminds me of vaguely threatening terraces, so I named the image "Darkest Terraces". The calculation time of 1-2/3 minutes will pass like lightning for the true fractal fan. The trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to view the finished image will also pass like lightning. With a temperature of 48F 9C, it was not too chilly here at F.C. on Wednesday, but thick clouds, fog, and near continuous showers kept it far from being pleasant. The fractal DSH cats agreed, and spent the day sleeping on the couch. My day was uneventful; the work was finished by 3pm. If the next 24 hours are just as uneventful, the FOTD for March 21 will appear at the end of that period. Until then, take care, and where was the Mandelbrot set 100 years ago? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Darkest_Terraces { ; time=0:01:38.10-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-0.002723103650706/+1.392157872857252/\ 91400.53/1/62.5/0 params=1.3/3/0.67/5/0/0/0/1.038 float=y maxiter=1500 inside=fmod proximity=0.001 outside=tdis logmap=yes periodicity=10 colors=000REibGgaHe_IcZKaXL_WNYUPWTSURUSRWSQYSQWTP\ VTPUTPSRQQPQOORMMRLKRKJQIHPHFNEEMCCK9AK79MCAOJAQMA\ OPBOSBQVBSZCUcCWhCYlCXiBXgBXeAXcAWaAW_9WX9WV9WT8VR\ 8VP7VN7VK7VI6UG6UE6UC5UA5U85S98QABOBEMCHKDKIENGFQE\ GTDGVEFTFFSFFRGEQHEPHEOIENJDMJDLKDKLDJLCHMCGNCFNCE\ OBDPBCPBBQBARA9RA8SA7SA6TB6TC6TD6TE6TF6TG6TG6TH6TI\ 6TJ6TK6TL6TM6TM69okBpiCpgEpfFpdGpcIpaJp`KpZMpYNpWO\ pVQpTRpSSpQUpPVpNWpMYpKZpJ_pHapGbpEcpD4_65a76b77c7\ 7d88f89g89h9Ai9Bk9Bl9CmADnAEpAEqBFrBGsBGuCHvCIwCIx\ CKwDLwEMwFOwGPwHQwHRwITwJUwKVwLXvLYvMZvN_vOavPbvPc\ vQevRfvSgvThvTfsUeqVdoWclWbjXahY`fY_cZZb_Ya_X``V_a\ U_bTZbSZeR_jQ_oP_tO`xNazMazLazKazJazJazIazIavIarHa\ mHahH`cG_cGZbFYbFXaFWaEW`EW`EW_DW_DXZDYZDX_DW_DV_D\ U_DT_DS_DS_DR`DQ`DP`DO`DN`DM`DM`ER_EV_EZ_FcZFgZFkZ\ GgWGdUG`SGYQGUNGRLGNJGKHGHFJKGMNHOPHRSITVIWXJY_J`b\ KcdLegLhjMjlMmoNoqNjoRemV } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 19-03-08 (E-Va-Po-Ra-Ted [7])
by Jim Muth 18 Mar '08

18 Mar '08

FOTD -- March 19, 2008 (Rating 7) Fractal visionaries and enthusiasts: Today's image is evaporated, which means that all points on the screen, though they might have wandered far afield, are ultimately 'trapped', and will never escape to infinity. Without the active 'bof61' inside fill, the image would be a totally blank screen. The parent fractal came about when I combined various negative portions of Z^(-6.6) and Z^(-1.6), then added (1/C). This parent is a large elliptical hole in a blank background with a small triangular area of chaos on its inside. A circular hole lies inside this triangle, with something resembling an obese gingerbread-man inside the hole. Small localized areas of semi- chaos are scattered around the outer edge of this gingerbread- man, and today's scene lies in one of these small chaotic areas. I named the image "E-Va-Po-Ra-Ted", which tells that it is not really there. I rated it at a 7 because that's what I think it's worth. The calculation time of 36 seconds is unusually short, though the finished GIF image may still be viewed without the need of calculation on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Tuesday started cloudy and chilly here at Fractal Central. The rain arrived in the afternoon and continued through the rest of the day, while the temperature of 43F 6C did nothing to help things. The cats of F.C. spent the day ignoring the weather. My day was a bit on the busy side, though nothing that could not be handled. The next FOTD is due, and will appear, in 24 hours. Until then, take care, and with fractals, reason sometimes leads to the wrong conclusion. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= E-Va-Po-Ra-Ted { ; time=0:00:36.38-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident center-mag=+0.2246660595676335/-0.289955784158471/\ 1.606143e+013/1/-60/0 params=-0.1/-6.6/-6/-1.6/0/\ 1e+100/0/0 float=y maxiter=1500 inside=bof61 periodicity=10 mathtolerance=0.05/1 colors=0004Xr2UwAIrF4pK0mP0jU0g_0ep0zz0zz0zb0z00_0\ 040470NA0zA2VIPUmd2Uh0Ub0I4000700K0AU0Se0gpUuzzzzz\ uzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzUcz_Fzbbzezzgzzjzze\ zwbzr_mmUSgS7bP0XN0SK0NK0IK0FK0AI04I00I00I00N02P04\ U04X07b0Ae0Ag0KU0UIIe4_p0rz0zz0zp0zX4mINS0e70u04z0\ Nz2ezAwzIzzPzzXzzbzzezzggzjNzm0zp0ur0ru0zg0zU0zI0z\ 40z00z02r27b7APCCCIU0Pm0Xj0_g0_e0_b0__0bX2bU4bU7bP\ SgKmmFzrAzw7zzbzezzIzz0uz_Czz0zzAgzjKzz0zz0zz0zz0z\ u0zp0zg0zb0zX0zp0uzUUzz2zz0zz0bz04zA0zK0r00A0AF0UK\ 0pP0zU2zXPzXmzXzzKzr7zb0zN0z70z00z00z00z22zCCzS7wg\ 2jw0Xz0Kz07z00z00XNzz04z4AzAFzCKzIPzKUzXgzjuzwzzzz\ zzzwzzpzzgzz_zzSzzKzzCzzNzzUzjbzUjzFrz0zz0zz0zz0zU\ 0z0Xz0IAb20z00w00e02N0I40U00X20_F0bU0eg0gu0jz0mz0m\ z0Sz07z00z00z7NzjzbzjgpImK0r00u00m00e0I_I_S_rKuzFz\ z7zz2zz0zz0zz0zz0zr0zb0zNNz7mz0zz0zz0gz00_04b0KbCX\ eUmepzgzzgzzbuz_pzXzze7_m } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 18-03-08 (Deeply Fractured [6.5])
by Jim Muth 18 Mar '08

18 Mar '08

FOTD -- March 18, 2008 (Rating 6.5) Fractal visionaries and enthusiasts: Today's image exists in the Z^(1.2)+C Mandeloid as it appears PI levels up the complex logarithmic ladder when no function is applied. The parent fractal at this level isn't much to look at, but it is surrounded on its west side by bits and pieces of cut-off spirals, and the image sits on a node of one of these pieces of a spiral. Actually, the pattern around the tiny minibrot at the center is unusually well organized for a scene in a fractal in this low exponent range, with tiny cut-off pieces of spirals hiding every- where, and the 4-way near-symmetrical arrangement of elements adding just enough interest to raise the rating to a 6.5 The name "Deeply Fractured" describes the broken-up nature of the scene. The calculation time of just over 1 minute will cause no one to lose patience. And if all else fails, the fin- ished image is or soon will be posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Monday turned out very pleasant here at Fractal Central. There could hardly be a better way to end winter than with a Saint Patrick's day of full sun and a temperature of 48F 9C. The local fractal cats must have agreed, for they got into a tussle over who would sit in the sunniest window. My day was mostly average; tomorrow should be the same. The next FOTD will be posted in about 24 hours. Until then, take care, and when science tells us that the universe is about 13.7 billion years old, what is doing the talking? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Deeply_Fractured { ; time=0:01:01.73-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident float=y center-mag=-2.704804574677948/+1.557515314601944/\ 4.747e+009/1/-10/0 params=1.2/0/3.14159265358979/0 maxiter=2400 inside=0 logmap=154 periodicity=10 colors=000F2EL5HR7KX9NbBQcETcGWcIZcKanbXcsdTzifzfz\ h0zzUQhNPXHOPAOF4xlpsohoqaksUguNhlPidQiXSjPTjHUcIV\ zIKzIKzIKgJXgJXfJYfJYdGTbEO`BJ_9Fm6Am45V21Y2B`2Lc2\ Ve2daLdZbdWtd_o_bjWfeSi`NzWJzRF8k09i29g39f59d69b89\ a9AdABfACiBDkBEnzFpzGsCGuCInFJhHLaJMWLNPNPJPQCRR6T\ N5VJ5XF5ZC4_84a44c14d86cE8cKAcRCcXEcbGccN`cTZc_Xce\ UclScrQcxOP`TBEXBMRBUKBaEDcFEdFFeFHfFIgFJhFLiFMjFN\ kFPlFQmFRnFToFUpFVqFWrFYlE_gEabDcYDeSCgNCiIBkDBm8B\ k9EjAGhBJgCLeDOdEQcFSaGV`HXZI_YJaXKc_LgaLjdMmfMpiN\ skNviOuhOtgOsfOrdOrcOqbPpaPo_PoZPnYPmXPlWPlZUiaYgd\ aefeciialm_nqYopWopVooUooTooRonQonPonOomNomLomKolJ\ olIolHkjFhiDdgBaf9Ze8bg7eh7ii7lj7pl6sm6wn6zo6tpBnq\ FhrKcsOYtSSuXMv`HwdBxi5ym0zq9znHzkPziYzfezcmzaizce\ zeazgYzhUzjQzlMznIzoHznHznGznGznGznFznFznEzmEzmEzm\ DzmDzmCzmCzmCzmEzkGzjIzhKzfMzeOzcQzaSz`UzZWzXYzWVz\ UazWezVizUmz9qzBtzDwzFzzH } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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FOTD 17-03-08 (Deeply Evaporated [8])
by Jim Muth 16 Mar '08

16 Mar '08

FOTD -- March 17, 2008 (Rating 8) Fractal visionaries and enthusiasts: Today's evaporated image has its problems, but despite its difficulties, it still rates a solid 8. Perhaps its greatest problem is that its magnitude of 1.67*(10^13) is beyond the range of perfect definition. But the resulting jagged edges actually add a kind of atmosphere to the scene. The parent fractal came about when I combined 7.5 negative parts of Z^(-1.1) with 0.75 negative part of Z^(-11.4) and added (1/C). It's a typical fractal of its type, with a N-S oriented string of large bays and a very prominent 'fan' extending east along the X-axis. Today's scene lies very deep indeed in one of the small areas of chaos on the bay-side edge of the fan. I named the image "Deeply Evaporated", which pretty much describes it. The calculation time of just over 6 minutes is a bit slower than ideal, but still well worthwhile for an image rating an 8. Of course, all thoughts of calculation may be banished by visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and enjoying the finished image there. Sunday turned out to be quite pleasant here at Fractal Central. There was not quite as much sun as on Saturday, and the temperature never rose above 45F 7C, but I actually did nothing for most of the day, which, after yesterday's workout, seemed perfect. The fractally-inclined cats agreed. The next FOTD will make its much-anticipated (I hope) appearance in 24 hours. Until then, take care, and how could the 'Big Bang' have made such a big bang if no one was around to hear the sound of the mighty explosion? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Deeply_Evaporated { ; time=0:06:12.34-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+1.537355049906006/+1.289379920883854/\ 1.677409e+013/1/79/0 params=-7.5/-1.1/-0.75/-11.4/\ 0/1e+100/0/0 float=y maxiter=1800 inside=bof61 periodicity=10 mathtolerance=0.05/1 colors=000KXLHg7If9IeAJdBJcDKbEKaFL`HL_Ifm5el6dl6c\ k7ck7sj8aj8ii9`i9_hAZhAZgAYgBXfBXfCWeCVeDUdDUdETcE\ ScFSbF`5H_DEZKBYR8XY5Wd2Vc4Uc5LZJTb7Sb8RaAQaBP`CO`\ EN_FM_H00MLsqLqoLpmLokLnjLmhLlfLkdLjcLiaLh_LgYLfXL\ eVLdTLcRLbQLaOL`ML_KwSKuTJtTJsTJqTJpUJoUJnUJlUJkVJ\ jVJiVJgVJfVJeWJInEHhBHc9HZ7HT4HO2HJ0gsqZngRiYJdOB_\ E3W4APMGIcMCuNPsOaqOmoPolQpjRqhSsfTtdTubQkXObSMTNJ\ KIHADF18HEDUTUJaMKmRLyVUnWacWjTWrIWz7WyBUyESyHQxLO\ xOMxRLqUHkWDeYA__6Ua3_Y6dV9`RDYNGVKKSGNOCQL9UI5XF2\ _S3Vd4Qq4MrFRsPVsZ_thctrgaaTKME260c0Jf5HhAGjEElJDn\ NCmKImIOmGTmEZlBdl9il7ol5to4pq4ls3iu3ew2ay2Zr4Tk5O\ d6JY7EcHPiR_o`jvzztdutZusTusNurHurBur6uuExxLzqTrk_\ jdgbZnV000acPi`QqRRyHRVLXn9iZRZzbbeYelUgeQjZMlTInW\ QmYYl_dkZdjZdiYdhYOgXcfnSjWcdWWcVbbVUaUb`Ua_TaZTQY\ SaXROWR`VQ`UQ`TP`SP_RO_QO_PN_ONZNMZMMZLLZK93jA6gB9\ eCBcDE`EHZFJXGMUHPSIRQJUN } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 16-03-08 (Typical Rings [No Rating])
by Jim Muth 16 Mar '08

16 Mar '08

FOTD -- March 16, 2008 (No Rating) Fractal visionaries and enthusiasts: Sorry for the late FOTD. On Saturday I unwisely volunteered to get the end-of-winter yard work started here at F.C. But what began as a 2-hour job turned into a job that was only half finished at day's end. As a result, the fractal for today suffered. Today's quickie image deserves no rating, and I gave it none. The name "Typical Rings" describes the appearance of the image, with its rings that are so typical of fractals of this double- negative type. The calculation time of 2 minutes means that no one will have invested much effort if they are disappointed by the image. And the finished product will be available on the FOTD web site as soon as Paul can get it posted. The web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A cloudy morning on Saturday was followed by a sunny afternoon with a temperature of 57F 14C here at Fractal Central. The fractal cats approved of these conditions. My day was over-occupied by outside work. I expect tomorrow will be much better. The next FOTD will be posted in around 12 hours. Until then, take care, and turn to rational science for some of the answers. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Typical_Rings { ; time=0:02:03.01-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+1.60777245459127900/-8.336287136733802\ 00/5.021824e+008/1/-145/0 params=-5/-1.15/-0.75/\ -7.5/0/0/0/0 float=y maxiter=1500 inside=0 logmap=160 periodicity=10 colors=0000AA0AA0AA0AA0AA0AA0BA0CA1D85E7AH9FKAKNBP\ QDUTEZWFcZGhaImdJrgKvjMzmNzpOzrPzeJzTDsH8mLBhODbRG\ YVISYLN`NHdQCgS7jUKlXWmZgnaimYkkUdhKYeAXbBX`CXZDWX\ EWVFWTGVRHVPIVNJVLKUMOTMRSMVSNYRNaQNdQOhPOkOOoOOrz\ UKzkIzw0zv3zzzzzzzzzzzzzzzzzzzqOzpRzpUHoXFn_DnbCme\ Alh9ljFjeKi`QhWVgS_eNedIjcDob9kXAhSAeNAaIAZDAW8AT3\ ALF7DQ5MHIU8Va0gcIke_ngqqfmpfioffnfbmf_lgZkhcziczi\ czjczkczlVzlUzmUznTfoSeoSeiPjdNoZKtUIyWItXIpZIk_Ig\ `IbbIZcIVdIQfIMgIHhIDjI8kI4lI0mH5mG9nFEnEIoEMoDRoC\ VpBZpAcqAgq9kr8pr7tr7xeMlT`aWXcZUfaQhdNkgJmjGpmCrp\ 9tmBsjDsgFreHrbJq_LqYNqE_oVPpSRpPToNVoKXnHZnRcWPcZ\ Oc`MccLceJcgIcjGclGcjFclFcmAcr7cvBcrZUNXUQVUSUUUSU\ XQZZPc`NhcLmeKrgIvjGzlSzlLzmGz4Fz9FzDFzHFzMFzQFzUF\ zYFzbFzfFzjwz_pzbjzdczfYzhRzjLzlZzcXzdVzeUzfSzgQzh\ PziNzjLzkKzlIzmGzn7zB8zF9zJAzMAzQBzUCzXDz`DzdEzgFz\ kCzQDzSDzUDzVDzXDzZEz_Eza } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 15-03-08 (Forever Fractal [8.5])
by Jim Muth 15 Mar '08

15 Mar '08

FOTD -- March 15, 2008 (Rating 8.5) Fractal visionaries and enthusiasts: Unless I'm mistaken, today is that ill-fated day, the Ides of March. And what better way to celebrate the day than with a fractal. The fractal in question is a near-Julia set of the Seahorse Valley area of the (-Z)^1.44+C Mandeloid. The difference between a near-Julia set and a pure Julia set is immense. To see the difference, change the (p2) parameter to 0,0 and re-run the parameter file. Actually, a near-Julia set is simply an oblique slice through the four-dimensional Julibrot figure, very close to but not exactly in the Julia orientation. The unusually terraced effect of the image was created by rendering it with the outside set to 'tdis', which draws the bands according to how far the points travel before passing beyond the escape radius. I named today's image "Forever Fractal". Fractals are creations of mankind as much as the complex numbers that bring them into being. I rated it at an 8-1/2, including an extra 1/2 point for my coloring expertise. Finally, the calculation time of 2-1/2 minutes should cause no one to feel impatience. And as always, the finished image is available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> An unusually pleasant day graced Fractal Central on Friday, when lots of sun and a temperature of 61F 16C brought out the best in both man and cats. The lighter than expected work gave ample time to enjoy the outdoors. Unfortunately, rain moved in just after nightfall, and Saturday will not be nearly as pleasant. But whatever, the next FOTD will appear, probably on schedule in 24 hours. Until that enlightening moment, take care, and to where is our over-developed intellect and under-developed wisdom leading us? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Forever_Fractal { ; time=0:02:31.65-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=EvenMoreSlices center-mag=-0.289695/0/\ 1.253133 params=1.44/0/0.004/0.004/-0.7393818/\ 0.0302556/0/0 float=y maxiter=10000 inside=0 outside=tdis periodicity=10 colors=000HhzHczGZzGUvFPmEKcEFUD0K70BA0CD0DF0EI0FL\ 0GN0HQ0ET0BQ18T49V79XA9ZD9`F9bI9dL9gOAiRAkTAmWAoZA\ qaAsdAze7wf9ufAsfCqfDofFmfGkfIhgJfgLdgMbgO`gPZgRXg\ SUhUShVQhXOhYMh_Kh`IhbFicDieBif9ih7ii5ik1kn3il5gk7\ fj9diBbgCafE_eGZdIXbKVaLU`NS_PRZRPXTNWUMVWKUYIS_HR\ aFQaEPbCNcAMd9Le7Kc4Dc5Ge6Jg7Mi8Pk8Sm9VoAYqB_rCbsC\ etDhuEkvFnwGqzFwxGuwGsuGqtGorGnqGloHjnHhlHgkHeiHch\ HafI_eIZcIXbIV`ITeMLbKP_ISXGVUEYRC`OAcL8fJ7iK9hLBh\ MCgNEgNFfOHfPIeQKeRLdRNdSOcTQcURbVTbVUaWVaXV`YW`ZW\ _ZX__YZ`_Za`YbnYas`boZbkYbgXbdWb`VbYUbWTbTSbQRaOQ`\ LP_IOYEOYGNZHN`JNaKNbLNcNMcOMcPMcRMcSMdULdVLdWLdYL\ dZLd_LeaKebKedKeeKefKfhJfiJfjJflJfmJgoHfnJfmKflMek\ NejOeiQehRdgTdfUdeVcdXccYcbZca`b`ab_cbZdbYeaXgaWha\ Vi`Uk`Tl`Sn`Ro_Qp_Pr_Os`Lu_Nt_OtZPtZQtZRtYTtYUtYVt\ XWtXXtWZsW_sW`sVasVbsVdsUesUfsUgsThsTjrSkrOlzNmzNm\ zMmzMmzLmzKmzKmzJmzJmzImz } frm:EvenMoreSlices {; Jim Muth ; P1--exponent, P2--angle, ; P3--M center, P4--J center, z=pixel+(p4), c=p3+(pixel*p2): z=(-z)^(p1)+c, |z| < 16 } END PARAMETER FILE=========================================

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FOTD 14-03-08 (Arc of Evaporation [7.5])
by Jim Muth 14 Mar '08

14 Mar '08

FOTD -- March 14, 2008 (Rating 7.5) Fractal visionaries and enthusiasts: The March issue of 'Sci-Am' magazine has an article about the expanding universe that I found interesting. It appears that in the unimaginably distant future the universe will have expanded until all the galaxies except those of the local cluster will have receded beyond the event horizon. And also by that time, all the galaxies in the local cluster will have condensed into a single giant elliptical galaxy, consisting of very slowly dying red-dwarf stars. The most distant objects visible will be dim red stars perhaps 200,000 light-years distant, and all evidence of the expansion of the universe and therefore of the 'big-bang' that we presently assume created the universe will have vanished. If any astronomers still exist in that remote future time, the thought of an explosive 'big-bang' origin of the universe would never have entered their minds. They would have no clues as to how the 'universe', which by then would be a single elliptical galaxy filled with small dying red stars, came into existence. Most likely the astronomers of the year 10-trillion would invent ingenious scientific theories that would appear logical to them, but would seem ludicrous to us with our present broader view. Of course, when we consider our current 'big bang' hypothesis, we are in the same situation as those distant future astronomers would be. We have no idea of what might have caused the assumed 'big bang' that created the universe. The simplest way out is to brush the problem aside by claiming that time as we know it did not exist before the 'big bang'. If we assume this, we can then claim that it is meaningless to ask what happened 'before' the 'big bang'. But this is really spinning our way out of the problem. As I said a week or two ago, we don't even know what we don't know, and this is especially true of me. I do know something about today's image however. It exists in the same parent fractal as the past 3 days' images, and lies just beyond the edge of the 'fan'. The name "Arc of Evaporation" describes the prominent dividing line that runs diagonally through the image and separates the 'evaporated' from the 'unevaporated' parts of the scene. This apparently straight line is actually an arc of a circle that is centered at the origin of the parent fractal. The line appears straight because only a tiny part of the whole circle is visi- ble. The evaporation is spreading from the lower left toward the upper right, and is controlled by changing the escape radius, which is set by the imag(p3) parameter. To add a bit of spice, I rendered the scene with the inside set to 'atan', though a couple of the other inside fills also do a good job. After careful study, I rated the image at a 7-1/2. The calcula- tion time of under 1-1/2 minutes is speedy enough for all but the most restless fractalists. And as always, the finished image can be seen on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> An enjoyable end-of-winter day prevailed here at Fractal Central on Thursday, with sunny skies and a temperature of 54F 12C. The cats of F.C. were more concerned with the local pigeons than the generous sun. My day was as close to normal as days get. With any luck at all, tomorrow will be the same. The next FOTD fractal will appear in 24 hours or so. Until then, take care, and time will never come to a complete halt, but it will never stop slowing down either. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Arc_of_Evaporation { ; time=0:01:24.43-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+5.507580654866794/-0.4053643733147778/\ 2809.232/1/35/2.96780140046637442e-009 params=-5/-1.15/-0.75/-7.5/0/76235000000.0/0/0 float=y maxiter=800 inside=atan periodicity=10 colors=000d0aa0dZ0hW0iT0mQ0zN0zL0zI0zG0zD0zA0z70z4\ 0z20z00z00z04z0Bz0Iz0Oz0Wz0cz0kz0sz0zz0zz0zz0zz0zz\ 0zz0zz0zz0zx0zv0zt0zq0zo1zl2zk4zh6zf7zd9zf9zf9xf9v\ f9sfAofAlfAkfAhfAdfBafB`fBYfBVfBTfAQ`9OW7NR6LN4KI2\ ID1H90G40E00D00E00E00G01G01H01H01H02I02I02K04K04L0\ 4L04L09O0DQ1HT2KV4OY6TZ9YaA`cBdfDihEnkHqqIvxKzzczz\ NzzuzzKzzHztDylAvd6tY2qQ0oI0nB0o60q00s00v00u02u04z\ Q6zQ7zQAu0Bv0Dw0Ew0Dw0Bt0Bs0Aq0An09l07i07h06f06k49\ nGBqQDtaGxlHzyKzzLHWWDY`AZd7`h4al1cq0dt0fy0fz0`x7V\ tDQqKKlQGiYAfc6ak0Zq0Wi0`a0cW0hO0kH0oB0sG0qK0qN6oR\ AoVGnZLnaRlfWliaknhkqlktkaxiTyhKzfBzd2zc0zOLzAlz0z\ lHkTcKGiN2nO0sQ0oT0lW0kY0h`0da0cd0`f0Yi1Wk2Tn2Ro1T\ f1VZ1VR1WI1WB1Y41Y09Q9GKKNEWV9ha2sWAoQHlKOkEWh9af9\ af9af9`f9`d9`d9`d9`d9`d9`c9Zc9Zc9Zc9Za9Za9Za9Za9Ya\ 9Y`9Y`9Y`9Y`9YZ9YZ9WZ9WZ9WY9WY9WY9WY9VY9VW9VW9VW9V\ W9VV9VV9TV9TVz0Tt0Vo0Yi0` } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 13-03-08 (The All-Seeing Eye [?])
by Jim Muth 13 Mar '08

13 Mar '08

FOTD -- March 13, 2008 (Rating ?) Fractal visionaries and enthusiasts: Today's curious image reminds me of the pyramid with the all- seeing eye on top, which appears on the back of the U.S. one- dollar note. There are all kinds of legends as to exactly what the symbol means. One of my favorites is that the world's most powerful governments are secretly under the control of space aliens from the Sirius or some other nearby star system, and the eye represents the watchful eye of the aliens, who keep constant watch over us to prevent us from destroying ourselves. This might or might not (probably not) be true, but one thing for certain is that the empty area in today's image is not your everyday minibrot. The image lies in the handle of the fan of the parent fractal, which is the same parent that gave us the past two day's images. For added interest, the scene has been evaporated and the remaining inside stuff resurrected by the bof61 inside fill. There is also a bit of skewing in the image, to straighten the all-seeing pyramid. I had no luck at all trying to decide what rating to give the image, so in the end I let it go with a question mark. The calculation time of 13 minutes is admittedly a bit burdensome for an image of such questionably quality. But if curiosity gets the better of you, and you have no desire to calculate, your desire may be satisfied at the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the image is or soon will be posted for immediate viewing satisfaction. Well, my thunder was stolen by the 'dark and stormy night' web site. Yes, the line first appeared as the opening of the 1830 novel "Paul Clifford" by Lord Bulwer Lytton. But I have a 100- year-old book of the entire novel lying next to me as I write this, and the last sentence of the novel is almost as hilarious- ly terrible as the first sentence. In fact, the whole novel is hilariously terrible. The last sentence, which is printed in capital letters, reads, "THE VERY WORST USE TO WHICH YOU CAN PUT A MAN IS TO HANG HIM!" But my favorite version of the opening sentence, perhaps penned by snoopy on his dog house, perhaps partly altered by myself, reads, "It was a dark and stormy night -- a door slammed, the maid screamed, a pirate ship sneaked into the harbor, guns blazing!" A cloudy morning, partly cloudy afternoon, and a temperature of 45F 7C made Wednesday notably un-notable here at Fractal Central. The cats of F.C. were not at all impressed. I am enjoying the return to near normalcy here at F.C., and if nothing goes awry, tomorrow will be another near-normal day. The next FOTD will appear in 24 or so hours. Until then, take care, and what if time has no end, but what if it does? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_All-Seeing_Eye { ; time=0:13:07.30-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip center-mag=-0.23700214367252690/+0.051971778823846\ 56/3.277993e+009/1/-17.4999973863296674/-24.921469\ 1935744206 params=-5/-1.15/-0.75/-7.5/0/9.99999999\ 9999999e+074/0/0 float=y maxiter=5000 inside=bof61 periodicity=10 colors=000C16603RHQIBH958NKPHFIBAC5561QoNmnH`aBPPl\ RhMEsbJtsOurMpqKlpIhoGdn3YoF`pRcrhcpafoWhmQjlKljEn\ i8ph2rb5lY8fTB`OEWJHQEKK9NE2FA4Q95_80g96i7Ck5Il3On\ 1CDiLXNTo0NeUWStIXwK9PCNg4`zDWrMRjVMccHWlCOt8H9QxI\ bqRokSiiTdgU_eUUcVPaWK_yOujJiWFYp04Z6EHBNLDLOFJSHH\ VIFZKDaMBeO9xH3hP8IU0TPAUWCVbEZk9VhGReMMfPNcSN`UOY\ XOVZPSaAMnPQcbTTBYUpWJnTGlQEjNBiK9gH6eE4i91fB2dC2b\ D2`F2ZG2OagTRNXH2ZF4`E5bD7dC8fB9hABj9C4Z`k8DeBI_DM\ UFQOIUIKYCMaIEm1Vm6OeBHYB6RGBQKFQPJQTNQYm4XaFXRQXF\ `a0mX4jS8hNCeIGcDK`8OZ4SXIOWuslVLWXNYYOZ_P_`RabSbc\ TcJutUgldUdpDhoFbnHYmJSmLNlNIkPCjR7jT2UT3DT3_TeKgY\ 4vQPldicrbepXfnRglLhkQVmVIo_5q0J78U7Gd7No7Qm4Tl1Qd\ BNYLMdRLkWKr`JxeOlfTafXRfkgbyxZt`lpEyoMjoUWoaHwwzH\ ELwZBcN72KKKB3TbUEJFY5NM3FB17lhf_XWOMLCBAz7gV3MH_I\ 8I9SafEJL8VxBvphnSMPEPAoC5QJfzCSe6ELrQ5dJ3RD2D61TA\ TL7LE5E727zSMxEybMYO2DI19 } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 12-03-08 (Testing Testing [7.5])
by Jim Muth 12 Mar '08

12 Mar '08

FOTD -- March 12, 2008 (Rating 7.5) Fractal visionaries and enthusiasts: I named today's image "Testing Testing" because I found it almost by accident while I was running a time test. The rating of a 7.5 includes 1/2 point for my semi-skilled coloring, which is responsible for the rather moody silvery-blue palette. The parent fractal is the result of combining various negative portions of Z^(-1.15) and Z^(-7.5), then adding (1/C). This parent consists of a north-south string of large bays, with the southernmost bay being the most mandel-like. The filaments extending from the buds along this bay terminate in rings, shaped more like lima beans than circles. Today's image is located in the inside of one of these lima-bean rings. The calculation time of 31-1/2 seconds is surprisingly short for such a pleasing fractal. No one with a computer that can still handle DOS has a reason not to run the included parameter file. And those with machines unskilled in DOS may see the image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A pleasant day prevailed at Fractal Central on Tuesday, with partly cloudy skies and a temperature of 46F 8C. The fractal cats spent the afternoon enjoying the periods of sun and being sulky when the clouds blocked the sun. My day was eminently average, which, after the recent hectic activity, was all that could be hoped for. The next FOTD will be posted in 24 hours. Until then, take care, and who first wrote 'It was a dark and stormy night.'? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Testing_Testing { ; time=0:00:31.57-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip center-mag=-2.946876788769/-4.19126281472/11868.3/\ 1/-167.5/0 params=-5/-1.15/-0.75/-7.5/0/0/0/0 float=y maxiter=280 inside=0 logmap=29 colors=0008HOCLSGPWKT_OXcSYgTcjQclUhoUjqbmscpvkrxm\ tzzzzzzzvvvmmmcccUUUKMCFOFFRKGTPHWUIYZJ`cKbhLemMgr\ NjvOlzPozQqzRszQrzPrzPrzOrvOrrNrmNrhMrfLrcLraKr_Kr\ YJrWJrUIrSIrQ7dSD`UJXWOTXUPZ_L_dHajDbp9du5ez1gz0hz\ 0_z0Rz0Iz0Az0Fz0Kz0Pz0Tz0Yz0bz0gz0kz0pz0uz0yz3sz6n\ zAhzDczGZzpSzkZzfezalz_mzYnzXozVpzUqzSrzQszPtzNuzM\ vzKwzJxzIszHnzGjzGezF`zEXzDSzDOzFSzGWzHZzIbzJfzKiz\ LmzOqzRtzUqzXoz_mzbjzehzhfzkcznazq_ztazwbFzcHzeKzf\ MzgPziRzjUzkWzlXzmXzmXzmXznYznYznYzoYzoZzoZzpZzpZz\ pWzoTznKzC`zFZzIYzKXzMWzO`zMezLjzJozItzGxzFvzKuzPt\ zUszZqzcpzhozmnzrmzmlzilzekz`kzXjzTjzPOzTQzWRzZSza\ TzdUzgRzdPzaMzZKzXSzU_zRgzPozMwzJzzHqzjkzaezT`zLFz\ gIzZLzQOzH`zMlzRxzVzzczzlzzuzzsyzqwzouzmrzjpzhnzfl\ zdjzblzZmzWnzTpzQqzNrzKtzHuzEvzBxz8yz5zz2zzRzznvzi\ ozehz`azXVzSOzOPzJQzFRzARz6YzEdzLjzTqz_xzgzznaztAz\ zJzvRzrZzogzkozgwzdszeYzN } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 11-03-08 (Feathery Fantasy [7])
by Jim Muth 11 Mar '08

11 Mar '08

FOTD -- March 11, 2008 (Rating 7) Fractal visionaries and enthusiasts: In today's image we enthusiastically return to the workhorse MandAutoCritInZ formula, where we envision great fractal things, making us enthusiasts who see visions of things that are not really there. But let's not concern ourselves with whether fractals are subjective things existing only in the mind, wherever that is, or objective things existing 'out there' wherever that is. Fractals are fun to look at, and that's all that matters. Today's feathery image most certainly does exist objectively. All who run the parameter file will see the same thing. Yet it most certainly is also subjective, for all we can know of it is a picture on a screen. The scene is located at the edge of the 'fan' of the parent fractal, which itself is a north-south string of large bays, the whole thing surrounded by cut-off rings of all shapes and sizes. The entire fractal is a fantasy, a "Feathery Fantasy", which I have rated at a 7. The parameter file runs in 1-2/3 minutes, making this FOTD quite a bargain. And as always, the finished image is available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Rather pleasant conditions prevailed Monday here at Fractal Central. The temperature of 48F 9C and warm sun felt quite spring-like. The dynamic duo of fractal cats agreed as they watched a pair of squirrels searching for nuts in the yard. In my department, the work backup is actually coming under control. The next FOTD is due, and will likely actually appear in 24 hours. Until then, take care, and the answer is 42, but what is the question? (As amatter of fact, I doubt that there ever was a question.) Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Feathery_Fantasy { ; time=0:01:39.85-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+1.95824372537/-2.95794068526/665.158/1\ /47.5/0 params=-5/-1.15/-0.75/-7.5/0/0/0/0 float=y maxiter=1500 inside=0 logmap=90 periodicity=10 colors=000Oc8Od8Oe8Pf8Pg8Ph8Qi8Qj8Qk8Qk8Sh9TfAUdBV\ bCW`DXYDYWEZUF_SG`QHaNHbLIcJJdHKeFLfDLcCKaCK_BKXBJ\ VAJTAJQ9IO9IM8IJ8HH7HF7HC6GA6G77D86G96IA6KA6MB6PC6\ RC6TD5VE5YF5_F5aG5cH5fH5hI4jJ4lK4oK4qL4sM4uM4wSBvX\ IvbPugWumbtritzqwwotumqsknqikngilefjccha`e_ZcYWaWT\ _UQYSOWUQUWRSYTQ_UOaWMcXKeZIf_GhaEjbCldAne8pg6zz4y\ z3zz6zz8zzAxzDkfFieHgdKdcMbbO`aRZ`TW_VUZYSXVPWXNV_\ LUaJTcGSfERhCQj9Pm7Oo5Nq3Mo7OmBQlFSjJThNVlRXjVZhZ_\ gbaefcekedjdcjdbidaidaid`hd_hdZhdYgdYgdXfdWfdVfdUe\ dUedTedSddRddQcdQcdPcdObdNbdMdcNbdO`eP_eQYfRWfRVgS\ TgTShUQiVOiVNjWLjXJkYIkZGl_DnZFlZGkYIjYJiXLhXMgWNe\ WPdVQcVSbUTaUU`TWZTXYSZXS_WRaVRbUQcSQeRPfQPhPOiOOj\ JOkNUlR`mVgnYfoZfpZfq_fr_es`et`euaevaewbdxbdycdzcd\ zdezdgzeizekzfmzfozgqzgszhuzhwzizzmzzizzezzazzZzzV\ zzRzzNzzJzzKzzKzzKzzLzzLzzLzzLzzMzzMzzMzzMzzNzzNzz\ NzzNzzOzzOzzOzzOzzPzzPzz8 } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 10-03-08 (The Last Straw [5])
by Jim Muth 10 Mar '08

10 Mar '08

FOTD -- March 10, 2008 (Rating 5) Fractal visionaries and enthusiasts: The trip to Old Fractal Central on Saturday was filled with difficulties. On the way down route 15, I ran into a pea-soup fog that cut speed to 35mph. When I got to Baltimore over an hour late, I found the power off at Old F.C. and the phone dead due to a wind-storm that had just passed. Luckily, the old fractal cats, Thomas and Tippy, who are showing their age, were not disturbed by the darkness, but I did not enjoy the thought of spending a night in the dark and cold. The power returned around nightfall, which made my overnight stay there at least comfortable. On Sunday morning I managed to find a working computer at a neighbor's house and determined that conditions in Cleveland were not as bad as I had feared, which meant my sister would likely make it back to Old F.C. on Sunday evening as planned, and I could return to New F.C. early Sunday as scheduled. By the time I got back to New Fractal Central at 11am Sunday, my sister had already left a message on the answering machine, telling me that she would arrive at Old F.C. that evening. It is now just after 5pm Sunday, and I have just contacted her near Breezewood, PA, which is about 2 hours from Old F.C. The old fractal cats will not be alone tonight. Fractal lady, who kept New F.C. going while I was away, found the whole thing rather amusing. The new fractal cats agreed. I got rather grumpy. It's easy to make light of a frustrating situation when it is happening to someone else. Now on to the business at hand. Today's image lies in the parent fractal that results when Z^(1.618034)+C is iterated at a height of 1.4142 on the complex logarithmic ladder and no function is applied. This parent fractal is split along the entire X-axis and resembles nothing as much as a mis-shapen sweet potato, sometimes called a yam. Today's scene is located on the eastern shore of the main bay, just below the X-axis split, where some unusual features caught my eye. No more need be said about the hastily-found image, which I named "The Last Straw" and rated at a 5. It will speak for itself when the included parameter file is run. And running that parameter file can be accomplished in under one minute. Another way to hear the image speak for itself is to view it on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Saturday was stormy at Old F.C., with a surprising temperature of 66F 19C. Sunday was sunny but windy and chilly here at New F.C, with a temperature of 36F 2C. The new fractal cats took advantage of the sun. In my work department, things are at last showing signs of getting caught up. The next FOTD will likely be posted in 24 hours. Until then, take care, and be on the alert. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Last_Straw { ; time=0:00:48.40-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident center-mag=+1.230922957934507/-0.1029202290921805/\ 3365054/1/-95/0 params=1.618034/0/-1.1412/0 float=y maxiter=1800 inside=0 logmap=122 periodicity=10 colors=000GAPHDLKGVKIQKK_6KYKK`KKjKK`KKkKKaKKkKKaK\ KlKKbTKlSKbRKlTK_VKfXKUZKa`KPbKWhIHeGJWDLLBNB8P16Q\ 6ARADREHSJKSNOTRRTVVU_YUcaVgdVlhWpkWtoXxrXwmVwhUwc\ TvZRtUQqPPoKOlFMlALl5Kl0Jm8WnFgoMsrQqsTptWouZntamu\ dlvhkvkjvnivqhvtgvwflmeccdVUcMKbDAbHCcKEdNFdQHeTIe\ WKfZMfbNgePghQhkShnUiqVitXjwYjo_ahaU`cLUeDWdFXcHYb\ JZaL_`M`_ObZQcYSdXTeWVfVXgUZhT_eRZbPY_OXXMWULVSJUP\ HTMGSJERGDQDBPBAPFCNIEMMFKPHJSIHWKGZLEbNDeOBhQAlR8\ oT7rU6qTAqSDqSGpRJpRMpQPoQSoPVoOZnOanNdnNgmMjmMmmL\ pmLsdKTfKShKQjKNlKNnJLpIIrGFtECuDAuM9uU8ua8uj7ur6u\ z6uvBurGunLukQugVuc_u_duXhsVjqTkoRlmPnkNojLphJqfHs\ dFtbDuaCv_FrZIoYLlWOiVRfUUbSX_R_XQbUOeRNhNMkKKnHJq\ EItBJuAKvALw9Mx9Ny9Oz8Pz8Qz8Rz7Sz7Tz7PzHzzQzzZzzgz\ zpzzyzzjzzgzzezzczzazz_zzYzzWzzUzzSzzQzzOzzMzzKzzI\ zzGzzPzzYzzazzdzz_zzVzzRzzMzzIzzDzz9zz4zz0zzNzzizz\ azzVzzNzzGzz8zz1zz9zzFzzF } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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FOTD 08-03-08 (No Name [No Rating])
by Jim Muth 08 Mar '08

08 Mar '08

FOTD -- March 08, 2008 (No Rating) Fractal visionaries and enthusiasts: Not only has the F.C. DSL modem gone kaput, now the F.C. heat has gone down with a burned out circulator pump. In addition, the regular work is still quite heavy and I must go to Old Fractal Central on Saturday to feed and water the old fractal cats Thomas and Tippy while my sister spends the week-end in Cleveland, where a major snow storm is in progress. No wonder the FOTD's are suffering. Today's image lies in the Z^(sqrt(2))+C Mandeloid as it appears 1.618034 levels up the complex logarithmic ladder when no function is applied. One quick glance will show why I gave it no name or rating. The only good thing I could find in it is the calculation time of a speedy 1-1/3 minutes, which means no one will be wasting too much time on it. Perhaps the best way of all to see the image is to go to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view it there. Morning clouds were followed by afternoon and evening rain here at Fractal Central on Friday. The temperature of 46F 8C was quite convenient however, especially with the heat down. But the fractal cats complained about the cold radiators. All in all, my day was frantically busy. Due to the rush here at F.C., and the trip back to old F.C., there will be no FOTD for March 9, but the FOTD for March 10 will be posted in 48 hours. Until then, take care, and see you soon. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= No_Name { ; time=0:01:21.77-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-0.773915011110409/+0.2947948326063251/\ 92948.72 params=1.4142/0/1.618034/0 float=y maxiter=2500 inside=0 logmap=110 periodicity=10 colors=000eTedPgcLjcImbEpbBrLGuRJjXM_aPQgSFlU5ccMV\ lbMurXYcX_cX`cXbcXccXecXfcXhcXicZkkUlZPmMLmAMgCMbE\ NYFNTHOOIUS8_S8dT9iU9nU9mOBlJCkDEj8Fj3Ge9IaEJXKKTP\ LOVMK_NFeOBjPEmLHoIKrENtBQw7Ty4Px8MwBIvEFuHBtK8sN9\ nPAjRBfTCaVDYXEUZEQ_LS`STaYVbdWcjXdqkwljrhimchi_hd\ Wg_RfWNeRJeNNgPRiRVkSZmUboVfqXjsYfkRbcKZWDVP7UMFUJ\ MUHTTE`TBgT9nV8fW8ZX7RY7JZ6B_64`5Ga5RcANdFJfJGgOCi\ T8jX5iYBhYGgYLgYRfYWeY`eYedTZdPTcKMcGGcCA_GEWJISNM\ OQQKTUGXYC_a8bdXfiuinqcpnYqkSsgMtdGvaBweEthHqkKnnN\ kqQhtTewWbzY`qaXidTahPTkLLoHDrD5u9CpGJlMPgSWcYbZch\ VioQouMuS8iR9jQAjPAkOBkNClMClLDmKDmcFnvKnqPnmUniZn\ dcn`cnXcn_ciacedc`fcXihSkmOnrJpvFpzEpzDpzCdzOUz_Jz\ jPz`VzS`zJfzAnz1zz3zz5zz7zz8zzDzzHzzLzzPzzTzzXzzkz\ zhzzezzbzz_zzdzzizznzzszzwzzpKziKzbJzWJzPIzIIzC9zg\ GzaMzXTzRZzMVzOSzPPzQTzTWzW_zYbz`fzbizelzgszkyznvz\ kszhqzfnzclzaizZgzXfz_ezb } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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FOTD 07-03-08 (Complex Minibrot [No Rating])
by Jim Muth 07 Mar '08

07 Mar '08

FOTD -- March 07, 2008 (No Rating) Fractal visionaries and enthusiasts: The rush continues here at Fractal Central, made more difficult by a DSL modem that appears to be going kaput. The problem with the missing FOTD's on the philofractal list is that the mailing list apparently does not accept posts from AOL, and with Mindspring having problems in the local area, I must post some FOTD's through AOL. Today's image shows a complex minibrot, thus the name. Since I found it almost without effort, I could give it no rating. But it's still a bit interesting to study. The scene, with its mixture of total chaos and bits of semi- order, is located in a mis-shapen valley in yesterday's image. The calculation time of 2 minutes will be inoffensive. Perhaps the most convenient way to view the image is to visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the fully-calculated image is posted. A really nice day prevailed here at Fractal Central on Thursday, with lots of sun and a temperature of 50F 10C. Too bad we were too busy to enjoy it. The fractal cats did enjoy it however as they spent most of the afternoon lounging in the sun streaming in the front window. As stated above, my day was quite busy. But busy or not, the next FOTD will be posted in 24 hours. Until then, take care, and wonder why I end the FOTD discussions with silly statements and questions, such as: last night I dreamed of an elephant. When I woke up, I realized that the elephant was a dream and had therefore existed only in my mind. But my mind is in my head and my head is much too small to hold an elephant. Where then was the full-sized dream elephant located? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Complex_Minibrot { ; time=0:02:02.19-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotMixImag2 function=ident center-mag=-0.1104658812691925/+0.748116709982013/\ 355.0296/1/-30.5/0 params=1/2/0.002/1.5/0/0 float=y maxiter=4200 inside=0 logmap=23 periodicity=10 colors=000SQNPPPNORJMTLNSNNRONRQNQSNPTNPVNOWNNYNN_\ OM`OLbOLcOKeOJgOJhOIjOHlS5kOHjLSjHbiEmiBxaIrUOmMVg\ E`b5gZ7fY8eYAeXBdXCcXEcWFbWGaWIaVJ`VK_VM_UNZUOYUQY\ TRXTSWTUWSVVSXUQWVSVVTUVUTWVTWXSWYRXZQX_QX`PYbOYcN\ YdMZeMZgLZhK_iJ_jJ_kI`mH`nG`oFapFarEasDbtCbuCbvDau\ EauFauGauHauI`uJ`uK`uL`uM`uN_uO_uP_uQ_uJbzQ_uXXqbV\ miSioQejPbfO_bNYZNVVMSRLQNKNJKLIMOIOQIQSHSVHUXHVZH\ X`GZcG`eGbgEdgGciHcjIbkJblKbmLaoMapN`qO`rNarP`sQ`s\ R`sS_sT_sU_sWZsXZsYZsZYs_Yt`YtbXtcXtdXteWtfWtgWtiV\ tjVtkVulUumUunUupTuqTurTusSutSuuSuvSueOjPK`5FM8HRB\ IVDJZGKbILfHQdGUcFZbFbaEg_DkZCpYCtXDsYErYFqYGpYHoY\ InYJmZKlZLkZMkZNjZOiZPhZQg_Rf_Se_Td_Uc_Vb_Wb_XcZYc\ ZZcZ_cZ_dY`dYadYbdYbeXceXdeXeeXqroeeXVUDUTETTETTFS\ TFRTGRTGQTGPTHPSHOSINSINSIMSJLSJLSKKSKKSKIUJHVIGWI\ EXHDYGCZGA_F9`F8aE6bD5cD4dC1dA3eC4fD6gE7gG9hHAiICi\ KDjLFkMGlNIlPJmQKnRMnTNoU } frm:MandelbrotMixImag2 {; Jim Muth z=p3, c=fn1(pixel), a=real(p1), b=imag(p1), d=real(p2), f=imag(p2): z=(a*(z^b))+(d*(z^flip(f)))+c, |z| <= 100 } END PARAMETER FILE=========================================

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FOTD 06-03-08 (Lop-Eared Rabbit [3.25])
by Jim Muth 06 Mar '08

06 Mar '08

FOTD -- March 06, 2008 (Rating 3.25) Fractal visionaries and enthusiasts: New formula alert! I think this is the first fractal I have posted that was created with the MandelbrotMixImag2 formula. The hurried image shows a very distorted period-3 north bud, which to me resembles a lopsided lop-eared rabbit, thus the name. I posted the image partly as a curiosity and partly because I had no time to search for a better fractal. The rating of a 3.25 indicates my dis-satisfaction with the result, though I did add 1/4 point for my minor coloring effort. The calculation time of 1 minute is about the same time it will take to visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view the completed image at leisure there. Wednesday started with a thunder-shower here at Fractal Central. The rest of the day was cloudy and breezy with a temperature of 39F 4C. The fractal cats spent the day relaxing by the heat. My day continued unusually busy. Fractal lady is back in action, but the work is quite heavy. If all goes well, as it usually does, the next FOTD will be posted in 24 hours. Until then, take care, and fear not the dark. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Lop-Eared_Rabbit { ; time=0:01:01.11-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotMixImag2 function=ident center-mag=-0.114024/0.772774/6/1/2/0 params=1/2/0.002/1.5/0/0 float=y maxiter=4200 inside=0 logmap=5 symmetry=none periodicity=10 colors=000I7FJ8GK9GLAGNBGPCHSDHVEHYFH`GKcHMfIOiJQl\ KToKUrKUwKUwKUtKUqKSnKQlKOiKMfLKdNMaPOZQQWSTUUVRVX\ OXZLUaMY`N`_Oc_PfZQiZRlYSoYTrXTuXUqTVmQWjMXfJYbGZ_\ C_W9_T6YS5WS4US3SR2QR1OR0NP1MR0LT0KV0KX0JY0I_0Ha0H\ c0Ge0Ff0Eh0Ej0Dl0Cn0Co0Fn2Im4Ll5Ol7Rk8UjAXjBZiDahF\ dhGggIjfJmfLpeMsdOudPqaRm_SiYTfWUbUWZSXWQYSOZOM`LK\ aHIbDGc68fAEdEJbIO`MTZPYXTbVXgT`lRcqQarO_sNYsLXtKV\ tJTuHSuGQvFOwDMwCLxBJx9Hy8Gy7FuAFrDFnFEkIEhKEdNEaP\ DYSDVUDSXDOZCLaCHcCEfA9jCBhEDfGFdHHbJJ`LK_NMYOOWQQ\ USSSTTRQXUO_XLb_JebGheElhBok9rn6uq4xs6up7rn8pl9mjA\ khBhfCfdDcbF`_GZYHWWIUUJRSKPQLMOMKMSQLYWKbaKhgJnmI\ ssIqtLouNmvPkwSixUgyWezZdz`bzb`zeZzgXziVzlTznUzuSz\ pQzlOzhMzdKz`Fz`IzXKzTNzPSzGPzMNzRLzXJzaGzgEzlCzr9\ zyAzzBzzCzzCzzDzzEzzFzzFzzGzzHzzIzzIzzJzzKzzKzzLzz\ LzzLzzLzzMzzMzzMzzMzzOzzMzzLzzJzzIzzHzzFzzEzzDzzBz\ zAzz9zz7zz6zz0zz5zzTzzSzz } frm:MandelbrotMixImag2 {; Jim Muth z=p3, c=fn1(pixel), a=real(p1), b=imag(p1), d=real(p2), f=imag(p2): z=(a*(z^b))+(d*(z^flip(f)))+c, |z| <= 100 } END PARAMETER FILE=========================================

4 5

FOTD 05-03-08 (Incomprehensibility [3.5])
by Jim Muth 05 Mar '08

05 Mar '08

FOTD -- March 05, 2008 (Rating 3.5) Fractal visionaries and enthusiasts: It's rare that I post a FOTD that rates as low as a 3.5, but in all honesty, that's all I could give today's image. It's colors are bland and its theme, if any theme exists, is vague to say the least. The parent fractal is a grossly overblown thing created when 4.5 negative parts of Z^(-1.5) are combined with 1.5 negative parts of Z^(-4.5) and (1/C) is added. This parent is better seen than described, though I will remark that today's scene is located in the western branch of the valley that forms the northern border of the largest bay. I named the image "Incomprehensibility", which has little to do with the image. The word was the longest one I knew how to spell in the third grade. (I had not yet found the longer word "antidisestablishmentarianism".) The calculation time of just over 2 minutes can be reduced to next to nothing by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Moderate to heavy rain fell all day Tuesday here at Fractal Central, while the temperature hovered around 39F 4C, making it a most unpleasant day. The fractal cats interrupted their sleep several times to check the weather. My day was busy, and it shows in the lackluster Fractal of the Day. The next FOTD, hopefully with much more luster, will be posted in 24 hours. Until then, take care, and why are we so concerned with a "theory of everything", which few people are really concerned about, when we don't even know the meaning of life, which everyone is concerned about. (Denying that life has a meaning, or claiming that its purpose is merely to propogate our genetic material is an evasion unworthy of a rational being.) Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Incomprehensiblity { ; time=0:02:09.39-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip float=y center-mag=-0.1601622567412782/-1.596215437932805/\ 10728.1/1/67.5/0 params=-4.5/-1.5/-1.5/-4.5/0/0/0/0 maxiter=3800 inside=0 logmap=144 periodicity=10 colors=000gXUd_TbcT_fTXjSUmSSpSSnRSlQSkPSiOShNSfNS\ eMScLSaKS`JSZJSYISWHSVGSTFXSFVWG_UG`aGcdGfgGikHlnH\ oqHrtHuwHovNivScuYYubSthMtmGssAsxHqoNpgTn_ZmRdkJjj\ Bpi3oj7okAnlEnmHmnLmoOmpRinUelWajZYh`UfcQeeMchIajE\ _mAYo7Xqhm_mQLq37n7DlAJiEOgHUdK_bOd_RjdUoWTn_QmSTl\ DOgW_iaffflcls`qyYmwXiuWfsVbqU_oUXmSUkRSiQPgONeNKc\ MIaKF_JDYIHXNLWSOWXSVaVUeZUjaToeSthSxgPrfMleJfeG`d\ DVcAPc8KYGNSOPMWRHbTIdVJeXKfYLg_Mi`NjbOkcPleQmgRoh\ SpjTqkUrmVsnTokSkiQggPceN_cMWaLS_JOYIKWGGUFCSE9QGC\ NHEKIGHJIEKKBLM9ON8QN8SN8UN8WN8YN8`O8bO8dO8fO8hO8j\ O8iPAiUBhVChVDh`Eg`GgaHgfIfgJfbKfYLgWNhUOiSPjRQkPS\ lNTmLUnFVoDXpBYq9Zr8_s6at4bu2cu1dt0bs0`r0_r0Yq0Wp0\ Vp0To0Rn0Qm0Om0Ml0Lk0Jk0IhCXfNkeQidTgcWebZdaab`d`_\ gZZjYYmWXpUXrT`sOctKfuFjvBmw6px2ny7lzCjzGhzLfzQezU\ bzS`zRYzQWzOUzNRzMPzKMzJKzIIzGFzFDzEAzC8zB6zADzHKz\ ORzVYzadzhkzorzVozVmzUjzU } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

2 1

FOTD for March 04, 2008
by JimMuth＠aol.com 04 Mar '08

04 Mar '08

1 0

FOTD for March 03, 2008
by JimMuth＠aol.com 02 Mar '08

02 Mar '08

1 0

FOTD for March 02, 2008
by JimMuth＠aol.com 02 Mar '08

02 Mar '08

1 0

FOTD for March 01, 2008
by JimMuth＠aol.com 29 Feb '08

29 Feb '08

1 0

FOTD for February 29, 2008
by JimMuth＠aol.com 29 Feb '08

29 Feb '08

2 1

FOTD for February 28, 2008
by JimMuth＠aol.com 27 Feb '08

27 Feb '08

1 0

FOTD for Feb 27, 2008
by JimMuth＠aol.com 27 Feb '08

27 Feb '08

1 0

FOTD for Feb 26
by JimMuth＠aol.com 26 Feb '08

26 Feb '08

1 0

FOTD 25-02-08 (FOTD for Feb 25 [No Rating])
by Jim Muth 25 Feb '08

25 Feb '08

FOTD -- February 25, 2008 (No Rating) Fractal visionaries and enthusiasts: Today's quickie image deserves neither name nor rating, and it receives neither. It's a scene in the Z^(2.003)+C Mandeloid, and it's located just east of the large midget complex on the main stem of its parent, in an area that at least to me looks like a railroad switching yard. In the Julia sets of this area, curious rectangles often appear, though I have never seen rectangles in the Mandelbrot slices. The calculation time of 1-1/4 minutes is fast enough to keep everyone happy. The finished image is also posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Full brilliant sun prevailed here at Fractal Central on Sunday. The temperature of 39F 4C and light winds made it feel almost like spring, though the snow still on the ground hardly gave an impression of flowers ready to bloom. The fractal cats kept much to themselves. Maybe they don't like my grouchy mood of late. The next FOTD will be posted in all its glory in 24 hours. Until then, take care, and get with the flow. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= FOTD_for_Feb_25_08 { ; time=0:01:14.19-SF5 on P4-2000 reset=2004 type=formula formulafile=slices.frm formulaname=MandelbrotN passes=1 inside=0 center-mag=-1.74308494249748400/+0.000240622105290\ 26/8.82777e+007/1/-22.5/0 params=2.003/0/0/0/0/0 float=y maxiter=1650 logmap=161 periodicity=10 colors=000gmQdkPbjN_hMYgLVfKTdJQcHOaGL`FJZEGYDEXCB\ YK9YS6Y_4Yg8ZhC_hF_hJ`iN`iQaiUajXbj`cjdckgdkkdkoel\ relvflyfllmc`tVQsaFrh4rn9ofDm_HkTLiMPgFTe8Xc1V`3TZ\ 5RW7PU9NRBLPDJMFIKGl6`HIDIJCIJCIJCJKCJKCJKCKLBKLBK\ LBLMBLMBLMBNI7LMBKPFJTIIWMHZPGbTFeWEh_DlbCofBriGnj\ KkjOhkSekWbk`_ldXlhUllRmpOmtLmtJmsImsGnrFnrDnd8bd8\ ed8gT7bH6Z04Z55V96SD7OH8LL9HPAETBAXC7`C4hLsaKqWKpQ\ KoJKmDKl7Kk1Kj3Tf5`b0pa7h_D`ZJTYQLWWDV`6Xa5Ub5Sc5P\ d5Ne5Lf5If4Gg4Dh4Bi49j46k44k42e68_7ESX`TX`UYaVYaWY\ bXZbYZc_Zc`_da_db_ec`ed`fe`fbbd_dbYf`VhZTjXQkWNmUL\ oSIqQGsODuMBvLAuQ9uV8tZ7tc6sg5sl5spConJkmQglWckb_j\ iWipShvPgr`knknjvqgulethbsc`r_YqWWpRToNRoJShMTbPUX\ SVRVWLYXF`Y9cZ3ef9VmFKtKAsNCsQDsSEsVFrYHr_IrbJreKr\ gLqjNqmOqoPqrQqtRrsSrrTrqTspUspUsoVsnWtmWtlXtlXtkY\ ujZuiZuh_uh_riXpjUnkSllPilMgmKenHcoEaoCcpFepHgqJiq\ LjrNlrPnsRpsTqsVnqTlpSinR } frm:MandelbrotN {; Jim Muth b=p1, z=p2, c=p3+pixel: z=z^(b)+c, |z| <= 16 } END PARAMETER FILE=========================================

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FOTD 24-02-08 (Carnival Classics [No Rating])
by Jim Muth 24 Feb '08

24 Feb '08

FOTD -- February 24, 2008 (No Rating) Fractal visionaries and enthusiasts: The fractals continue unrated because I continue to give them short shrift. Today's image shows a minibrot (as do most FOTD images). This minibrot is located in the parent fractal that results when 2 parts of Z^(-2.2) are subtracted from 1.5 parts of Z^(0.85), and (1/C) is added. It's kind of a twisted S-shaped parent, not too promising at first glance, but yielding a few surprises when checked closer. It might yield even more surprises if checked even closer, but that's a job for a day when I'm filled with energy, a situation that certainly does not prevail at this particular time. I named the image "Carnival Classics" because of the festive colors. (At least, they're trying to be festive.) It takes just under 5 minutes to calculate the image from the included parameter file, not too bad a time. It takes even less time to surf over to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and see the finished image there. A cloudy day with a high temperature of 36F 2C here at Fractal Central on Saturday melted a good part of the ice that fell on Friday. The fractal cats gave the whole thing the cold shoulder. My day was filled with quiet and recuperation. If all goes according to plan, the next FOTD will appear in 24 hours. Until then, take care, and if reason cannot answer the big questions of life, what can? (Don't question the questions.) Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Canvival_Classics { ; time=0:04:56.12-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-0.9421721847/+0.2921284597/42907.3/1/\ 160/0 params=1.5/0.85/-2/-2.2/0/0/0/0 float=y maxiter=1500 inside=0 outside=tdis periodicity=10 colors=000kMsjLrjKqiJpiIpiIohHnhGngFmgElztDwmJtgOq\ aToWYlQbiKgM_sQWqUSpXPo`LndHmBEMMEVXEcyYNwWQuUStSV\ rQXpOZoNamLckJejHhhFjco`dibeddeZffUgfOigJkZyVam_ca\ ceQhKuzSfu_Spu7_r9bpAdnBfkChiDjEhAoRpmOokLnjJmhGlS\ 6RL7T_8V`9Xa9ZbA`cBbdCdeCffDhTfDVeDXeDZeC`dCbdCddC\ ffDhhEjjEllFnnFppGrrGttHuvHssJqpKomLmkMkhOiePgbQe`\ RfYPgWNhTLhRJiOHjMFjKDkHBlF9mC7mA5n73o51o30p9LpFdp\ KxkHtfFpaDmXBiT9eO7bJ5ZE3VA1SOIGQPDSWBUb9VaAVaAVaA\ V`AW`BW`BW_BW_BX_CXZCXZCXZCgxgewfcvebud`uc_tcYsbWs\ aVr`Tq_Sq_`g`hZ`pQ`xH`wN_vS_uY_ub_th_sm_sr_locemfZ\ kiSilLgoEer7cu1ax3`v5`u6`t8_r9_qB_pC_nEZmFZlHZjIZi\ KYhLYfNYeOYdNZeM_eL`fLafKbgJcgIdhIehHfiGgiFhjFijEj\ kDkkDkk6b27`57_87ZA8YD8XF8WI8VL9TN9SQ9RS9QVAPYAO_A\ NbAMdIKcPIcXGccEcjDchEhiG2hF6hF9hFDhFGhFJhFNhFQgET\ gEXgE_gEbgEfgEiBRsGPrKNqOMpSKoWIn_HmcFl7hXBeZEb_H`\ `KYbNWcQTdTQfWOgZLhaJjdGk } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 23-02-08 (So Low It's High [No Rating])
by Jim Muth 23 Feb '08

23 Feb '08

FOTD -- February 23, 2008 (No Rating) Fractal visionaries and enthusiasts: I just don't seem able to shake the after-effects of whatever bug has been bugging me for the past week. Today's discussion is therefore once again brief. The image shows a minibrot in the Z^(1.09)+C Mandeloid. This is a fractal of an unusually low order in which to find a minibrot, but with my secret patented minibrot finder, they can easily be found. I named the image "So Low It's High", a name that makes as much sense as a double-slit experiment. Since I put so little effort into finding the scene, I gave the image no rating. Most of the calculation time of almost 9 minutes is consumed by the inside part of the minibrot, which is at a maxiter of 250,000. This time can be cut considerably by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the finished image soon will be posted, and viewing it at leisure there. A most unpleasant day prevailed here at Fractal Central on Friday. Light snow all morning was followed by light sleet and freezing rain in the afternoon, while the temperature hovered just below freezing. After dark, everything changed back to light snow, leaving a total of about 3-1/2 inches, or 9cm, of sloppy slush covering the ground. The fractal cats spent the day ignoring the outside conditions. The next FOTD will appear in 24 hours. Until then, take care, and find the proof. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= So_Low_Its_High { ; time=0:08:50.25-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident center-mag=-7.065004112040637/-1.161770134502639/\ 1.472453e+008/1/-147.5/0 params=1.09/0/0/1500 float=y maxiter=250000 inside=0 logmap=247 colors=000dqFcsFbuFawF_rKYmOXiSVhUThWRhYPh_NgaLgbJ\ gdHgfFfhDfjBfl9fmEbkI_iMXhQUfVQeZNcbKbfH`jE_iHahJb\ hMcgOegRffTgfWheYje`kdblddm`cjXbgUadQ`aM_ZJZXFYUBX\ R8WO4VL1UJ5VH9VGCWFGWEJWCNXBQXAUX9YY8`Y6dY5gZ4kZ3n\ Z2lg1ko1fl4bj6Zh8VeARcCMaFI_HEXJAVL6TN2RP4QO5PN7OM\ 8OLANKBMJDLIELHGKGHJFJIEKIEbRBt_8oWSkTkeUm`UnVUoQU\ pLUrFUvAWz5Yz6Zz6_z6`z6az6bz7cz7cz7cz7cz7cz8bc8ba8\ c`8dZ8dY7aX6ZW6WV5TU5QT4NS3KR3HQ2EP2BO18N15M93FH18\ O02HTAAuHEtGItGMtFQtFUtFYtE`sEdsDhsDlsDpsCtsCwsCsm\ JogQlaWm_UmZTnYRnXQoWOoUNpTLpSKqRIqQHrOFrNEsMCsLBt\ K9tJ8rIApIBnICmHDkHEiHFhHGfGIdGJbGKaIL_KMYMNXOOZQP\ _SP`UQbWQcYRd_ReaSgcSheTigTjiUlkUmmVnoVoqVmsXluYkw\ _iz`hzbgzcfzddzfczgbzi`zj_zlZzmYznVzjZzfczbhzZmzVr\ zRvzNzzJzzFzzCzzIzzOzzTzzZzzczzizznzztzzyzztzzpzzk\ zzgzzczzZzzVzzQzzMzzIzzDzz9zz5zzJzzXzzizzfzzczz`zz\ YzzWzzTzzQzzNzzKzzIzzFzzC } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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FOTD 22-02-08 (Complex Pachyderms [No Rating])
by Jim Muth 22 Feb '08

22 Feb '08

FOTD -- February 22, 2008 (No Rating) Fractal visionaries and enthusiasts: I never rate fractal images that I find while I'm not feeling up to par. They lack my full involvement. But I do sometimes give them names, and I have thoughtfully named today's image "Complex Pachyderms". The 'complex' part of the name indicates that the power of (-Z) being iterated is complex. The 'pachyderms' part indicates that the scene of the action lies in the remains of a once-perfect East Valley, which has been nearly obliterated by the addition of 0.3 part of the number 'i'. So what does a complex minibrot or a complex elephant look like? The minibrot itself is of an irregular shape similar to those we have seen many times in the fractals of fractional real powers, though the 2,4,8... sequence has been lost, while the elephants have distorted beyond recognition. The calculation time of 1-1/2 minutes is quite palatable. And the finished image is also posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A really pleasant late-winter day prevailed here at Fractal Central on Thursday. Full sun, light breezes and a high tempera- ture of 28F -2C were just what the doctor, actually the first doctor I have seen since I sprained my ankle, ordered. The fractal cats agreed. The next FOTD will be posted in 24 hours. Until then, take care, and watch for the hamiltonian. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Complex_Pachyderms { ; time=0:01:29.15-SF5 on P4-2000 reset=2004 type=formula formulafile=slices.frm formulaname=MandelbrotMiN passes=1 center-mag=+0.1016915941521/+0.048942857122051/\ 2.274516e+009/1/-62.5/0 params=2/0.3/0/0/0/0 float=y maxiter=7500 inside=0 periodicity=10 colors=000EvTFYbG9kIBhJCeLEcMF`OHYPIWQKTSLQTNOVOLW\ QIXRGWTFVVFVWFUYEUZET`ESbEScDReDRfDQhDPjCPkCOmCRsA\ OnCLjEJfGGbIDYKBUM8QO5MQ3IR7NTARUDVWGZXJbYMg_Pk`So\ bVscYwdZra_mZ`iWadTb_QcWNdRKeMHfIEgDBq86h98i29`A9T\ I9LQ9DY95e9HUFSIKXFKaCKe9Kj6Kh0Sn4Krzzmzvhzrczpavo\ `ro_ooZkoYhoWdoVaoUYoTVoSRoPKqROoTRmUUkWYiX`gZce_f\ cYebWeaUe`Se_QeZPeZNdYLdXJdWHdVFdUEdUIeXLf_PgbSgeW\ hhZikWsrainf`jkSglPblNZlLVmIQmGMmEInBDn99m13n75oD7\ oI8pOAqUCqZDrdFshEriGrjIrkKrkMqlOqmQqmSqnUqoWppYpp\ _pqaprcprdmlbjf`ga_Va5ZjEasMysWfoSOkO5hKIOeU3zM9yF\ Fy8KyGSlN__LRcKIgJ9kI1o2Qi7QO1JY1DN06BGCCPhcCMKCUo\ 9Mb6FQ37DtWreOdSGRE8Db3rJ1RJ_zERj9IVR9Fl6nf4aT3PE1\ C1NU0HM0BF057_Ha3FRnPu_ZvONbCBJ7IZA6w53UEeo9SY4EHf\ ZsWQeLHSA8Ek8L_6FO4AC25d6kU4_K3OA1CWRYR93I62931Ler\ FVdALR5ADqB6_74I32kmOWXGGG8cmBz3He2BL15Kf9FW6AL45A\ 2nmlYXWHGGnzoYeYHLHu6lfcp } frm:MandelbrotMiN {; Jim Muth b=p1, z=p2, c=p3+pixel: z=(-z)^(b)+c, |z| <= 16 } END PARAMETER FILE=========================================

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FOTD 21-02-08 (Further Exploration [No Rating])
by Jim Muth 21 Feb '08

21 Feb '08

FOTD -- February 21, 2008 (No Rating) Fractal visionaries and enthusiasts: Since I'm still a bit under the weather, the discussion will once again be brief. The most unusual feature about today's image is its magnitude of 2*(10^13), which is beyond the point where definition begins to break down. But the image has such a soft overall feeling that the slight jaggedness is barely noticeable. Since I put very little effort into the image, I could not give it a fair rating, but I did name it "Further Exploration", since it is a trip much deeper into a fractal that closely resembles the parent of yesterday's image. A infinitesimal minibrot does lie at the center, but it is well beyond the range of conventional math. The calculation time of just under 3 minutes will try the patience of no one. And finally, the finished image is available for viewing on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A sunny but chilly morning on Wednesday here at Fractal Central was followed by a cloudy afternoon with a temperature of freez- ing, and light evening snow. The fractal cats slept most of the day. The next FOTD will be posted in 24 hours. Until then, take care, and give a fractal at least a ghost of a chance. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= FurtherExploration { ; time=0:02:50.82-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=mandautocritinz function=recip passes=1 center-mag=+0.4383547998851132/+1.724578478231173/\ 1.981275e+013/1/22.5/0 params=-5.5/-1.5/-0.5/-5.5/\ 0/0/0/0 float=y maxiter=1250 inside=0 logmap=330 periodicity=0 mathtolerance=0.05/1 colors=000AASAATAAUAAVAAWAAXAAYAA_ACa9Fc7Ie5Lg7OgA\ RjFUlK`nPdpRisZmucswhxxmyziyxeuxaqwYpwUnvQmvMlvIkw\ HjwIiwIhwIhwJgwJfwKewKewKdwLcwLbwLbwLRrLGmL5hM7fM9\ dNBbND`NEZOGXOIVPKTPMRPNPQPQRQRRRSSSSTTTTUUUVUVWVV\ XWWYXXZXX_YY`ZYaZZfXZkVZpUZuSZyRegKkQDlRFmSGnSIoTJ\ pTLqUMrVNsVPtWQuWSvXTwXUuZVt`VrbVqdVofVnhVljVkkVjm\ VhoVgqVesVduVbwVayV`zVayXaxYawZbv`bvabubctccsecrfd\ rgdqhdpjeokenlenm_liUkeOjaIiYChUGdVJaWNYWQVXURYXOY\ `KZcH_gD_jA`n6aq3aicSgdUfdWedXddZcd_ada`db_ddZdeYd\ gXdhW`eVXcUU`TQZSNWRJUQGSSFUUEWWDYXC_ZBa`Aca9ec8ge\ 7if6kh5mj4ok3qm2so1up1wm4tj6qg9ndBkaDhZGeWIcTL`QNY\ NPVKSSHUPEWNDXLDYJDZIDZGC_FC`DCaBCaABb8Bc7Bd5Bd4Ae\ 7AfAAfDAgG9hJ9hL9iO9iR8jU8kX8kZ8la7md7mg7nj7nlAkjC\ ihEggHeeJbcL`bOZ`QX_SUYVSWXQVZOTaLRcJQeHOgFN`EMVEM\ PELIDLCDK6DKITWUhgdwrevqevpeuoeunetmetlftkfsjfsifr\ hfrgfrfbqbRbNQ`SQZXPXaOVf } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 20-02-08 (Fractal Sponge [No Rating])
by Jim Muth 20 Feb '08

20 Feb '08

FOTD -- February 20, 2008 (No Rating) Fractal visionaries and enthusiasts: Since I am not yet feeling up to par, today's discussion will again be brief. The image is a scene in the fractal that results when 7 negative parts of Z^(-1.5) are combined with 1 negative part of Z^(-6.6) and (1/C) is added. I gave the image no rating, though for some reason now forgotten, I named it "Fractal Sponge". The calculation time of 2 minutes is brief enough to give no one trouble. And for even more convenience, the finished image will soon be posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A typical midwinter day prevailed here at Fractal Central on Tuesday, with partly cloudy skies, a few stray flakes of snow, and a temperature of 34F 1C. The fractal cats enjoyed the sunny periods, rolled over, then went to sleep. After taking it easy all day Tuesday, I hope to be back to near full prodctivity by Wednesday. (I write the FOTD discussions on the previous day.) The next FOTD will likely be posted in 24 hours. Until then, take care, and search for something. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Fractal_Sponge { ; time=0:02:02.68-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+1.325464621083165/+0.049273549792319/\ 1.948911e+007/1/7.5/1.23877376398406902e-007 params=-7/-1.5/-1/-6.6/0/0/0/0 float=y maxiter=1200 inside=0 logmap=157 periodicity=10 colors=000LJLzyuzsuzquzvuzkozokzhgziduaZwdVrXRrZNm\ VHmTEhPAhL6hJ0cG0cE0ZA0X60T40R00P00ER04qRAk`GggJdk\ LbmNZoRXqTTsVRuZNv`LzbHzeGzgCziAzm6zo4zq2zkAzgGzdL\ z`RzXZzTdvPiuLosGivCex8`z4Xz0Rz0Nz0Hz0Ez0Az0HgAPCN\ V0LZ0Lb0Je0Ji0Hm0Hq0Hu0Gx0Gz0Ez0Ez0Ez0Gz4GvHHoVHgg\ J`uJTzJLzPNzTPzXPxbRqeTiiTbdVXZXRVXLPZGJ`AG`4Ab04d\ 00d04Z06T0AN0CH0EC0H80J20L00P00R00T00R00P00N00L00L\ 00J20H60GA0GE0EH0CL0AN08R08V06Z04b02e02g06g0Ag0Eg0\ Gg0Jg2Ng2Rg4Tg6Xg8`gAbgCegCigEmgGogHsgJvgLxgLPbX0Z\ gHmgezgzzgzzdzzbzz`zzZzzXzzTzzRzzPzzNzxLzxJzvGzuEz\ sCzqAzo8zm4zk2zi0zg0ze0ze0zi2vkAsmGooNksVgu`dvg`xm\ XuqVqsTmvRixNezLbzJZzHVzGTz00A00E00H00L00N00R20V40\ X80`A0dE0eG0iJ2mL4oN6sRAvTCxXEzZGz`HzLZx8oo0ze0zZ0\ zb0zd0ze0zg4zk8zmCzoHzqLzsRzvVzx`zzdzzgzzmzzqzzvzz\ zzzzzzvzzozsgzg`zXTzNLzCEz06z00z00z0zzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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No FOTD for Feb 19
by Jim Muth 19 Feb '08

19 Feb '08

There will be no FOTD for Feb 19 because I came down with a case of the Hong Kong, or something else, flu. I almost never get the flu, but this time I did. I seem to have reached the recovery stage however, and unless there is a serious relapse, The FOTD for Feb 20 will appear on schedule. JIM

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FOTD 18-02-08 (Two Sides of a Coin [7])
by Jim Muth 18 Feb '08

18 Feb '08

FOTD -- February 18, 2008 (Rating 7) Fractal visionaries and enthusiasts: Unfortunately, with a viral attack, I am not feeling up to par, (me, not the computer), so today's discussion will be brief. The left half of today's image is half evaporated; the other half is normal. And the dividing line runs right through the center. I'll not describe the parameter tricks that created the unusual effect. They are clear from the parameter readings. The rating of a 7 seems appropriate for such an unusual image. The name "Two Sides of a Coin" describes the two dis-similar halves of the picture. The calculation time of 10-1/4 seconds is so fast as to be completed almost before it starts. And if running parameter files is inconvenient, the finished image is posted for instant enjoyment on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The temperature reached 41F 5C here at Fractal Central on Sunday, but heavy clouds kept the mood depressed. At least, the forecasted rain held off until after dark. The fractal cats held off asking for their daily treats until after dark also. Ignoring the coughs and sneezes, my day was fair enough. The next FOTD will be posted in 24 hours. Until then, take care, and search through the darkness for the light. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= 2_Sides_of_a_Coin { ; time=0:00:10.16-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip center-mag=+9.91007278492382100/+5.580966722131834\ 00/287477.6/1/-20/0 params=-4/-1.6/-0.8/-7.7/0/\ 11666860000000000.0 float=y maxiter=1000 inside=atan periodicity=10 colors=000btTgvOmxJrzEpwQnt`lqkjovklrlinmgjndfobcn\ camd_keZjfXigVhhTfiSejQdkOclNeiWggcidljbth_rfYqdWo\ bTn`RmYPkXNjUKhUIgPGdQEdJBZM9a00KJ5_C8VSAaSDa`FbeH\ ciKczZdrOezcezTfzZfzcazhYzUUiTPdTLZTHUSCOS8JS4ES0e\ vPzzZpoUpeZpWbqMgqClq2pDdGCgLCiQBkVBm_BpdAriAtnAvr\ 8tm6rh4pd2n_0mW6pYBrZGt`LvaRuSXtJbsAhr1cc5ZP9VBCbT\ BijBldDn_EqVFsQHvLIxGJzBKtDcoFvtGqxHltMopQqlUshYuv\ hFsmPpqYmufjyoglZd_JaO3cRBeUIfXQh_XjbdkdkjYejS_iMU\ iGOiAIxWoecnOkn6sn6jm6al6Tk6Kj6CjKRdXeZitTgoWekYdf\ _bbbaYd_UfZQhVPfROeNNcJMbFLaBK_7JZ3IYDQUMYQVeMcmIl\ uFfrD`pCVmAQk9TdBWYCZSEaLFcFG_AUW6fS2sO9nLGiINdFU`\ B`W8gR5nM2uIRTQo0Yl6_jBahHbfMddRenQowQxnYVee1h_1jV\ 1lQ1nL1pG1rB1qAEpARo9co9pjCofEnaGmYJmTLlPNkLPkMTdN\ WZO_SObMPfFQi9Ql3ZpDftNnwXko`hgde_hbSl_KpXDtbKmgQf\ mW_raTfh_WofLvmOjnQZoSNpUBqW0r`sRakWbc_cXccPhdIleA\ pe3tVIsKXsAjsGlmMnhRpcXrZ } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 17-02-08 (Going to Pieces [7])
by Jim Muth 17 Feb '08

17 Feb '08

FOTD -- February 17, 2008 (Rating 7) Fractal visionaries and enthusiasts: Visionaries see things, sometimes supernatural things, that ordinary people miss, but skeptics know that these things seen by visionaries exist only in the visionaries' minds, and therefore are not real. So far, so good, but then we get to fractals, which exist only as ideas in the mind until they are made real by a computer. So, depending on the definition of the word 'real', fractals can be real, unreal, or somewhere in between. Of course, it does not necessarily follow that the supernatural visions of visionaries are real . . . or could they be real . . . ? Regardless, today's image is worth the 7 points I gave it. It's a scene quite deep in the western east-style valley of the Z^(2.99)+C Mandeloid. In the case of the Z^2.99 fractal, the east and west valleys are quite different. Instead of broadening into a wedge, the valley on the west side of the main bay of today's parent fractal is starting to pinch off. The pinching has little effect on the presence of cubic minibrots, which are quite numerous and quick to find. I named the image "Going to Pieces", though I have forgotten why I gave it this name. The calculation time of 6-1/3 minutes is about what would be expected for an above-average image. (Can so many images actually be above average?) Why not escape the chore of calculation by viewing the already-calculated image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A really pleasant midwinter day prevailed here at Fractal Central on Saturday, with full sunshine and a temperature of 34F 1C. The fractal cats must have agreed, for they passed much of the afternoon at the back window, watching for squirrels. My day was spent taking it easy, an occupation that takes some getting used to. The next FOTD will appear in 24 hours. At least, it is scheduled to. Until next time, take care, and when skeptics tell you that fractals are all in the mind, remind them that the mind is quite real. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Going_to_Pieces { ; time=0:06:21.85-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotN float=y center-mag=-0.4160061105507027/-0.0015889616893713\ /9.619985e+011/1/-23.5/0 params=2.99/0/0/0/0/0 maxiter=10000 inside=0 logmap=1054 periodicity=10 mathtolerance=0.05/1 colors=000b_MbZNbYObXPbXQbXREFBGKCIOCKSCMUCOUCQUDS\ UDUUDWUDYUDZUDYUCXUCWUCVUCUUCUUBTUBSUBRUBQUBQUAPUA\ OUANUAMUAMUALUDKWFKYHJ_JIaLIcNHePGgRGfTFeVEdXEc_Db\ aCacC`eBZgAYiAXk9Wm8Vo8Uq7Ts5Qz7Su8UpAWkBXfDZaE`XG\ bSFbMHcOJcQKcSMcUNcWPcYQcZSc`TcbVcdWdfYdhZdj`dkadm\ cdoddqfdsgduidwjdxgfpehicjaalV_nNYoGTlMPiRLgWHd`Da\ e9_j5Xo1Vt7XnCYiI_cN`ZTbTYcOcgGbdJbaLbZNbWQaTSaQUa\ NXaKZaH`TTcLceCUh4Uj6Uh7Ug8Ue9UdAUbBUaCU_DUZEUXFUW\ HUUIUTJURKUQLUOMUNNULOUKPUIQUHNUPKUWHQcF7jH9hJAfKB\ dMCcNDaPF_QGZSHXTIVVJUWKSYMQ_NPaONcQLeSKgUIiWGkYFm\ _DoaBqcAseFJBJ40NJ6HYCBkI6lJ7lK9lLAmLCmMDnNFnOHnPI\ oPKoQLoRNpSOpTQqTSqUTqVVrWWrXYrXZqY_qY`pZ`pZapZao_\ ao_bo_cn`cn`dmadmaelbelbflbgkcgkchjdhjdijdjiejiekh\ fkhflgglggmggnfhnfhoeioeipUj2VkJWlMXmPXnSYoVZpY_q`\ _rc`sfatibulbvocwqdxteywMzzOzzPzzQzzRzzSzzUzzVzzWz\ zXzzYzzZzzbzzbzzbzzbzzbzz } frm:MandelbrotN {; Jim Muth b=p1, z=p2, c=p3+pixel: z=z^(b)+c, |z| <= 16 } END PARAMETER FILE=========================================

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FOTD 16-02-08 (Iteration Feathers [8])
by Jim Muth 15 Feb '08

15 Feb '08

FOTD -- February 16, 2008 (Rating 8) Fractal visionaries and enthusiasts: Today's image is a further excursion into the debris at the edges of East Valley wedges. The scene of today's fractal is actually in the valley on the west side of the main bay of the Z^(3.01)+C Mandeloid, but this valley is a mirror image of the valley on the east side of the bay, and therefore has the same characteristics. In my opinion, the image is one point better than yesterday's, and honestly earns its rating of an 8. If I had a bit more time to work on the coloring, I might have been able to raise the rating to an 8-1/2. The fractal picture reminds me of nothing as much as fancy feathers, which is why I named it "Iteration feathers". The calculation time of 3-1/4 minutes is suitably brief. The finished GIF image is available as always on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Heavy clouds and a chilly temperature of 36F 2C made Friday a rather unpleasant day here at Fractal Central. The only plus was that it stayed dry. The fractal cats were too busy chasing each other around the place to be concerned with the weather. My day was perfectly average, as I suppose tomorrow will be. The next FOTD is due in 24 hours. Until then, take care, and branch out into those curled-up higher dimensions. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Iteration_Feathers { ; time=0:03:15.26-SF5 on P4-2000 reset=2004 type=formula formulafile=slices.frm formulaname=MandelbrotN passes=1 center-mag=-0.3862006268294/+0.0060172237532/\ 2.616311e+009/1/35/0 params=3.01/0/0/0/0/0 float=y maxiter=2400 inside=255 logmap=418 periodicity=10 colors=000iVJiVJiUIhUIhTIgTIgTHfSHfSHeRHeRGdRGdQGc\ QGcPFbPFbPFaOFaOE`NE`NE_NE_MDZMDZLDYLDYLCXKCXKCWKC\ WJCVJBUIBUIBTIBTHASHARGARGAQG9PF9PF9OE9NE8NE8MD8LD\ 8LC7KC7KC7JB7IB6IA6HA6GA6G96F95E95E85D85C74C74B74A\ 64AEW9EV9DU8DS8CR8BQ7BP7AO7AM69L69K58J58I57G47F000\ 46E45D35C34A2492382371261241130120018ym7wk7vj7ti7s\ h7qg6pf6oe6mc6lb6ja6i`5h_5fZ5eY5cW5bV4aU4_T4ZS4XR4\ WQ4VP3TN3SM3QL3PK3NJ2MI2LH2JF2IE2GD2FC1EB1CA1B9197\ 186075054043022ZKKilObcKXVGPOCBK8474q2gk1be1Y_1TU1\ OO0JI0EC09604mtWlsVkrVjqUjpUioThnTgnSgmSflRekRdjQd\ iQciPbhPagOafO`eO_dN_dNZcMYbMXaLX`LW_KV_KUZJUYJTXI\ SWIRVHRVHQUGPTGPSGORFNQFUUZUPUUOUKNDJMCJLCIKBHKBGJ\ AGIAFH9EG9DF8DPcCE8BD7BC7AB69A68A58957846745635534\ 52342231221110000ozAmz9lz9jz9gz8gz8fz8ey8cx7bw7`u7\ _s7cq6ho6mm6rk5vi5zg5ze5zc4zc4zc4zc4zc3zc3zc3zc2zc\ 2zc2zc2zc1zc1zc1zc1zc0zzz } frm:MandelbrotN {; Jim Muth b=p1, z=p2, c=p3+pixel: z=z^(b)+c, |z| <= 16 } END PARAMETER FILE=========================================

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FOTD 15-02-08 (A Whole New World [7])
by Jim Muth 15 Feb '08

15 Feb '08

FOTD -- February 15, 2008 (Rating 7) Fractal visionaries and enthusiasts: While searching for fractals Thursday, I found a whole new world -- not that this was much of a discovery, since I find a new world every time I visit fractal land. But this discovery was a bit more interesting than usual, and in my opinion, it was worth the name I gave to today's image. The new world is in East Valley of the (-Z)^(2.1)+C Mandeloid, which has started to broaden into a wedge. At first glance, the inside edge of this wedge appears perfectly featureless, but with fractals, things are seldom as they appear. When I checked this edge more closely than ever before, I found tiny irregulari- ties, which enlarge into curious gill-like features filled with minibrots like the one in today's image. If there had been more time to work on the coloring, the image might have rated an 8. As it is, the rating of a 7 will have to do. The calculation time of 5 minutes is slightly slow, though still well within reason. Also within reason is the trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to view the finished image there. A mostly sunny day with light winds and a temperature of 37F 3C graced the Fractal Central area on Thursday, while the fractal cats graced their shelf by the window, watching for excitement. I graced the work desk most of the day, but finished in time to find the day's FOTD. The next in the near-endless series of moderately impressive fractal images will be posted in 24 hours. Until then, take care, and when we run out of ideas, a miracle sometimes happens. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Whole_New_World { ; time=0:05:04.78-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotMiN passes=1 center-mag=+0.256859403185/-0.075292790494/\ 8.72292e+007/1/-155/0 params=2.1/0/0/0/0/0 float=y maxiter=2600 inside=0 periodicity=10 colors=000f9gg8fh7ei5cj4bk3al2`j5Zh7Yf9XdBWbDU`FTZ\ HSYJRXPUWUWV_YUd_UiaXebZbca_dcXefTfhQgkNhmKizwizpc\ zm6yh9xcCwZFuUIsPLqKOoFRmATk5Vi8WgAYeAWcAUbASaAQ`A\ OZAMWAKUAIUA7UAJIhmJgmKfmLemMdmNcmNamO_mPYjQWgRUdR\ SaPRZNPWMPTKPQJPNHPKFPIEPJCPKBPL9PM8PMO4_WIebVjjhp\ quukffeTT_FEV10X44Z78`ACbDFdFJfINhLQjOUlRYmT`kUZiV\ YhVXfWWeXVcXUbYT`ZR_ZQY_PX`OV`NUaMSbLRbKTWJUQIWJIX\ DHY7H`0Lb0Pd1Tg2Xi4`k5dn6hp7lr8on9lkAihAgeBdbCb_C_\ WBWTATQAPMAMIAIECGGEIIGJMIMPKOTLRWMTZNW`OXcNZeN_hN\ ajNbmMdoMerMgtMhDy_Gu`IqaKmbNicPfdRceU`fWYgYWhVWeS\ WcPW`MWZKWWHWUEXRBYP9ZNA_PB`RCaTDbVEcXFeZGg`HhbIjd\ JkfKmhLojMplNqnNppMolLniKlfJicIg`HeYGbVG`SFZPEWMDU\ JCSGBQDAPAAO7BP8CR8CT9DW9EZAEaAFdBGfBGiCHlCHnCOYLU\ IUTJVSJWRKXRKXQLYPLZOMZOM_NN`MN`LOaLObKPbJPcIQdIQd\ `EbdHghJllMqoOvpPupPupQupQtpRtqRtqStqSsqTsqTsrUsrU\ rrVrrVr`HoaGmbFlcDkdCjeBh } frm:MandelbrotMiN {; Jim Muth b=p1, z=p2, c=p3+pixel: z=(-z)^(b)+c, |z| <= 16 } END PARAMETER FILE=========================================

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FOTD 14-02-08 (Split in Infinity [7])
by Jim Muth 14 Feb '08

14 Feb '08

FOTD -- February 14, 2008 (Rating 7) Fractal visionaries and enthusiasts: Though today's image looks nothing at all like a typical scene in East Valley, it actually is an East Valley scene. Well, to be honest, it's not East Valley of the Mandelbrot set that the scene lies in, it's East Valley of the Z^2.01+C Mandeloid. And to further confuse matters, the parent fractal has been rotated about 180 degrees by the MandelbrotBC3 formula, so that East Valley lies on the west side of the complex plane. As a result of the rotation, the negative X-axis split now intersects East Valley, and works no end of mischief with it. Instead of terminating in a point, the valley has broadened into a wedge, with totally new elements along the north and south corners of the wedge. Today's scene lies in some of this new stuff on the south side of the valley-wedge. I rated the image at a 7, even though I was a bit cursory with the coloring. Then I named it "Split in Infinity". The name implies that fractals are infinite, and the East Valley in today's parent fractal is all split up. The calculation time of 7-1/2 minutes is slightly slow. So why not get relief by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> By the way, sometimes Paul cannot calculate and post the images immediately. If they are not there when you visit, try again a little later. Freezing rain fell all morning here at Fractal Central on Wednes- day, while the temperature hovered just below freezing. Strange- ly enough, when the temperature rose 3 degreess above freezing in the afternoon, the rain changed to snow. The fractal cats amused themselves watching the passers by slipping and sliding on the icy sidewalks. My day was spent working. The next FOTD is due in 24 hours. If all goes well, it will appear on schedule. Until then, take care, and seek the right light. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Split_in_Infinity { ; time=0:07:33.03-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-0.252278582924513/-0.008434427532035/\ 7.078046e+012/1/165/0 params=2.01/0/20.3/0 float=y maxiter=5000 inside=0 mathtolerance=0.05/1 colors=000c8Mc9McAMdBMdCLdDLdELeFLeGLeHLeIKfJKfKKf\ LKfMKfNKdMJcMJbLJaLJ`KJ_KIZJIYJIXIIWIIUHHTHHSGHRGH\ QFHPFGOEGNEGMDGLDGKDGMHKOLOQOSRSVTWZVZbXbfYfi_imam\ qbptcqqcqocrldrjdrhdsedscesaetZetXeuUfuSfuQfvNfvLg\ vJgwGgwEgwCMvE0vGCnDOfA_Z7jR5fO9cMC_KFXIIUGLQEONCR\ JAUG8XD6_F4`G3aI1bJ0brV1pZHobXnekoelofmofnneomeome\ oldokdokdpjdpjcpicphcphbqgbqfbqfbqeaqeardarc`rc`rb\ `rb`raYo`Vl_Si_PgZMdYJaYH_XGYXGWXGUXGSWFQWFOWFMWFK\ WFIVEGVEEVECVEAVE9UJAUOAUTAUYAUbAUgAUkAViCWgEWfFXd\ HXbIYaKY_LZYNZXO_VQ_UR`ST`QUaPWaNXbLZbK_cIacHbcIbd\ KbdLbeMbeNbfPbfQbfRbgSbgUbhVbhWbhXbfZdd`ebaf`cgZeh\ XfiVhjTjkSkl4ca5rWIkaVdfgYksSppTmmTkjUigUgdVebVcYW\ aTX`PX_KYYGYXBZW7ZV8XU8VU8UT9ST9QS9PS9NSALRAKRAIQB\ GQBFPBDPBBPCAOC8OC6ND5ND3MD1MD0MDI6HL7KO7OR8RT8UW8\ YZ9``9cc9gfAjiAmkAqnBtqBwsBuoLtkUsgcrdlp`ioYgmVdlR\ bjO`iLYgIWfEUdBRc8Pb5Nc7M } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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FOTD 13-02-08 (Golden Pilgrimage [6])
by Jim Muth 13 Feb '08

13 Feb '08

FOTD -- February 13, 2008 (Rating 6) Fractal visionaries and enthusiasts: New but minor formula alert! Today's image is based on a formula I wrote some time back as a speed test. I'm not sure if it's the fastest way to draw the (-Z)^(1.618)+C fractals or not, but I know that some of my formulas that draw the same figures are notably slower. The image shows a minibrot lying rather deep in the northern branch of Seahorse Valley of the parent Mandeloid. Since I can find nothing extraordinary about it, I rated it at a measly 6. The name "Golden Pilgrimage" is simply a rather poetic phrase referring to the golden ratio, which is the exponent of Z in today's image. The calculation time of 11 minutes borders on slowness, so I recommend viewing the image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Light snow Tuesday morning here at Fractal Central turned to heavier snow in the afternoon, while the temperature hovered around 16C -9C. By evening about 5 inches, 12cm, had piled up. The fractal cats observed the action with disinterest. My day was occupied with more serious work. The next FOTD will appear in 24 hours. Until that wonderful moment, take care, and get the smickey-algebroe curve. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Golden_Pilgrimage { ; time=0:11:05.21-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotGold passes=1 center-mag=-0.74240875714785280/+0.032914523503643\ 36/434085.6 params=0/0/0/0 float=y maxiter=10000 inside=0 outside=tdis periodicity=10 colors=000ceG_`JVXMRSPNNTIJWEEZAAaCL_DWZEfYFpXHnSI\ lOKjKLhFNfBOd7Qb5R`5SZ5FgO7pp7mo7jn9gmBemDblF_kHXj\ JVjLSiNPhPNhRMdRM_QMTPJOQIMRILUIPZJVdL_hLcgKbgJbfJ\ bfIaeIaeHadHadG`cG`cF`bF`bE_aE_aD_aD__E`YF`WGaVGaT\ HbRIbQIcOJcMKdLKdMSaMZ_MeXMmVMtSMzQMzOPzSRtWTm_Vfb\ X_fZTj`Mm_LlZKkYJjXIiWHhVGhUFgTEfSDeRCdRBdJAOCA7FF\ DHKIKNNMNSPOXROaUOfWOkYOpYNpVLjTJeRH_PGVNEPLCKJAEH\ 998OI7aR7q57r57r59r5Dr5Hr5Kr5Or5Rr5`h7j_CsRGrVDqYA\ qa7pd5oh5ok5no5nr5ct5TuIIwV8xgCwhGwiKwjOwkSwkWwl_w\ mcwngwnkwoowpswqvwqssppopnkokhohdnf`ncYmaUmZQlWNlU\ JkRFkPCkKMTFWBGTCGRDHPEHNFHLGLJHPIHTHHXGI_FIcDIgCJ\ kBJoAJr9JqAIpBIpCIoDInEInFHmGHlHHlIHkJHkJHjINjISiI\ XiHbhHghHl7sC7pD7nE8lFCiFFgGIeHMbHP`ISZJWWJZUKaSLd\ QLZNPTLTNJXHH`BFd7Dh7Bl8CfHCaPCXYDReDMnDHvDCtHEsLF\ rOGpSIoWJnZKmbLkfNjiOimPgqRftSexTdzUczScyQbxObwMav\ KauI`tG`tFcqKdoIfmGgkEhjC } frm:MandelbrotGold {; Jim Muth z=p1, c=p2+pixel, a=((sqrt(5)+1)*0.5): z=(-z)^(a)+c, |z| < 16 } END PARAMETER FILE=========================================

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FOTD 12-02-08 (Eastern Enterprise [7.5])
by Jim Muth 12 Feb '08

12 Feb '08

FOTD -- February 12, 2008 (Rating 7.5) Fractal visionaries and enthusiasts: With a load of work to clear away on Monday, I had only limited time for a fractal search. But I still managed to find a respectable one for today's FOTD. The search left little time for the FOTD discussion however. Today's image is a near-Julia set of one of the East Valleys of the (-Z)^(1.467)+C Mandeloid. I say one of the East Valleys because the Mandeloid has several of them. The valley in question is little more than a string of scattered, only loosely connected bits of fractal stuff, making a near-Julia set that consists of mostly inside area brought to life by the 'bof60' inside fill. I named the image "Eastern Enterprise" when I could think of nothing better. Then I rated it at a 7.5, which includes the usual 1/2 point for my coloring. The calculation time of 4 minutes is reasonable, but not quite as reasonable as a trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to instantly view the completed image there. After a morning low of 5F -15C the temperature rose to 18F -8C here at Fractal Central on Monday. The sky remained clear, but with such frigid temperatures and a biting wind, the sun gave little comfort. The fractal cats kept close to the heat most of the day. As for me, I kept myself busy wrapping up the big job. The task was almost finished when I called it quits at 4pm. The next FOTD will be posted in 24 hours. Until then, take care, and see you in fractal land. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Eastern_Enterprise { ; time=0:00:00.00-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=EvenMoreSlices passes=1 float=yes center-mag=0.223837/0.0792099/0.8378746/1/75/0 params=1.467/0/0.075/0/0.603771266/0.249173157/0/0 maxiter=1750 inside=bof60 logmap=yes periodicity=10 colors=0000EK0FONGSQHWTI_VJcXKgZLk`MobNsdNufQugTti\ VsjYqk`pmbnnekogiqjgrmdtobur`vuYxweyzfzzzwzztxzqvW\ ntYkrZhp_enablb_jcXheUffRdgObiL`jIZkFYlHZiI_gJ`eKa\ cMbaNcZOdXPeVRfTSgRThOUiMWjKXkIYlGZmEUpMPsUKv`RwdX\ xgbxjiymoypuzszzvvyuryumyuiyudxu`xuWxuSxuNwuJwuEwu\ Awu6wu7rr7np8jm8ek9ah9Yf9TdAPaAL_BGXBCVB8Tdz7az9_z\ AYwCVuDTrERoGPlHMjJKgKIdLGaND_OBXQ9UR7SSAURCVQFWPH\ XOKYNMZMO_LR`KTaJWbIYcH`dGbeFdfFagI_hLYiOVjRTkURlX\ Pm_MnbKoeIphGpjJohLofOndQnbTm`VmZYlX_lVbkTdkRgjPij\ NkjMzlc_yVWpXShZO``KTbHLcKNdNOdPQdSRdVTdXUd_VebXed\ Yeg_ej`elaeuUmxVqzVuzVywPsqKnnNmkQlhTkeVkbYj_`iXch\ Uehuaekf_bjVdfZebafZdgVgiRjjNmkJplFskJpjMmjPkiShiV\ fhYch`a`jYTtULzRHtMEkIBbD8U9EVAKWBQWCWXDaXEgYFmYFk\ cJiiNhoQfuUezXWxUMwSOxQQyPRyOzzNzzLzzKzzJzzIzBzzRu\ zfpzulzwgzybzzYzzTzzOzzJzzEuxGspIqhKckURnbEqkJmdNj\ YRgRWcK_`DvXsyUqzQozNmgMe } frm:EvenMoreSlices {; Jim Muth ; P1--exponent, P2--angle, ; P3--M center, P4--J center, z=pixel+(p4), c=p3+(pixel*p2): z=(-z)^(p1)+c, |z| < 16 } END PARAMETER FILE=========================================

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FOTD 11-02-08 (East Revisited [6])
by Jim Muth 11 Feb '08

11 Feb '08

FOTD -- February 11, 2008 (6) Fractal visionaries and enthusiasts: Today's image is a new view of the East Valley minibrot that made its debut in the FOTD of February 8. Today's view happens to be sliced in the Parabolic direction, which is defined by the real(c) and real(z) axes. Actually, the oddly shaped hole at the center is not exactly the same one that was the minibrot of Feb 8. Minibrots in the Mandelbrot set come in families, the members of which are located by examining the position of the holes in the minibrot's Julia set. I named the image "East Revisited" for obvious reasons. I rated it at a 6 because I feel that's what it's worth. The calcula- tion time of 6-1/2 minutes is quite reasonable, as also is viewing the finshed image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Sunday here at Fractal Central could have been better. The temperature started at freezing, but fell steadily during the day to 10F -12C by 8pm. In addition, a series of heavy snow squalls with near white-out conditions left the ground covered with 3 inches, 7cm, of blowing snow. The fractal cats observed all this with dis-interest, rolled over, and returned to sleep. My day was busier than anticipated. I'm not sure about tomorrow, but the next FOTD is due to be posted in 24 hours. Until then, take care, and where does it all go? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= East_Revisited { ; time=0:06:25.47-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot2 passes=1 inside=0 center-mag=+0.00000000025482716/+0.000000000000000\ 00/3.105068e+008/1.447e-005/90/2.4233320905509e-010 params=0/90/0/0/0.275976577981/-0.006756061446/0.4\ 04325508607/0.658046718998 float=y maxiter=6000 logmap=460 periodicity=10 colors=000RcTOe`8gZCeYGdYKbYOaXS_XWZX_XXcWWgUWkTWo\ SWfZXZeXQkXIrXAxXFsUJoRNkORgLVcIZ_FbWCfSAaU8XW7SY6\ N_5Ia4Db3Fd8GfCHhHJiLKkQLmUMnYLkWKhVJeUIbSH_RGXQFU\ OFRNEOMDLKCIJBFIACG99F86E84DB6FE8GG9HJBILCJOELRGMT\ INWKOYOPVVJSdDPn7Mx2Pt4Rp5Tl6Wi7Ye9_aAbZBdVCfREiOF\ kKGmGHpDJr9Kt5Lv2Mr4Pn6Sk7Ug9XdAZbD`aFb`HdZJfYLhXN\ jVPkURmTToRVqQXsPZuO`vYWtgSrqOqdImTDjH8gKAeMBdPCcR\ DbUEaWF_ZGZ`IYcJXeKWhLUjMTmNSoORqPQRcZ1rf6sdBtbGu`\ LuZQvXVuV_qTai_c_feRl8EVBJTENSHRQKVPNZOQbMTfLWjJZn\ IvrHjjNUbTRWZNOcKHdG9eD2eF7cHCaIH_KMYMR`NWmPjzQozQ\ lzQjzQhzQ`zQczQXzeLYwFLwGRwGXwGawQgFSdJUaNWZQXWUZT\ Y`QzaNzcKzeHzmEoZ1pX7qVCrTHsRNtQSuOXvMbwKgxJluKmsL\ mpLmnMnlNniNngOoePobPo`QoZRpWRpUSpSTqPTqNUqLUqOVpR\ WpUXoXYo_Znb_nd_mg`mjalmblpcksdkuhksmirrgqyepzcoza\ nz_mzYlzWkzUizShzQgzOfzMezKdzIczGbzEazDZzJXzPUzVSz\ `PzfNzlOzhOzdOz`PzXPzTPzP } frm:SliceJulibrot2 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 10-02-08 (FOTD Feb 10, 08 [No Rating])
by Jim Muth 10 Feb '08

10 Feb '08

FOTD -- February 10, 2008 (No Rating) Fractal visionaries and enthusiasts: Due to an unexpected rush job on Saturday, today's FOTD is late. It's the same job that came in rather unexpectedly last February and caused me to miss about 2 week's FOTD's. Luckily, this year the job is much smaller. In a pinch on Saturday, I tracked down a miniscule minibrot on a filament of a larger minibrot on a filament extending northwest from the next bud beyond the large period-2 bud on the main spike of the Mandelbrot set. At the magnitude of today's image, the minibrot itself is still far beyond sight, but I have been down there and can report that it is a rather routine one, sur- rounded by a basin of attraction that consists of little more than fancy circles. Most of the action lies much farther out in the magnitude range of today's image. Since the image more or less found itself, I gave it neither a name nor a rating. And the calculation time is a rather slow 18 minutes. But to save calculation time I have sent the comple- ted image on ahead to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where it will soon be posted for real-time viewing. Saturday proved rather unpleasant here at Fractal Central, with cloudy skies, a temperature just above freezing, and about 2 inches, 5cm, of wet sloppy snow. The inclement day ended with lightning and thunder. As the fractal cats watched the action, they were glad to be inside. I was glad to be inside also, though I will be even more glad when the work is wrapped up. If all goes well, this will be Sunday evening. The next FOTD will hopefully be ready in 24 hours. Until then, take care, and keep hopping and hoping. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= FOTD_for_Feb_10_08 { ; time=0:17:59.67-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-1.4234484737142403742012167263542/\ -0.15642423746912204882900998109289/2.962351e+027/\ 1/-155/0 params=0/0 float=y maxiter=4200 colors=000jTFmSDpRBrQ9uP7xO5zN3DBrGEnIGkLJhNLeQObS\ Q_VTXXVU_YRa_OdbLfdIigFkiCnl9sm3pn6nn8loAioCgpEepG\ bpJ`qLZqNWrPUrRUuRSrTQpVOmXMkZKi`IfbGddEbfC_hAYj9W\ lBYhD_dFa`HbYHcZGc_FdaFebEecEfdDgeCgfChgBihoNBmODl\ PEjQFiRGgRIfSJeTKcULbVM`VO_WPZXQXYRWZSUZUT_VR`WcVw\ aVv_Vv`XxYVvVUtTTrQSpORnLPlIOjGNhDMfANhBLdBJaBIYCG\ VCERCDODBKD9HD8DE6AE46G22E33D34B34A458457465464572\ 5715805826C46G66K86O96SB7WD7_F7cH7gI7kKBjMEiNHiPKh\ RNhSQgUTfWWfXZeZae`ddagd`Vi_JnZ5w_7r`8n`9jaAebBabC\ YbETbFP`FLZFGYFCYH5XH8UHBWHEXGHYFKZFN`EQaDUcCYdBae\ BefAkh9oi8sj7wm2zj7wgCreHmbLh_QcYVZV_TWaNTcPReQPgR\ NiSLkTJlUHnWFpXDrYBtZ9v_2yd7w`BvYFuVJtSNsPRqMVpJZo\ GbnDikBfmAcn9`p8Yq7Wr6YoAZmD_kGaiJbgMcePecSf`WgZZi\ XajVdkTgmRjnPmsProNplLoiJmeIlbGj_EiWDgTBfQ9dM8cJ6a\ G4`D3_J9YPFWULV_QTdWSjaQwiRofPgdO_bNT_LLYKDWJ6UIMb\ XP`VS_TVZRXYP_XNbWLeVJgUH } END PARAMETER FILE=========================================

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Re: AOTD
by JackOfTradeZ＠comcast.net 09 Feb '08

09 Feb '08

. Animation of Jim Muth FOTD January 26, 2008 (Pentagon Heptagon) is posted: http://www.fractal-animation.net/vid/polygonz.zip "Journey to the Black Hole" 640x480 WMV , 1 min 45 sec, 17 MEG Enjoy! JoTz .

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FOTD 09-02-08 (The Blob Returns [6])
by Jim Muth 09 Feb '08

09 Feb '08

FOTD -- February 09, 2008 (Rating 6) Fractal visionaries and enthusiasts: I really enjoy those junky old sci-fi and creature-feature movies - the cheap B&W ones they made before the era of computer graphics. One of my favorites was 'The Blob'. The original blob was quick-frozen and dropped somewhere in the arctic, where it was supposed to remain forever frozen. But I fear global warming has melted the blob and returned it to life. The reconstituted blob was last seen in East Valley of the Z^2+C Julibrot, where it was busy absorbing and digesting helpless fractal stuff. But the gray alien creature was spotted by an alert fractalist, who took a picture of its illicit activities. The picture is today's image. Actually, the image is an oblique Julibrot view of the same mini- brot that was featured in yesterday's image. The remnants of the minibrot are visible near the center of the stretched-out gray blob, which was caught in the act of oozing toward its next victims. I named the image "The Blob Returns", which is self explanatory. Then I rated at a 6, which is a little but not too much above average. The calculation time of 1-3/4 minutes is well within reason. The image is also available for viewing on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Cloudy skies, light snow flurries, and a temperature of 39F 4C made for a less-than-ideal day here at Fractal Central on Friday. The fractal cats must have agreed, for they were un-obtrusive most of the day. The work in my department was rather heavy, but it was finished on time. The next FOTD will appear in 24 hours. Until then, take care, think positive, and make it so. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Blob_Returns { ; time=0:01:44.68-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot2 passes=1 center-mag=+0.00000000906052697/-0.000000209298904\ 66/8.685462e+007/0.0248/-92.5881870469584527/89.31\ 640322573726 params=88.552/78.706/139.555/-114.465\ /0.27597657825/-0.00675606143/0.27597657825/-0.006\ 75606143 float=y maxiter=6000 inside=0 logmap=460 periodicity=10 colors=000BZbC_bD_bD_bE`aF`aGaaHaaHaaIbaJb`Kc`Kc`L\ c`Md`Nd`Oe_Oe_Pe_Qf_Rf_Rf_VeZYeY`eXceWgdVjdUmdTpdS\ sdSiZZ`TdRNkIIqBJf4JX6LZ8N_APaBRbDTcFUeHWfIYgK_iMa\ jNbkO`jPZjPXiQWiRUhRShSQgTPgTNfULfVJfVIeWGeXEdXCdY\ BcZ9cZ7b_5b_4bZ7_Z9YZCWYEUYGSYJQYLOXNMXQKXSIXUG_RJ\ bPLeNNhLQkISnGUqEXtCZwA`v9_u8_t7_s7_r6_q5_p4_o4_n3\ _m2_l1_k1_i3Xg5Ve6Sc8Qa9N_BLYCIWEGUFDSHBRI9UMAZQBc\ UChYDmaEreFviGzmHzqIzuJzyKzvJzsJzpJzmJzjJzgJzdJvaJ\ rZJmWJhTJdQJgNJiLJeJIaHIZGIVEHRDHOBHK9GG8GD6G95F53\ F22F44G56H68I7AJ8CJ9DKAFLBHMDJMELNFNOGOPHQPISQJURK\ WSLXSOWTQWUSWUUWVWVVYVW_VXaVXdUYfUYhUZjU_lT_nT`pT`\ rTatTapUemVhjWkgXndYqaZtZ_wW`zVauUbqTcmTdiSeeRfaRg\ XQhTPiPPjLOkHNlDNm9QnDToHWpKZqOasSduVgwZjxbmyepzir\ zlmzkizkdzk`zkWzkSzkNzkJzkEzkAzk5zk1zk3zl5zl6zl8zl\ 9zmBzmCzmEzmGznHznJznKznMzoNzoPzoRzoSzpUzpVzpXzpYz\ pXzoWznWznVzmVzlUzlUzkTzk } frm:SliceJulibrot2 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 08-02-08 (Just Plain East [Unrated])
by Jim Muth 08 Feb '08

08 Feb '08

FOTD -- February 08, 2008 (Unrated) Fractal visionaries and enthusiasts: After a mentally-congesting spate of confusing hyper-images, today's FOTD returns us to the good old East Valley we know so well, where we find a perfectly routine minibrot lying in the star of the period-19 radical on the southern shore. The image is so routine that I could hardly rate it, though I did give it a name. I named it "Just Plain East", which describes it as well as anything could. The calculation time of under 3 seconds is less than the time required to visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view the image there. But calculating the image is not nearly as convenient as viewing it on the web site. After a heavy thunder-storm Wednesday night, Thursday dawned cloudy, breezy and chilly here at Fractal Central. The tempera- ture of 39F 4C was not too cold, but the strong wind made it feel a bit chilly in the open. The fractal cats spent the day taking life easy, while I spent the day trying to finish the work. The fractal of the day from East Valley was an added attraction. The next FOTD will appear right here in 24 hours. Until then, take care, and stick with common sense. It is most likely to be right. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Just_Plain_East { ; time=0:00:02.90-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=+0.27597657825/-0.00675606143/2.56e+008\ /1/180 params=0/0 float=y maxiter=6000 inside=0 logmap=460 symmetry=xaxis periodicity=10 sound=off colors=000ccbOe`8gZCeYGdYKbYOaXS_XWZX_XXcWWgUWkTWo\ SWfZXZeXQkXIrXAxXFsUJoRNkORgLVcIZ_FbWCfSAaU8XW7SY6\ N_5Ia4Db3Fd8GfCHhHJiLKkQLmUMnYLkWKhVJeUIbSH_RGXQFU\ OFRNEOMDLKCIJBFIACG99F86E84DB6FE8GG9HJBILCJOELRGMT\ INWKOYOPVVJSdDPn7Mx2Pt4Rp5Tl6Wi7Ye9_aAbZBdVCfREiOF\ kKGmGHpDJr9Kt5Lv2Mr4Pn6Sk7Ug9XdAZbD`aFb`HdZJfYLhXN\ jVPkURmTToRVqQXsPZuO`vYWtgSrqOqdImTDjH8gKAeMBdPCcR\ DbUEaWF_ZGZ`IYcJXeKWhLUjMTmNSoORqPQRcZ1rf6sdBtbGu`\ LuZQvXVwV_wTah_cVfeHl8EVBJTENSHRQKVPNZOQbMTfLWjJZn\ IqrHYjNUbTRWZNOcKHdG9eD2eF7cHCaIH_KMYMR`NWmPjzQozQ\ lzQjzQhzQ`zQczQXzeLYwFLwGRwGXwGawQgFSdJUaNWZQXWUZT\ Y`QzaNzcKzeHzmEoZ1pX7qVCrTHsRNtQSuOXvMbwKgxJluKmsL\ mpLmnMnlNniNngOoePobPo`QoZRpWRpUSpSTqPTqNUqLUqOVpR\ WpUXoXYo_Znb_nd_mg`mjalmblpcksdkuhksmirrgqyepzcoza\ nz_mzYlzWkzUizShzQgzOfzMezKdzIczGbzEazDZzJXzPUzVSz\ `PzfNzlOzhOzdOz`PzXPzTPzP } END PARAMETER FILE=========================================

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FOTD 07-02-08 (A Sea Change [8])
by Jim Muth 06 Feb '08

06 Feb '08

FOTD -- February 07, 2008 (Rating 8) Fractal visionaries and enthusiasts: Today's FOTD pictures the same scene as yesterday's image, which was kind of split in half. But what a change the different parameters have made. I have gone negative with the real(p3) parameter and increased the real(p4) paremeter to 1.5*(10^-101). As a result, the minibrot that lies at the center is no longer half folded up, it is totally transformed. A real 'Sea Change' has taken place, which is the name I gave the image. Once again, I will not even try to explain what is going on in the image, mainly because I have no idea. It's hard enough to think in 4 dimensions when dealing with the Julibrot figure, much less the 8 dimensions of the HyperJulibrot. All I can do is sit back, study today's image, take a deep breath, and say 'wow'. The rating of an 8 reflects the mathematical interest. The pictorial worth is closer to a 6.5. But I'm just getting started with the HyperMandelbrot set. There's a whole new world waiting there, ready to be explored. Sooner or later some great fractal images are sure to emerge. The calculation time of 1-3/4 minutes is quite fast, and if 'quite' is still too slow, the completed image may be viewed at leisure on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The mild temperature of 57F 14C here at Fractal central on Wednesday was not spoiled by the cloudy skies and fog bank hanging over the river. The fractal cats agreed that the day was pleasant, and renewed their demand for an early treat. My day was spent working and wondering what fractal wonders will be found. The next FOTD, most likely another variation of the scene of yesterday and today, will be posted within 24 hours. Until then, take care, and if empty space holds dark energy, is it possible for absolutely 'nothing' to have ever existed? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Sea_Change { ; time=0:01:43.42-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=HyperMandelbrot2 passes=1 periodicity=0 center-mag=+0.301038546627/+0.023570365936/\ 1.7e+007/1/-152.5/0 params=0/0/0/0/-5.89/0/\ 1.5e-101/0 float=y maxiter=3600 inside=0 logmap=247 colors=000jKQiK5hK6gK7fK8eM9dOAcS8bU7aW6`Y4__3Za2Y\ _1XY0YW0ZU0_S0aM0bG0c90d30i39m3Hr3Qv3YdIeOXm7jtMrV\ `z6Wp9SfBOXEKOGQKJWMMaMPfPSlUVrZYwc_zg9VHGXGN_FTaE\ _cDffClhBsjAykGZlL9jMEiMJhMOgMTfMYeMbdMfURWVWMY`BZ\ e1ghBljLejaXiiSfyVcpT_gXW_WRRYOJUNAUL2TH5RC6O77Q2D\ T8IYDK`LDlR7kdPnpmzzz3CA2IAKQAPXKUbSZhTcnUcuVczcUz\ pcztmzwzzzLGPcKHmO9wm1cL2UF2Z92b32TLCJbLAsUJnRSiP`\ eMi`KrXISSZ2OnJpZNi_Qb_TW`XP`_IabCaZ9SW7JS4AP21`JD\ l_OmXSnVVoSYoQ`pOdqLgrJjrHmcWeQiYCwQHqSLlTPfUTaVXW\ W`RX`SX`SW`TWaTWaUVaUVaVUaVUaWUaWTaXTbXSbYSbYSbZRb\ ZRb_Qb_QmC5iKCeSJ3md6kb9jaCi`Fh_HgZKfYNeWQdVScUVbT\ YaS``RvEktGisHhrIgqJfpLdoMcnNbmOalP`jRZiSY_UZcVUfW\ QiXRkXSnYTpYUrYVuZWwZXyZXrYUkXReWPZVMSUJMUHVTUcSfl\ SsdRjXRbPRUHRM9RECTDFUDIWDLXDOZDR_DUaDWbD_aCc`Cf`C\ j_BnZBqZBpXCoVDnTEmRFlPF`WWQblZecghVpkMynDqoBjoAbo\ 8Wo7Pp59nkPYpcHur1yS3q24j } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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Re: Re: [Fractint] Re: Fractint Question
by JackOfTradeZ＠comcast.net 06 Feb '08

06 Feb '08

. Thanx Jim - I knew about the minimum iter count, guess I can use that also. BTW, animation of the polygons almost finished! JoTz .

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FOTD 06-02-08 (Seeing Double [6])
by Jim Muth 05 Feb '08

05 Feb '08

FOTD -- February 06, 2008 (Rating 6) Fractal visionaries and enthusiasts: When I found the first version of today's image with the Hyper- Mandelbrot2 formula, I shifted to the type=hypercomplex formula, thinking it would be faster. I was totally surprised when the type=hypercomplex formula took almost five times as long to draw exactly the same image. Since then, I have made a few minor changes to the parameters, so the final version that appears as today's FOTD cannot be drawn by the type=hypercomplex. But it is only fair to comment that the periodicity need not be turned off with the type=hypercomplex, which means that images with a significant amount of 'inside' area, may run in about the same time under both formulas. Today's image shows a minibrot in East Valley. The little guy is in a bit of trouble, for it appears he is starting to close up. Actually, the HyperMandelbrot set consists of two classic M-sets that can be made to overlap in various ways, and this is what has happened to the minibrot in today's image. The surrounding elements have split apart, which is why I named the image "Seeing Double". I rated it at a 6 because I can see nothing out of the ordinary with it, nor did I put any signifi- cant effort into the coloring. Perhaps the best thing about the image is its fireball calcula- tion time of under 2 minutes. And even this speed might be exceeded by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the finished image there. Heavy clouds and occasional rain spoiled the mild temperature of 48F 9C here at Fractal Central on Tuesday, while the fractal cats spent the day watching the world pass by. I spent the day working and trying not to work. The work won. The next FOTD will be posted in 24 hours. Until then, take care, and did reality really exist before someone dreamed up the concept? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seeing_Double { ; time=0:01:55.40-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=HyperMandelbrot2 passes=1 center-mag=+0.301038546627/+0.023570365936/1.7e+007\ /1/115/0 params=0/0/0/0/-0.0025/0/1e-008/0 float=y maxiter=3600 inside=0 logmap=247 periodicity=0 colors=000N0UO0UP0UQ0UQ0UQ0UQ0UQ0VR0WR0XR0YR0ZR0_S\ 3`S3aS4`S4_S4ZS4YP7aM9eJChGElDHpAJsCMqEOpGQoISnKUm\ MWlOZjQ`iSbhUdgWffYieYlgZidZfa_bZ_ZW`VT`RQaNNaJKbF\ Ha7KbBEcF8cI3nPJyVYuTVrSToRRlQPhPNeOLbMI_LGWKETJCQ\ IANH8NC3RG6VJ8`NBeQDlUFtXIw`KzdJy`MxVOwMQzDUwEStFQ\ qGOnHMkIKhJIeKGbLE_MCXMAXNBXNBXOCXOCXOCXPDXPDXPDXQ\ EXQEXRFXRFXRFXSGXSGXSGZTH`VIbWJdYKfZLh`NjbOlcPneQp\ fRrhStiTvkUxlVufWraXoXYlSYiUWfWUcXS`ZQY_OVaMSbLPdJ\ MeHJgFGhDDjBAkAAjBBiCChDDgEEfFFeGFdHGcIHaKI`LJ_MJZ\ NKYOLXPMWQNUSOTTOSUPRVQQWRPXSOYFyNGvOHsPIpQJmRKjSL\ gTMdUNaVOZWPWXQTYRQZ3Tc8RcDQfIPdNObujZmdZfZZZTZpzF\ nvGmsHloIkkJiiKhgLgfMfdNdcOcaPb_QaZR_XSZWTYUUXTVVR\ WUQXTOY5jP6iQ7mQ8qR9wRAwRBmSBhSChSDiTEjTFkUGlUHmUH\ nVLoVPpVUqWZsWcuXhwXmzXrzYvzYzzYzzZzzZzzuzzqzznzzk\ zzgzzdzzazzKzzLzzLzzMzzMzzNzzNzzOzzOzzPzzPzzQzzQzz\ RzzRzzSzzSzzTzzTzzUzzUzzV } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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FOTD 05-02-08 (Infernal Landscape [8.5])
by Jim Muth 05 Feb '08

05 Feb '08

FOTD -- February 05, 2008 (Rating 8.5) Fractal visionaries and enthusiasts: I began the day by winning the Spanish Lottery. After that, I was specially selected to buy a 5-day cruise to the Bahamas for $99. Finally, I was contacted by the vice-president of a bank in Burkina Faso, who wants to transfer 18-million U.S. dollars into my bank account. After all this bad news, my attention turned to fractals and the day started to improve. These fractal ogives appear to be everywhere in the HyperMandel- brot set. I found the strangely scalloped one that appears in the background of today's image hiding in a nest of concentric circles in a bud in Seahorse Valley of the large minibrot on the negative X-axis of the Mandelbrot set. I named the image "Infernal Landscape". It does have a kind of hellish aura about it. Then I rated it at an 8-1/2, including, of course, the half-point bonus for my coloring, which makes the entire image. And actually, I feel it's one of the best colored FOTD images to date. The downside is the calculation time, which runs to over 1/2 hour on the fastest computers. I hate to think of the time required to calculate the image on an older machine. But like the bad news I got this morning, all bad news has a bright side, and today's bright side lies on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the finished image is posted for quick and total satisfac- tion. Monday began with 1/2 inch, 1cm, of light snow here at Fractal Central, but the snow ended as fast as it began, and by midday, when the temperature reached 39F 4C, it had completely melted. The fractal cats observed all this with disinterest. For me, most of the day was routine, which left ample time to work on the fractal coloring and earn the extra half point. Tomorrow will likely be a repeat. Until then, take care, and how many fractals does it take to change a light bulb? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Infernal_Landscape { ; time=0:38:17.15-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=HyperMandelbrot2 passes=1 float=y center-mag=-1.76838718877224100/+0.002032313175440\ 55/5241100/1/-86/0 params=0/0/0/0/0.1/0/1e-012/0 maxiter=12000 inside=0 logmap=-1955 periodicity=0 colors=000CWhCWgCWgCWgCWgCWgCWfCWfCWfBWfBWfBXeBXeB\ XeBXeBXeBXdBXdBXdBXdAXdAXcAXcAXcAXcAXcAYbAYbAYbAYb\ AYb9Ya9Ya9Ya9Ya9Ya9Y`9Y`9Y`9Y`9Y`8Za9Y`AY`AX_BX_BW\ ZCWZDWYDVYEVXEUXFUWGTWGTVHTVHSUISUIRTJRTKQSKQSLQRL\ PRMPQNOQNOQONQONPPNQPMPQMPRLORLPSLOSLOTLNUKOUKNVLO\ VLNWKNWKMXLMYLLYLLZLKZNK_MJ`MJ`NIaMIaNHbMHcMGcLGdL\ FdLFeKEeKEfJDgJDgIChJChKBiLBjMAjNAkO9kP9lQ8lR8mS7n\ T7nU6oV6oW5pX5qX4qX4rX3rX3sX2sX2sX2sX2tX2tX2tW2tW2\ tV2tV2uU2uU2uT2uT2uS2vS2vR2vR2vQ2vQ2vP2wP2wO2wO2wN\ 2wN2xM2xM2xL2xM2xM2xM2vN3uO4tO5sP6rP7qQ8pR9oRAnSAm\ SBkTCjUDiUEhVFgVGfWHeXIdXKcYMbYOaZQ__SZ_UY`WX`YWa_\ VaaUbcTceScfRdgQdhOeiNfjMfkLglKgmJimIjmHjmGkmFknEm\ oCnpBnqAor9os8qt7ru6rv5sw4sx3ty2tz3tz3tz3tz3tz3vz3\ vz3vz4vz4yz4xz4xz4xz4xz4xz5xz5yz5yz5yz5yz5yz5yz6yz\ 6yz6zz6zz6zz6zz6zz7zz7zz7zz7zz7zz7zz7zz7zz9zzAzzCz\ zDzzFzzGzzIzzJzzLzzMzzMzz } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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Re: [Fractint] Re: Fractint Question
by Jim Muth 04 Feb '08

04 Feb '08

At 05:34 AM 2/4/08 +0000, you wrote: >. > > >you know if you set the max iterations to say, 1000000, that doesnt mean every pixel iterates that many times, they all bail out according to the nature of the fractal and algorithm at some number less than that. but i assume the lake regions use the max. > >is there a way to determine the maximum number of iterations that any pixel(s) actually did? > >i think there is a way but i cant find it You can get a pretty good estimate of the iteration count by setting the logmap feature to 2, which checks the edge of the frame and automatically resets the logmap to the lowest iteration count it finds there. JIM

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Re: Fractint Question
by JackOfTradeZ＠comcast.net 04 Feb '08

04 Feb '08

. you know if you set the max iterations to say, 1000000, that doesnt mean every pixel iterates that many times, they all bail out according to the nature of the fractal and algorithm at some number less than that. but i assume the lake regions use the max. is there a way to determine the maximum number of iterations that any pixel(s) actually did? i think there is a way but i cant find it thanx if anyone can help JoTz .

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FOTD 04-02-08 (Ogive to Infinity [7.25])
by Jim Muth 04 Feb '08

04 Feb '08

FOTD -- February 04, 2008 (Rating 7.25) Fractal visionaries and enthusiasts: Today's image, with all its Moire patterns, lies in the eastern part of the large period-2 bud of the Mandelbrot set. I named it "Ogive to Infinity". An ogive is a pointed gothic arch, and the ghostly arch in the background of today's image certainly is pointed. The buds on the arch are of various shapes. Yesterday's image was a close up of a similar bud on a similar ghostly arch in the vicinity of East Valley. The rating of a 7.25 includes a 1/4 point bonus for the effort I put into the coloring. If I had not been so hasty, I might have earned a 1/2 point bonus. The image is rather striking; the calculation time of 25-4/5 minutes is also striking. But it should be no surprise that the completed image is posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Today's image is actually many images in one. Every change of size or resolution totally changes the pattern inside the arch. Sunday began with dense fog here at Fractal Central, but by midday a breeze arose from the west and swept away the fog almost by magic. The rest of the day brought lots of sun and a temperature of 45F 7C. The fractal cats were unusually quiet for some reason. My day was lazy. The next FOTD will appear in 24 hours. Until then, take care, and is it real or isn't it? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Ogive_to_Infinity { ; time=0:25:49.45-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=HyperMandelbrot2 passes=1 center-mag=-0.861346/0/35.65062/1/90/0 params=0/0/0/0/1/0/1e-100/0 float=y maxiter=15000 inside=0 logmap=-1068 periodicity=0 colors=00091OA2OA2NA3NA3NB4MB4MB4MB5MA5MA6M96M86M8\ 7M87LA8MA8LA9LB9LC9LCAKDALDBKDBLFBKFCKFCJFDKFDJGEJ\ GEIGEIGFHGFHHGGHGGHGFHHEIHDIIDIICIICIJCJJCJKCJKCJL\ CJLDKMEKMEKMEKNELNHLNGLOGLOHLPHMPIMPIMQKMQJMRINRLN\ SLNSLOSLOTLOTMPTMPUMPUMQVNQVNQWNRWNRWNRXOSXOSYOTYO\ TZOUZPUZPV_PV_PW`QW`QXaQXaQYaQYbRZbRZcR_cR_cR`dS`c\ SadSadSbdVbeUceTceScfRdfQdfPegOegNegMfhLfhKfhKghKg\ hKghKhiKhiLhiLiiLijLijLjjMjjMjkMkkMkkMkkMlkNlkNllN\ llNmlNmlOmmOmmOnmOnmOnnPnnPonPonPooQooQpoQpoRppRpp\ RqpRqpSqqSqqSrqSrqTrrTrrTsrUsrUssUssUtsVtsVttVttWu\ tWutWuuXuuXvuXvuYvvYvvYwvZwvZww_ww_xw`xw`xx`xxayxa\ yxayybyybzybzyczyczzczzdzzdzzezzezzfzzfzzgzzgzzhzz\ hzzizzizzjzzjzzkzzkzzlzzlzzmzzmzznzznzzozzozzpzzpz\ zpzzqzzqzzqzzrzzrzzrzzszzszzszztzztzzuzzuzzvzzvzzv\ zzwzzwzzwzzwzzxzzxzzxzzxzzyzzyzzyzzyzzyzzxzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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FOTD 03-02-08 (Astral Adventure [7.5])
by Jim Muth 03 Feb '08

03 Feb '08

FOTD -- February 03, 2008 (Rating 7.5) Fractal visionaries and enthusiasts: Skeptics know that ghosts are not real, though I doubt that the ghosts know it. Ghosts or no ghosts, today's image is a picture of a bonafide ghost, or what I call a ghost bud. The perturbed Mandelbrot sets are filled with ghost buds that can be returned to their unperturbed glory by resetting initial Z to 0,0. But the ghost in today's image cannot be returned to its full glory because I don't know where to find it. All 4 parts of initial Z, (p1) and (p2), are already set to zero. Like all ghosts, the one in today's image seems to exist in another world, and only fleeting glimpses of it can be seen in this world. The location of today's scene is in the vicinity of East Valley, though some distance offshore, where nothing but trapped inside points should exist. I named it "Astral Adventure" because the astral plane is where ghosts are supposed to exist. The actual nature of the astral plane is another topic for another day, but at this time I will say that, though I am a skeptic, I am not a born-again skeptic. And I hear a lot of talk among theoretical physicists about many, though not necessarily astral, worlds, as well as much rebuttal from the born-again skeptics. I would like to have been able to rate the image at an 8 or 9, but I just couldn't find anything in it worth such a rating, so the scene ended up rated at a 7.5. The parallel comb-like fore- ground arms plus my coloting add the extra point. The calculation time of 9 minutes is not too much for such an unexpected image. But if this time is a little inconvenient, convenience may be regained on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the finished image will soon be posted. I'm slightly sorry for the lateness of today's image, but I had to make an unscheduled trip to Old Fractal Central on Saturday, and didn't get back to New Fractal Central until near midnight. I can report that the old fractal cats, Thomas and Tippy, are still as lazy as ever. They actually raised their heads when I walked in. The new fractal cats, Nicholas and Cassie, stayed here with fractal lady all day, and she says they hardly noticed that I was gone. The next FOTD will appear in around 12 hours. Until then, take care, and rational thinkers know that ghosts are mere fantasies in the minds of the superstitious, but the ghosts, who have not heard that they are mere fantasies, continue their haunting. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Astral_Adventure { ; time=0:09:49.37-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=HyperMandelbrot2 passes=1 center-mag=+0.09608900268348/+0.0117053191216819/\ 1114.51/1/15/0 params=0/0/0/0/10/0/1e-100/0 float=y maxiter=7500 inside=0 logmap=820 periodicity=0 colors=000YOEYOEZOEZODZODZOCZOCZOC_OB_OB_OB_OA_OA`\ O9`O9`O9`O8`O8aO7aO7aO7aO6aO6bO5aO6aO6aO6aO6`O6`O6\ `O6`O6_O6_O6_O6_O6_O7_O7ZO7ZO7ZO7ZO7ZO7ZO7ZO7ZO7ZO\ 7ZO7YO8XO8XO8XO8WO8WO8WO8WO8WO8VO8VO8VO8VO9UO9UO9U\ O9UO9UO9UO9TO9TO9TO9TO9TO9SPASPASPASPARPARPARPARPA\ RPAQPAQPAQPAQQBQQBPQBPQBPQBPQBPQBOQBOQBOQBOQBOQBNR\ CNRCNRCNRCMRCMRCMRCMRCMRCLRCLRCLRCLSALSAKSAKSmKSmK\ SmKSmJSmJSmJSmJSmIRmJSmJSmKSmKSmLSmLSmMTmMTmNTmNTm\ NTmOTmOUmPUmPUmQUmQUmRUmRUmSUmSUmSTmTTmTSmUSmUSmVS\ mVRmWRmWQmXQmXPmXQmYPmYPmZPmZPm_Om_Pm`Om`OmaOmaOma\ OmbPmbPmcPmcPmdPmdPoePqeQsfQufQwfQygQzgQzhRzhRziRz\ iRzjRzjRzjRziSziTzhTzhUzhVzgWzgXzgYzfZzf_zg`zfazfb\ zfczedzeezefzdgzdhzdizcjzckzclzcmzbmzbmzbmzamzamza\ mz`mz`mz`mz_mz_mz_mz_mzZmzZmzZmzYmzYmzYmzXmzXmzXmz\ WmzWmzWmzWmzVmzVmzVmzUmzUmzUmzTmzTmzTmzSmzSmzSmzSm\ zRmzRmzRmzQmzQmzQmzPmzPmz } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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FOTD 02-02-08 (Deep HyperRadical [9])
by Jim Muth 02 Feb '08

02 Feb '08

FOTD -- February 02, 2008 (Rating 9) Fractal visionaries and enthusiasts: Unless I have an operational time machine hidden in the garage, the year it was 24 hours ago is, always was, and always will be 2008. But old habits are like old fractals. They die hard. Today's image takes us to a bud on the north shore of HyperEast Valley. I named the image Deep HyperRadical because it sits deep in the interior of the bud, and buds, along with their associated elements, are sometimes called radicals. This parti- cular bud is a very tiny one with a very high periodicity, which lies comfortably between much larger buds of much lesser periodi- city. I have no idea why today's image, which lies inside this tiny bud, should appear to have a cycle of 6. Yes, there are more unusual scenes of varying cycles lying as deep as it is possible to go into the center of today's image, and likely extending to infinitesimal infinity. These scenes are not mere boring fractalish repeats of the top scene. Each level has a character of its own. The maxiter of today's image is an arbitrary choice. As the maxiter is increased, the open areas with the twisting greenish arms gradually fill in, until ultimately they are filled solid with fractal debris. In my opinion, the image rates an honest 9. It is worthwhile artistically and interesting mathematically. And its calcula- tion time of 3 minutes is not bad either. Of course, for extra convenience, the finished image is posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Absolutely miserable weather prevailed here at Fractal Central on Friday. The day began with one inch, or 2.5cm, of sleet on the ground. The sleet changed to freezing rain by 9am, and it rained steadily for the rest of the day, while the temperature slowly rose to above freezing by afternoon, leaving an inch of heavy wet slush everywhere. The fractal cats watched from the front window shelf as I squeegeed away the sloppy mess by hand. The rest of my day was easy enough, though a small but hurried design job is expected tomorrow. The next FOTD will appear in about 24 hours. Until then, take care, and is the Mandelbrot set infinite or half infinite? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Deep_HyperRadical { ; time=0:03:13.47-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=HyperMandelbrot2 passes=1 center-mag=+0.2689640429736179/+0.005486652797290\ 472/5.9811e+007/1/105/0 params=0/0/0/0/1/0/1e-100/0 float=y maxiter=1900 inside=0 periodicity=0 colors=000hzRizQizPizPjzOjzOjzNkzNkzMkzMlzLlzKmzKm\ zJmzJnzInzInzHozHozGozFpzFpzEpzEqzDqzDqzCrzCrzBszA\ rzBrzCrzCqzDqzDqzEqzEpzFpzFpzGpzGozHozHozIozInzJnz\ JnzKnzKmzLmzLmzMmzMlzNlzNlzOlzOkzPkzPkzQkzRjzRjzSj\ zSjzTizTizUizUizVhzVhzWhzWhzXgzXgzYgzYgzZfzZfz_fz_\ UzKWzRXzXZzc_ziazpbvvVruNntGjtFfsGMeHNhIOkJPnKQqLR\ tMSwNTzAAA3F8CH9KH9NH9QHATHCWHDZHEaHFdHGhHHlNFpTDt\ `AwfKtiUqlcynmzpzzrzztzzvzzxzzzzezSdzXcz`cRdMqKMqK\ MqJMqJMqIMqIMqIMqHMqHMqGMqGLrFMqGMqGNqHNqHNqIOqIOp\ JPpJPpKPpKQpLQpLRoMRoMRoNSoNSoOSoOTnPTnPUnQUnQUnRV\ nRVmSWmSWmTWmTXmUXmUYlVYlVYlWZlWZlXZlX_kY_kY`kZ`kZ\ `k_ak_ak`bj`bjabjacjbcjbcjcdicdideideieeiefiffhfgh\ gghgghhhhhhhiigiigjigjjgkjgkjglkflkfmlfmlfnlfnmfom\ eonepnepneqoeqoerpfsoernernermdrmdrldqkcqkcqjcqjbq\ ibphbphapgapQEzZQugapnpgooipnkpmlqlnrkprjqsisthuuh\ ythwthvthtshsshqshprgoqgo } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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Date
by David M Fisher 01 Feb '08

01 Feb '08

Jim, You are a year late with the FOTD. David M Fisher

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FOTD 01-02-08 (One in a Googol [9.9])
by Jim Muth 01 Feb '08

01 Feb '08

FOTD -- February 01, 2007 (Rating 9.9) Fractal visionaries and enthusiasts: Today's image must be seen to be believed. If it's a result of imprecision, which is still a possibility, then imprecision must be considered as a formula for good fractals. BTW, doubling or halving the real(p3) parameter makes a noticeable difference in the purplish pattern filling the minibrot. I did not want to rate today's image at an absolutely perfect 10, so I gave it the next best rating, a penultimate 9.9. As promised, it's a scene in Hyper-East Valley of the HyperMandel- brot set. I named it "One in a Googol" because a perturbation of only one-googolth part of 1 makes all the difference. To see how much difference 1/10^-100 can make, reset the real(p3) parameter to zero. I will not try to analyze today's image, it is far too complex and I'm already mentally congested as it is. I'll wait until the end of the month, when, after a month's exploration, I'll have a better idea of what's going on in Hyper-East Valley. But most likely, even then I'll have little idea of what's going on there. The calculation time of 2-1/2 minutes is quite reasonable for an image that comes so close to perfection. But a simpler way to achieve the near-perfection is to visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the finished image is posted, and view it there at leisure. Thursday turned out as good as could be expected in this part of the country in midwinter. Lots of sun and light winds made the temperature of freezing quite comfortable. The fractal cats chased each other up and down the hallway until they ran out of energy and settled for a rest in the sunniest spot they could find. Except for the day's fractal discovery, which IMO is one of the most serendipitous of all time, my day was totally average. The next FOTD will appear in 24 hours. Until then, take care, and be as skeptical of rogue fractals as a true-believing skeptic. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= One_in_a_Googol { ; time=0:02:30.03-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=HyperMandelbrot2 center-mag=+0.25874105460425120/-0.001343883319138\ 25/5.553303e+007/1/-162.5/-1.93254204222670367e-007 params=0/0/0/0/1/0/1e-100/0 float=y maxiter=3200 inside=0 periodicity=0 colors=000ZLgjGguCgtDftEftFftGftGftHftIfsJfsKfsKfs\ LfsMfsNfsOfuMssOfqPUoRHmO0nS4nW7p_AreDtjGvpczumrnc\ fdOYUPSLQQFQIBMLBRJESHGSIITKJTMLWOLYQMYSM`UNcVNfWO\ iXPlYRoZUr_Wu`Zxa`yc`zd_zfYtgWqeRocMiaId_F`YCXW9TX\ 6SX3SY7SYASZESZIS_MS_PS`TS`XSa`SacSbgSbkSfoQbnSZpT\ VsVSqWOqXKoZGm_Dk`9ib5gc2edNdbRd`UeZXeX_eVbeTebRh_\ PkXNnUMlSNjRNiQNgONeNNdMObLO`JO_IOYHORDPXGObJNhMMn\ PLtPKrPIqOHoNGnMFlLDkKCiJBhIAfG8eF7cE6bD5`C3_B2YA1\ X90YH2ZO3WW1ZV4`V7bVAdVCfVFhVIkUKmUNoUQqUSsUVuUYwU\ _qSXkQVeOS_MQVKOPILJGJDEG7CE2BC4AF69I88KA7NC6QD5SF\ 4VH3YJ2_L1bL0fM0dM3cN6aNA`ND_OGYOKXPNVPQUORVPTTPVR\ QWPQYNRZMR`KSaIScGTeETfDUhBUi9Vk7Yp2Vl6Sh9PdCQaDRZ\ DSXETUETRFUPFVMGWJGXHHXEHYBIZ9I_6J`3Ja0K`1J_5I_9IZ\ DHYGHYKGXOGWSFWWEVZEUbDUfDTjCQpBTmCVkCYiC_gCbeCdcC\ faDi_DkYDnWDpUDqQ8rSDrUHrWLsYPs_Ts`Ysbatdetfithmti\ qljhdj_YkSQkJIlABl2Ci4Dg6 } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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FOTD 31-01-08 (Seahorse Asymptote [7])
by Jim Muth 31 Jan '08

31 Jan '08

FOTD -- January 31, 2008 (Rating 7) Fractal visionaries and enthusiasts: Today is the last day of January, and the last day of the theme of January -- scenes in Seahorse Valley. The tour has taken us far afield, even into spaces of 8 dimensions to explore Hyper- Seahorse Valley. Today's image focuses on a point very near the point where the classic valley's two branches would reach the X-axis if they were calculated to infinity. I named the image "Seahorse Asymptote", a name that makes it look like I know what I'm talking about when I discuss fractal mathematics. Then I gave it a rating of a 7, a rather generic rating which means that, even though I can find nothing excep- tional in the image, I am not disappointed by it either. It is immediately apparent that HyperSeahorse Valley is a far more complex thing than classic Seahorse Valley. The hyper version of the valley has networks of arms spanning the empty spaces between major elements that are far more intricate than those in the more familiar valley. Today's image is but a small example of the intricacy lurking in the HyperSeahorse Valley. It is also apparent that the image is actually a perturbed one. Since the HyperMandelbrot set is 4-dimensional, the hyper-mini- brots within it must be 4-dimensional also. And I assume they are oriented in any possible direction within the 4-D Mandelbrot set, just as the classic minibrots are oriented in all possible directions in the classic 2-D M-set. But who knows what variety of perturbed slices this means are possible. The theme for February will be HyperEast Valley of the Hyper M-set. I will not refer to it as HyperElephant Valley, since elephants are already hyper enough without expletives added. I expect quite a few strange and perhaps entirely new things to show up on the eastern fringes of the main hyperbay. The calculation time of today's image is 6-1/2 minutes. This time may be cut by 1/3 by using one of the faster calculating algorithms, but when this is done, there is always a chance that some of the finer detail will be missed. Considering all of the above, the best way to see the complete scene intact is to visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where it is or soon will be posted for instant gratification. Overnight rain ended at daybreak Wednesday here at Fractal Central, and the sky cleared by 9:00am, but the high winds of 50mph (80kph) that prevailed for the rest of the day made the temperature of 34F 1C feel far too chilly for comfort. The fractal cats agreed and rolled over on their shelf on top of the radiator. My day was fairly busy; tomorrow will likely be the same. The next FOTD will appear in 24 hours. Until then, take care, and be at one with the secular universe. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Asymptote { ; time=0:06:38.48-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=HyperMandelbrot2 passes=1 center-mag=-0.74371926345344550/0/3475050/1/-90/0 params=0/0/0/0/0.1/0/1.091e-005/0 maxiter=1800 float=y inside=0 periodicity=0 colors=000q`MqZMrXMrWMrUMrTMrRMrPMrOMrMMrKMrJMrHMq\ ELrGMrHNrIOrKOrLPrMQrORrPRrQSrSTrTTsUUsWVsXWsYWs_X\ s`YsaZscZsd_se`veZsf`qfaogbmgcjgdhhffhgdhhaii_ijYi\ kWjmTjnRjoPkpNkqLkrKiqKgqJfqJdpJbpIapI_pIYoHXoHVoG\ UoGSnGQnFPnFNnFMmENmENmENmENmENmENmENmEOmEPmEQmERm\ ESmESmESmESmESmESmESmESmERmEShETcDUdDUaDTaDVcDZd9c\ n9bn9an9`n9_n9Zn9Yn9Xn9WnEVnIUnLTnOSnQRnTRnWWmYVm`\ TmcSmeQmhPmkOmmOmlRlkTkkUjjWiiXhiYhhZgh_fg`efadfbc\ eccedbdeacf`cg_bhZbiZajY`kX`lW_mVCvh_nVYlTWjSUiQSg\ PQeNOdMNbLL`JJ_IHYGFWFDVDBTCASBDUAGVAJW9LX9OY9RZ8U\ `8Wa7Zb7ac7dd6fe6if5lh5oi5qj4tk4wl3zm3zn3xl6uk9qjB\ nhEkgGgfJdeLacOYbRVaTS_WOZYLY`IXbP_ZWbVbeSihOplFoj\ LniQmhVli`mg_mf_md_nc_na_n`_nZ_oY_oW_oV_oT_pSZpQZp\ PZqNZqMZqKZqJZrHZrGZrEZqB`rDZsEYtFWtHVuITvJSvLQwMP\ xNNxPMyQKzRJzTHzUGzVEzXDzYBzZAz_9zaAzbBzcCydCxeDvf\ EugEthFsiGrjGqkHolIqcMqaM } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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FOTD 30-01-08 (Minibrot Madness [7])
by Jim Muth 30 Jan '08

30 Jan '08

FOTD -- January 30, 2008 (Rating 7) Fractal visionaries and enthusiasts: Today's image is a scene somewhere in HyperSeahorse Valley. The area of near total chaos at the center of attraction is the remains of a perfectly normal M-set minibrot. (To see the true minibrot, reset all parameters to zero.) As I continue to experiment with the HyperMandelbrot2 formula, I am becoming more convinced that the images it draws are true slices of the 4-D HyperMandelbrot set, and not mere artifacts. In the true classic M-set version of today's image, there are 8 well-defined yellow-orangish elements surrounding the minibrot, while in today's version, there are 14. What has happened is that the original 8 elements have each split into two, but two of the split pairs overlap in such a manner that they both appear as a single broader element, giving the impression of only 14 elements in all. Inside the space that once was the original minibrot, much the same thing has happened, but the area is so chaotic that little sense can be made of it. I will continue to work with this formula for a while, trying to figure it out. The image is named "Minibrot Madness", which is a fair name for it. The rating of a 7 means that I think it is above average, though not exceptional. The calculation time of 2-1/2 minutes may be eliminated by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Tuesday began with freezing rain and icy pavements here at Fractal Central. But by midday the temperature rose above freezing, and the rest of the day brought just plain rain. The fractal cats enjoyed the view for a while, then went to sleep. My day was busy enough for satisfaction, but not too busy for a fractal. The next FOTD will appear in 24 hours. Until then, take care, and it was hard enough to think in four dimensions. Now we have eight dimensions to worry about. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Minibrot_Madness { ; time=0:02:34.26-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=HyperMandelbrot2 passes=1 center-mag=-0.748072864967/+0.071474507622/773813/\ 1/-5/0 params=0/0/0/0/0.08/0/1e-012/0 float=y maxiter=1200 inside=255 logmap=316 periodicity=0 colors=000P28P38P48P58P68P88P98PA8QB8RC8TD8WG9ZJA`\ LBaOBbSCcVDc_EccEdgFdlGdnGanLZlPXkTUiXSg`PfeNdiKbm\ IaqF_uDZyEYtFXoGWjGVfHUaITXISTJROKQJKPFLOAMN5MN1RM\ 4WL6_K8dJBiIDmJFnOEoSEpXEqaDrfCsiApfAmaAjXAgSAdNAZ\ PAZRAZUAZXAY_AYbAYdAYgAYj9Ym7Yp5Yr4Zs7Zs9_tC_tE_uG\ `uJ`vLavOawQawSbxVbxXbxZawaavcaue`tg`si`rk_qn_pp_o\ rZntZmvZlxRhqJdjBadBdXBgPBjHCeMDaQEXVFTZGPbHKgIGkJ\ BpK7tK3xM7uOBrQFoSJmTKmUKmUKmUKmUKmUKmUKmUKmUKmUKm\ UKmUKmUKmUKmUKmUHmUAmU4lW8jYCi_FgaJfcNdeQcgUaiY`k`\ _hb`edcbgm`jrYnvVqzTuzQzzNzzLzzOnmRicUdZWZYZUXaPWc\ KVdMWeNWfOWgQWhRWhSWiNQiJKiFFhGGgGHfGIeGIdGJdHKcHL\ bHLaHM`HN`HNYIRWJUUKYRL`PMdNNgKOkIPnGQrEQuFVpG_lHd\ hIicJn_KsWUxScvRmuQzsPzrOmpNcoMYmL_lKajJciIdgHffGh\ dFjcElaDm`DnZCoXBpVAqT9rR8sP7tN6uL5uK4rM3pN3nO3lQ3\ jR3gS3eU3cV3aW3_Y3XZ3V_3Ta3Rb3Pc3O_5OX7OU8ORAOOBOK\ DOHEWJ7YF7_B8a78c39e09JFS } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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FOTD 27-01-08 (Steps on the Steppes [6.5])
by Jim Muth 29 Jan '08

29 Jan '08

FOTD -- January 27, 2008 (Rating 6.5) Fractal visionaries and enthusiasts: I know that today's FOTD is late, but the wait was worth it. The image shows a scene on the northeast shore line of the large period-2 bud of the HyperMandelbrot set, which is just starting to undergo some very strange things. The result looks surpris- ingly like a scene on some alien planet, perhaps even a fractal planet. I named the image "Steps on the Steppes". The buds appear to recede into the distance in a very step-like manner. I rated the image at a 6-1/2, which includes an extra half-point for my coloring efforts. And why not? The coloring is 98 percent of the image. The calculation time of 9-1/2 minutes is somewhat slow, especi- ally for an image that rates only a 6.5 and is almost 12 hours late. The image will soon be posted for instant viewing on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> But due to the lateness of the FOTD posting, Paul might not have a chance to post the finished image for several hours yet. So be patient and try later if the visit to the web site comes up blank. Some clouds, some sun, periods of light snow, and a temperature of 30F -1C mixed together here at Fractal Central on Saturday to produce a typical midwinter day. The fractal cats wasted most of the day sleeping, while I wasted most of the day pondering the meaning of fractals. Not surprisingly, I found no answer. But regardless, the next FOTD fractal will be posted in 24 hours. Until then, take care, and the meaning of fractals is most likely the same as the meaning of life. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= StepsOnTheSteppes { ; time=0:09:27.06-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=HyperMandelbrot2 passes=1 center-mag=-0.8342207552006937/+0.187609876583259/\ 1376.26/1/41.5/0 params=0/0/0/0/0.0125/0/1e-011/0 float=y maxiter=3850 inside=255 logmap=-100 symmetry=none periodicity=0 colors=000EBREBREBRDBRDBSDBSDBSDBSDBSDBSDBSDBSDBTC\ BTCBTCBTCBTCBTCBTCBUCBUCBUCBUBCUBCUBCUBCVBCVBCVBCV\ BCVBCVACVACWACWACWACWACWACWACWACWACX9CX9CX9CX9CX9C\ X9CX9CY9CY9CY9CY8CY8CY8CY8CZ8CZ8CZ8CZ8CZ8CZ8CZ7C_7\ C_7C_7C_7C_7C_7C_7C_7C`7C`6C`6C`6C`6C`6C`6Ca6Ca6Ca\ 6Ca5Ca5Ca5Ca5Cb5Cb5Cb5Cb5Cb5Cb5Cb4Cc4Cc4Cc4Cc4Cc4C\ c4Cc4Cc4Cd4Cd3Cd3Cd3Cd3Cd3Cd3Ce3Ce3Ce3Ce3Ce2Ce2Ce2\ Cf2Cf2Cf2Cf2Cf2Cf2Cf2Cf3Dg3Dg3Dg4Dg4Dg4Dg4Dg5Dg5Eg\ 5Eg5Eg6Eg6Eg6Eg6Eg7Eg7Eh7Fh7Fh8Fh8Fh8Fh8Fh9Fh9Fh9F\ h9GhAGhAGhAGhAGhBGhBGiBGiBGiCHiCHiCHiCHiDHiDHiDHiD\ HiEHiEIiEIiEIiFIiFIiFIjGIjGIjGIjGJjHJjHJjHJjHJjIJj\ IJjIJjIJjJKjJKjJKjJKkKKkKKkKKkKKkLKkLLkLLkLLkMLkML\ kMLkMLkNLkNLkNMkNMlOMlOMlOMlOMlPMlPMlPMlPNlQNlQNlQ\ NlQNlzmczmczlczkczjcziczhczgczfczecydbxcawb`v__uYZ\ tXYsXXrWWqWVpVUoVTnUSmURlTQkTOjSMiSKhRIgRGfRFeREdR\ DcRCbRBaRA`RB_RCZRCYRDN00 } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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Re: FOTD polygons and artifacts
by JackOfTradeZ＠comcast.net 29 Jan '08

29 Jan '08

. The pentagon-heptagon FOTD is one of the most interesting and unique images I've seen in a long time. If you back out you see a triangle and then a couple squares - else all the polygons are odd numbered, and they increase in number of sides forever untill a circle is approximated. The "black hole" in the center appears to be like the "peanuts" seen in The Canyon (REAL= -0.75, IMAG=0). in that there is no minibrot or lake structure there, the black just shrinks if you up the iterations. I think it is an infinite tunnel, but the render times start getting rediculous. Same with FOTD Jan 24. The parent fractal is awesome - has the form of a normal Mandelbrot but looks weird at the boundary. Animation sequence is in progress - looking way cool so far. FOTD Jan 27 - looks like a planet surface. I did an animation sequence on this type a long time ago if NY1 interested: http://www.fractal-animation.net/vid/planet.zip 6 Meg file. Stay Amazed! JoTz .

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FOTD 29-01-08 (Strange New World [No Rating])
by Jim Muth 29 Jan '08

29 Jan '08

FOTD -- January 29, 2008 (No Rating) Fractal visionaries and enthusiasts: Another late FOTD. My excuse -- none. Today's image is named "Strange New World". The name implies that the coordinates of today's image lie well within the main bay of the Mandelbrot set. Strange things happen when four more dimensions are added. In today's case, new material has spontaneously appeared within the main bay, and today's image is a close-up sample of this new stuff, which is arranged in a semi-regular pattern. I could hardly give a rating to an image that I did no work at all on, but it's still worth a look. The image might not be worth the 21-2/3 minutes required to calculate it from the para- meter file, but it is certainly worth the minute or so it takes to go to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and enjoy the finished image posted there. But give Paul a chance to post the image before visiting the site. Another typical midwinter day went unappreciated here at Fractal Central on Monday. The fractal cats did check the outside from their window shelf a couple times, but decided they would rather get into mischief. My day was close to average, though it turned a bit busy late in the afternoon. The next FOTD will be posted in about 14 hours. Until then, take care, and be any- thing but always right. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Strange_New_World { ; time=0:21:39.48-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=HyperMandelbrot2 passes=1 center-mag=-0.6664694298/+0.3167989708/11522.57 params=0/0/0/0/0/0.3/1e-015/0 float=y maxiter=6000 inside=0 periodicity=0 colors=000k_YqVdvQjqUfmYcia_eeX`iTXmQTqMPtJNmHLfGJ\ `FHVEFRDUOCUMBUMAULAUM9UK9UL8UL8UM7UM7UM6UM6UL9UKB\ UIEUHGUFJUELUCOUBQU9TU8VU6YUL_UPaUSgQ_mOhsNlxLovJq\ uHotFlrDiqBgpJ2QK4RL5RM6RN8RO9ROARPCRQDRRESSGSSHST\ ISUKSVLSWMSWNSZPPaRNdTLgVJjXHmZFp`DsbBuc9t_QsXfv_d\ xabrXemShhOkcJnYEqTAtO5wJ1yK2qK3iK4aMG9CKA2OA9UEGZ\ IMcMThQ_mUerYTnOGjF3g6WQ9x8Cr8Jl8Pf8Va8`_AZZCXYEWX\ GUWHTVJRULPTNOSPMRQLSROTSQUTTUUVVVXWW_WXaXYcYZfZ_h\ Z`j_am`bo`cqZYjXTcVOXTJQREJP9CO46N58M69L7BL8CK9DJA\ FIBGICHHDJGEKGFLIJNJMPLPRMSTOVVPZXRaZSd`UgbVjdXnfY\ qh_tj`wlazn_wlZtjYqhXnfWleUicTfaSc_R`YQZXWbR`fLejF\ jn9imEilIhlMhkQgjUgjZfibfhfehjegnegrdfqdfqcfqceqce\ qbeqbdqadqadqadqx2mw5jv8huBetDcsG`rJZqLWpOUoRSnTPm\ WNlZKk`IjcFifDhhBdfFaeJZcNWbRT`VQ_YMYaJXeGViDUmASq\ 7RtKOpXMmiKjvIgmDYd9OW5EPEBIN8BV6GSALQEQOIVMM_KPdI\ TiGXnE`sCdxAglKXaTN`jLeeS } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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FOTD 28-01-08 (Deep in the Depths [?])
by Jim Muth 28 Jan '08

28 Jan '08

FOTD -- January 28, 2008 (Rating ?) Fractal visionaries and enthusiasts: Today's 9-1/2 minute fractal is named "Deep in the Depths", a redundant name if ever there was one. It's actually a scene on the northeast shore line of the large period-2 bud of the HyperMandelbrot set. I gave it no rating because I have no idea how to rate the images in this new world of micro-parameters. The partly filled-in minibrot in today's image closely resembles the parent HyperMandelbrot set. In addition to the changes in the minibrot, the surrounding features have become infested with countless small holes, which do not exist at the same spots in the classic M-set. (To see the classic version of the scene, change all parameters to zero.) I have not yet investigated these holes very much, but they appear to be rather interesting. The parameter file calculates in 9-1/2 minutes. Those who would prefer instant fractal satisfaction can enjoy it on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the completed GIF image is posted. An average day with an average temperature of 34F 1C and an average partly cloudy sky went un-noticed here at Fractal Central on Sunday. The fractal cats, Nicholas and Cassie, spent a good part of the day sitting in the sun in the southwest window. I spent some of the day doing nothing and some more in doing the day's fractal. The next FOTD will appear in 24 hours. Until then, take care, and be of good cheer when things look drear. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Deep_in_the_Depths { ; time=0:09:24.53-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=HyperMandelbrot2 passes=1 periodicity=0 center-mag=-0.8332758481765483/+0.187712892187422/\ 4.388e+010/1/172.5/0 params=0/0/0/0/0.01/0/7e-020/0 float=y maxiter=6200 inside=255 logmap=-1260 colors=000cgwcgwcgwcgwcgwcgwcgwcgwcgwcgwcgwcgwcgwc\ gwcgwcgucgtcgtcgtcgvchvcivcju`ksZlrWlrUmrRmrPmqMmq\ KoqHqqFsqHpmJmiLjfNhbPe_RbWT_TUYPWVMYSIbPFfNBhK8oH\ 4pF1mE5eD9bCDVBHSALP9PM8TJ7XG6`D5cFA_GEXIIUJMRLRNM\ VKOZHPbERgASkXUocVspTbuRMNP5XR7WS8WU9WVBWWCWYDWZFW\ `GVaHVbJVdKVeLVgNVhOViPVjSRkUOlWLmYIzzKzzLzmMwmNmc\ PcdQXfRUgSShUPiVNjWLkXQj6KmBEpG9rKSYRaTLkOGiNHhNHf\ MHeMHcLHbLHaKH_KHZJHXJHWIHUIHTHHSHHVJJXLL_NNaPPcRR\ fTThVVjXXmZZo``qabqb_qcYqdWqeTqfRqgPqhMqiKqjIqkGql\ DqmBqn9qo6qp4qq2qr0WZEBFSCHSDJSDLSEMSFOSFQSGSSHTSH\ VSIXSIYSJ_SKaSKcSLdSMfSMhSNjSOkSOmSPoSPpSMVWJ9ZLBX\ MDWOFUPHTRJRSLQUNOVPNXRLYSKZUJ`WHaYGc_EdaDkcBqeAxg\ 8zi7zj6zi5zi5zi5zh5zh5zh5zh5zg5vg5rg5mf5hf5hf5jf5f\ e5ce5ce5cd5cd5cd5Yd5Ub8MaA8`DB_FDZHGYKIXMLWONVRQUT\ STVVSYXR__QaaPddOffNhiMkkLmnKopNrsUtuUvpZjlc_ghOcm\ D_r2`v3`z3az4az4az4bz5UUc } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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FOTD 26-01-08 (Pentagon Heptagon [8])
by Jim Muth 26 Jan '08

26 Jan '08

FOTD -- January 26, 2008 (Rating 8) Fractal visionaries and enthusiasts: NEW FORMULA ALERT! Today's image uses a new formula, which is simply yesterday's formula with initial 'b' generalized rather than set to 0,0. This might give a little more variety to the images it draws. I named the new formula HyperMandelbrot2. Today's image is named "Pentagon Heptagon" because of the very prominent pentagon. And there is also a heptagon, much smaller and closer to the center. And yes, the series of polygons with an odd number of sides does continue indefinitely. An outzoom will reveal a triangle, while a couple inzooms will reveal a nonagon, a hendecagon, and a tridecagon. (I think these are the right names for polygons of 9, 11 and 13 sides.) How far the series goes beyond this point is anybody's guess, but I suspect that, like so much else in the world of fractals, it continues without limit. I have made no effort to figure out the number series of the arms stretching between the polygons, though it probably has a logical order. But at the same time, I see that the arms within the pentagon are unevenly distributed. Two of the pentagon vertexes have arms connecting with them from within, while the other three are cut off from the center. Today's coordinates define a blank area in the classic Mandel- brot set. If real(p3) and real(p4) are set to zero, the result is a flat black screen. The area actually lies somewhat inside the main bay of the M-set. Even though I have no idea how today's image ranks among Sea- horse Valley images of the HyperMandelbrot set, I have rated it at an 8. Its mathematical interest is enough to be worth at least that rating. The calculation time of 4-1/4 minutes is fast enough to keep impatience at bay. And if it is not, the finished image will soon be available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Friday was bright and sunny here at Fractal Central, but it was also cold and blustery, making it a rather unpleasant day to be outside. The high temperature of 27F -3C fely cold even in the strongest sun. With numerous sources of heat inside F.C., the fractal cats had their problem deciding where to spend the day. I had no such problem however. I spent the day working, then searching for a FOTD. As today's image shows, I was successful. And the next FOTD image will be posted in 24 hours. Until then, take care, and where's it at? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Pentagon-Heptagon { ; time=0:04:14.05-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=HyperMandelbrot2 passes=t center-mag=-0.749480813398176/+0.031703452082799/\ 3.321327e+010/1/89/0 params=0/0/0/0/0.2/0/1e-020/0 float=y maxiter=3600 inside=0 periodicity=0 colors=000mL6lM9lNBlODlPFlQIlRKlSMlTOlURlVTlWVlXXk\ `_lYZmWYnUXnSXoQWpOVpMVqKUrITtCTrGTqJToMTnPTlSTkVT\ iYTh`TfcTjcYecT`cPXcKScGNcBMc4Jc7HcAEcCCcF9cI7cK4d\ N2cQ0cSgcaXcZKcVNcXQcZSc`VcbYcc_cebdgefigikjklmnno\ pzrszuuzzzzvtzvrzupvunrtkmtihsgcse`sbYr`VrZTqXQqUN\ pSLpQIpOGrJPsFYuBev7nt9Bw3vu4ss5pq6mo7jm8gk9di9agA\ ZeBWcCTaDQ_ENa7GZEKWKOURSRXWzz_zzczzfzzbzzZzzVzzRz\ zOifKndGrcCva8z`5tb6oc7ie8df9ZhAUiBOkCJlDDnE8oEAnF\ CmFEmGGlGIlHKkHMkIOjIUiJZiJchKhhKmgLrgLvkMwkMwlRwq\ NwrJwwGwxCws8wt6vt5rp4mp3hq7cmAZmKUnUPmcKmmFlvAnz5\ oz3pz3qz4lz4gm4bc5ZZ5UZ6UY6dY7dY7dY5sa7nY9jVBfRDaO\ FYKDUFGUHJUILUKOULQUNTUOVUQYUR_UTbUUdUWgUXiUYkRalO\ dnLgoJjlMeiOagRYdTUaWP_YLX`HUbDPb8Sd9VeAXgB_hCbiDd\ kEglFjmBimFijIhgLhcOg`RgYVfUYfR`eOceKfdHjdEmcApc7s\ c4va5r`5o_6kY6hX6dW7aV7YT7VS8RR8OV4RQ8LLBGGFA8H2CI\ 5GI8KIBNJERJHVJKZJNaKQeKT } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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Image artifacts due to precision problems
by Hal Lane 25 Jan '08

25 Jan '08

************************************************* Jim Muth in his "FOTD -- January 24, 2008" text says: >some of the images appear so unlikely that I >cannot shake the impression that they are >artifacts of mathematical imprecision rather >than true fractals. My question is: Can one determine if a fractal's features are precision problem artifacts by computing the fractal twice -- with two different values of the number of arbitrary precision digits -- and then comparing the two images? <---<< My hypothesis is that if you compare the two images calculated in the above manner and they are the same, then problems of precision are not the cause of a fractal's unusual features. Is this the case? <---<< If this method does correctly determine whether an image has artifacts or not, is adding the following items to an image's parameter file a valid way to exactly set the number of digits of precision used in a calculation? 1st image calc: --------------- MATHTOLERANCE=-1/-1 BFDIGITS=14 2nd image calc: --------------- MATHTOLERANCE=-1/-1 BFDIGITS=15 I cannot find the email sent to me that tells how to compare two images. Here is what appears to work -- please correct me if I am wrong: To compare two images that are in files: - Run FRACTINT *without* the command line parameter debug=50 - Load the first image from its file using <r> - Type <g> and then: debug=50 - Load the second image from its file. (Note that the File List selection page title is now: "Select File for 3D Overlay") - The image on the screen is the difference between the two images. Identical pixels in the two images are shown as color zero. Different pixels are shown as non-zero. - If this 'difference image' has any non-zero pixels the two images are different. Is the above procedure to compare two images in files correct? <---<< It appears that the color map of the images is used to display the difference pixels. If there are extremely dim color map values in the image one could be fooled into thinking that there were no differences between two images when in fact there were if the difference pixels that were displayed happened to use dim color map values. If this is a problem for a particular image one could get around it by loading a garish color map, say, a color map of 15 bright colors and black like: GOODEGA.MAP This makes all non-zero pixels be easily visible against a black background. I calculated a default Mandelbrot image at 640 x 480 using both the default integer math and then putting float=yes in my SSTOOLS.INI file. (I had forgotten to do this when installing FRACTINT onto my recent computer.) I was surprised to see a significant number of differences between the integer and float images. I constructed a color map that would allow me to see the difference image pixel values as follows: 0 0 0 This file shows the pixel values 127 0 0 1-6 as distinct recognizable 255 0 0 colors. All other pixel values are 0 127 0 dim gray, except for pixel value 0 255 0 zero which is black. 0 0 255 - HHL 1/24/08 0 0 127 64 64 64 64 64 64 64 64 64 . . . 64 64 64 The difference image showed a few dozen pixels with values of 1 - 6 and a few hundred dim gray pixel values with values somewhere in the range of 7 - 255. All other pixels were black. Is it likely that I did this comparison and analysis incorrectly, or is this difference between integer and float expected? <---<< Does anyone know if the pixel values of the difference image represent the absolute value of the difference between the pixel values of the two compared images as I am conjecturing they do? <---<< Also, am I correct in assuming that arbitrary precision works for formula file fractals? <---<< - Hal Lane ######################### # hallane(a)earthlink.net # ######################### *************************************************

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Re: FOTD
by JackOfTradeZ＠comcast.net 25 Jan '08

25 Jan '08

. Jim Muth ponders: ""It seems very strange that a value as tiny as 0.00000000000000000000007 would produce such a big change in an everyday scene in Seahorse Valley"" Ever hear of "Chaos Theory" and "extreme sensitivity to initial conditions" ? <G> That's why fractals is way cool! .

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FOTD 25-01-08 (Goodbye Minibrot [?])
by Jim Muth 24 Jan '08

24 Jan '08

FOTD -- January 25, 2008 (Rating ?) Fractal visionaries and enthusiasts: When I first saw today's image, all I could say was 'wow'. I have never seen this happen to a minibrot before. But in the world of fractals, the unexpected can only be expected. The image shows what happens to midgets in the 4-dimensional HyperMandelbrot set when the view is skewed in some unimaginable direction. I named it "Goodbye Minibrot" in memory of the minibrot that once was there but now is gone, and leaves its outline to carry on. Actually, I have no idea what's happening in the image, but what- ever it is, it is quite curious. Nor do I know how or why the HyperMandelbrot formula works as it does. It seems very strange that a value as tiny as 0.00000000000000000000007 would produce such a big change in an everyday scene in Seahorse Valley. But the details in today's image are consistent with those in the Seahorse Valley Julia fractals created by the type=hypercomplexj formula, when the value of C is very critical. To see the original Seahorse Valley scene, change the real(p3) parameter in today's image to zero, then sit back and be filled with awe and wonder. Since I have no idea where to rank today's image in a world that is virtually unexplored, I could give it no rating. The whole thing is a mystery, as made evident by the question-mark rating. The calculation time of 3-1/3 minutes is well within reason, especially considering that the periodicity checking is turned off, as it must always be when using this formula. The simplest and most convenient way to see the image is to visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view it there in solid comfort. Thursday was fair enough here at Fractal Central even though occasional heavy clouds and several snow showers spoiled the perfection. The high temperature of freezing was just about right for the coldest time of year. The fractal cats watched the big fluffy snowflakes for a half hour or so, then decided it was better to have a bit of fun by sitting on the work. After moving the sitting cats, I finished the day's real work with plenty time to look for fractals. The next FOTD, which will be a further exploration of the HyperMandelbrot set, will appear in 24 hours. Until then, take care, and reason it out. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Goodbye_Minibrot { ; time=0:03:19.54-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=HyperMandelbrot passes=1 center-mag=-0.74984503749226/+0.03360828961391/\ 155571.8/1/92.5/0 params=0/0/0.2/0/7e-023/0 float=y maxiter=1200 inside=0 periodicity=0 sound=off colors=000bWFmR6cWFV`OMeXDje4nm5nl6nk7nj8nj8ni9nhA\ ngBngBnfCneDoeEpdFqcFsbGubHtaIs`Ir`JqbJpdJofJngJmi\ JlkJkmJjnJipJhrJgtJfuKevLdvMcvNbvNavO`vP_vQZvRYvRX\ vrZut`ewaRubQscPqdOoeNmfMkgLihKgiJejIckHalG`lGZmFX\ nEVoDTpCRqBPrANs9Lt8Ju7Hv6Gv6Ep5Cj5Bd49Z47T46N34H3\ 3C36D68D8BEADECFEFIFHKFJMFLPGORGQUHSWHUYHX`IZbI`dI\ bgJeiJglKinKkpKnsLpuLrwLtvKruJptIosHmrGkqFjpEhoDfn\ CemBclBakA`j9Zi8Xh7Wg6Uf5Se4Rd3Pc2Nb1La2M`3M_4MZ5M\ Y6MX7MW8NW9NXANYBNZCN`AL_CNZEOYGPXIQXJRWLSVNTUPVUQ\ WTSXSUYRWZQY_QZ`P`bObcNddNeeMgfLigKkhHnkKliNkhPifS\ heUgdXeb_daab_daZkWTf`YadaXieTmiOrmJvqFzuGyrHypHxn\ IxlJxjJwhKwfKvcLvaMv_MuYNuWNtUOtSQtQSsNUsLWrJYrH_r\ FaqDcqBes8gq9io9kn9ml9mk9ni9oh9pg9qg9rfArfApdAnbAk\ _AhXFeUKbRP_OUYMUWKUULUSLUQMUOMPMNKKNFINAGM6FM5EL5\ DL5BK4AK49J38J37J37K0HXGRiW_uk`oe`j`adVa_QaUKbPFbJ\ 9bE4aI8aLBaOEaRHaUKaXOa_R } frm:HyperMandelbrot {; periodicity must be turned off a=(p1),b=(0,0): q=sqr(a)-sqr(b)+pixel, b=(p2+2)*a*b+p3, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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FOTD 24-01-08 (Hyperseahorse Valley [8])
by Jim Muth 24 Jan '08

24 Jan '08

FOTD -- January 24, 2008 (Rating 8) Fractal visionaries and enthusiasts: Today's circular image is a scene in Hyperseahorse Valley of the Hypermandelbrot set. I know that it looks nothing like a scene in the familiar Seahorse Valley, but Hyperseahorse Valley is a horse of an entirely different color. The HyperMandelbrot formula that created the image is the most enigmatic one in my active list. It appears to draw some of the Mandelbrot slices that the type=hypercomplex formula misses, though actually, I am not sure exactly what it does draw. We know that these hyper-elements exist in the 8-dimensional Hyperjulibrot figure because we see them in the images created by the type=hypercomplexj formula, which draws a far greater variety of slices than the type=hypercomplex formula, but some of the images appear so unlikely that I cannot shake the impression that they are artifacts of mathematical imprecision rather than true fractals. But whatever the images are, the HyperMandelbrot formula is infinitely versatile, and I have barely scratched the surface of what it can do. The rating of an 8 is based mostly on the mathematical interest of the image. The artistic worth is merely average. The name "Hyperseahorse Valley" describes the location of the scene in its parent fractal. The calculation time is a disappointingly slow 1/2 hour even on the super-speedster 2000mhz machine. The calculation is so slow because the periodicity must be turned off when working with the HyperMandelbrot formula. But all is not lost, for the completed image is posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where it may be enjoyed at leisure. A fairly average but brilliantly sunny day here at Fractal Central on Wednesday went un-noticed by the fractal cats, who spent the day chasing each other up and down the hallway. By the time the evening tuna treat was served, they were totally exhausted. My day was fairly busy, but under control. The next FOTD, which will be another scene in Hyperseahorse Valley, will be posted in 24 hours. Until then, take care, and what the heck are those 'rods' the UFO fans are talking about. I doubt that they are discussing the anatomy of the eye. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= HypersehorseValley { ; time=0:29:22.50-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=HyperMandelbrot center-mag=-0.743377645/+0.1010200296/4126.308 params=0/0/0.2/0/1e-007/0 float=y maxiter=32767 inside=0 logmap=212 periodicity=0 colors=000`PWaRYbS_cUadUbfUdgUfhUgiVijWkhXjcYiZZhU\ _gP`fOaePacQbaRbbSccTcdUdeUdfVegWehXfiYfjZgk_gl`hm\ ahnbiobipYghUfaQeVLcNHbGDa99`2DY7GVCJTHMQMPORSLWVI\ `YGe`DjcBof8ti6xhCvhHuhNthSshYrgbqghpgmogsngxmhsei\ nYjiQkdIl`AiZ9gX9eV8bT8`R7ZP7WN6UL6SJ5QH5NF4LD4JB3\ G93E72C52A32C45D58E6BG7EH8HI9JJAMLBPzCuzDmzDczBLvA\ 9rC9mE8cG8UI8RK7RM7QO6QQ6PS6PU5OW5OY4N_4Na4Mc3Me3L\ g2Li2Kk2Um1co1mq0wu0wz0mq3cm6Ui9KeCCaFBYIAUK9QN8MQ\ 7Iz6EW5Az46a33z9DdFNzLWzRezWnzUgzSazRW6SU8TTAUSCVR\ EWQGXPIYOJZNL_MN_LP`JRaITbHVcGWdFzeEzfDzgCzhBzhAvg\ BrfCmeDhdEgdFgcGgbHgaIg`Jh`Kh_LhZMhYNhYOhXPhWQhVRi\ USiUTiTUiSViRWiRXiQYiPZjO_jN`jNajMbjLcjKdjKejLfkMg\ kNgkOhlPhlQilRjlRjmSkmTkmUlmVlnWmnXnnYnnYooZoo_po`\ qoaqpbrpcrpdspdsqetqfuqguqhvrivrjwrjwrixqiypizohzn\ hznhzmgzlgzkgzjfzjfzifzhezgezfezfdzedzddzcdzcczdbz\ eazf`zf_zgZzhYzhXziWzjVzj } frm:HyperMandelbrot {; periodicity must be turned off a=(p1),b=(0,0): q=sqr(a)-sqr(b)+pixel, b=(p2+2)*a*b+p3, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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FOTD 20-01-08 (Spiritual Zen Tree [No Rating])
by Jim Muth 23 Jan '08

23 Jan '08

FOTD -- January 20, 2008 (No Rating) Fractal visionaries and enthusiasts: Every now and then I just have to create a fractal tree. Today the urge became irresistible, and the result was another fractal tree. Since this is the fourth or so similar fractal tree in the FOTD series, I did not give the image a rating, but it is a rather good tree and well worth a look, especially by those who have missed the previous fractal trees. I named the image "Spiritual Zen Tree" when I checked the day's snail mail and found the Jan 28 issue of 'Time' magazine in the box. The issue is yet another one claiming that 'love is just a brain chemical'. Its standpoint is that we are largely slaves of our genes, and our behavior is pre-programmed by random evolu- tion to perpetuate the species. But this makes me wonder. If we are slaves of our genetic pro- gramming, how can anyone be held responsible for a crime he was pre-programmed to commit? The same thing can be said in a dif- ferent way by claiming that we are pre-programmed by God's know- ledge of the future to do what God already knows we will do. The name of the image indicates that I feel the scientific arti- cles in the magazine, as well as the woefully lacking theories of conventional theology, are missing something very important of a very spiritual nature. The image lies in a near-Julia set of the (-Z)^sqrt(2)+C Mandeloid. It was created with the EvenMoreSlices formula, though a number of other formulas could have created it. The calculation time of the image is a zippy 51 seconds, about the same time it will take to view the completed image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Cloudy and chilly weather prevailed here at Fractal Central on Saturday, when the high temperature reached 36F 2C. The fractal cats, who still appear to be feuding, ignored the outside condi- tions. The better part of my day was spent reading a magazine. The next FOTD will appear by technological magic in 24 hours. Until then, take care, and for all we know, we might be as pro- grammed as the fractals we admire. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Spiritual_Zen_Tree { ; time=0:00:51.72-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=EvenMoreSlices passes=t center-mag=-0.766409/0.13473/39.4/0.7974/6.1233740\ 3837406224/-0.253135479727083945 params=1.4142/0/1e-005/1e-005/-1.125/0/-0.2/0 float=y maxiter=416 inside=255 logmap=312 symmetry=none periodicity=10 colors=0000Zzc_Pc_Qc_Qc_Rc_Sc_Sc_Tc_Uc_VcWVZSWUOXU\ KXZNYYQZYSZYU_YW`YYaZZa__b``caacbbdccebceecffdgfdh\ gchebCc`CaYC`WC_UB_TBZQBZOBYMBYKAXHAXGAXFAWEAWD9VB\ 9VB9UB9UB9TA8TA8S98S88W36S88OCAKGBGLDCPF7SF8UG9VHA\ cIBmJCtJDzKDzLEzMFzNGzNHzOIzPIzQJzQKzRLzSMzTNzUzzU\ zzVzzWzzXzzYzzYzzZzz_zz`zz`zzazzbzzczzdzzdzzezzfzz\ gzzgzzfzzfzzfzzfzzfzzfzzezzezzezzezzezzezzdi`dj_dj\ ZdkYdkYdkKek7fk7ej7dj7cj8bj8ai8`i8_i8Zi9Yi9Xh9Wh9V\ hAUhATgASgARgAQgBPfBOfBNfBMfBLfCKeCJeCIeCHeCGdDFdD\ EdDDdDCdDBcEBcEBbFBbFBaFBaGB`GB`GB_HB_HBZIBZIBYIBY\ JBXJBXJBYICYIDYIDYIEZIEZIFZIFZHGZHG_HH_HI_HI_HJ_HJ\ `GK`GK`GL`GLaGMaGMaGNaFOaFObFPbFPbFQbFQbFRcERcEScE\ ScETdEUdEUdEVdDVdDWeDWeDXeDXeDYeDYdEXdFXdGXcGXcHWc\ IWcJWbJWbKVbLVaMVaMVaNUaOU`PU`PU`QT_RT_ST_ST_TSZUS\ ZUSZVSYWSYXRYXRYYRXZRX_QX_QW`QWaQWbPWbPVcPVdPVeOUe\ OUfOUgOUhNThNTiNTjNTjN0Zz } frm:EvenMoreSlices {; Jim Muth ; P1--exponent, P2--angle, ; P3--M center, P4--J center, z=pixel+(p4), c=p3+(pixel*p2): z=(-z)^(p1)+c, |z| < 16 } END PARAMETER FILE=========================================

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FOTD 23-01-08 (Fractured Seahorses [6])
by Jim Muth 22 Jan '08

22 Jan '08

FOTD -- January 23, 2008 (Rating 6) Fractal visionaries and enthusiasts: Today's image shows a scene in Seahorse Valley of the Z^2.001+C Mandeloid as it appears at a level 0.03 up the logarithmic ladder when the function is eliminated. At this quite unlofty level, the parent fractal, which appears as a perfectly normal Mandelbrot set, is rotated clockwise just far enough for the southern arm of Seahorse Valley to intersect the negative X-axis. In the area of the X-axis some rather unusual things often happen to fractals with fractional exponents of Z, and today's image is no exception. The unfamiliar features are all caused by the nearness of the scene to the X-axis, which lies only 0.00001 to the south. Unable to find anything of knockout value in the image, I could rate it at only an everyday 6. The name "Fractured Seahorses" indicates that the scene lies in a very fractured part of its parent's Seahorse Valley. The calculation time of just under 10 minutes is a bit slow, but relief is at hand on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the image has been or soon will be posted for immediate gratification. Heavy clouds that threatened snow and a temperature that hovered around freezing all day made Tuesday rather unpleasant here at Fractal Central. The fractal cats made their day as pleasant as possible by hovering around the heat all day. Except for the fractal, which put up a bit of a fight, my day was peaceful enough. The next FOTD will be posted in 24 hours. Until then, take care, and knowing the future is the same thing as changing the past, though it is now seen from the opposite direction. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= FracturedSeahorses { ; time=0:09:55.84-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident center-mag=-0.76117950836326/+0.00001163773987/\ 8.014934e+008/1/-60/0 params=2.001/0/0.03/0 float=y maxiter=6250 inside=0 logmap=1075 periodicity=10 colors=000GGGFzzBrwCmsDihDjiEjiFjjFkjGkkGkkHllIllI\ mmJmmKmnKnnLnoLnoUibbdQk_DtV1qU7oUClUHjUMhUReTXcTa\ `TfZTkXTp`WncYmf`libjleioghrjfulexndijeld_o_UrUOtP\ JsOMsNPrNSrMVqLYqL`qKbpJepJhoIkoHnnHqnGtnGvhHubItX\ JtRKsMLsQRrUWrY`qafqekpippV_fGJX23N76QC9TGCVLFYQI_\ UKbZNecQggTjlWlqZou`qr_noZllYjiXhfWedWcaVaZU_WTXTS\ VQRTORRMOPLMOKKMJHLIFJGDIFAGE8FD6DC4CG5FJ5HM5JP5LS\ 6NV6PY6S`6Uc7Wf7Yi7_l7ao7cmAdkCeiEfgGgeIhcLiaNj`Pj\ ZRkXTlVWmTYnR_oPapNcqMeqOgmPhjQigRjcSk`UUYVXVW_RXa\ OYcLZcIVcGRbENaCJ`AF_9EZGEYMDXTDWZCPdCIyYB_B4zG7pK\ 9iPBcTDXXGQaIKeKDZH7zZBgOFfPJeQNeRRhUQjXQl_QnbPqdP\ sgPujOwmOyoOsmQnlRikSdiT_hVVgWQOXLdYGcZIc_Kc`Mc`Oc\ aQcaScbUccWccYcd_Odacecced`ceYbfVafT`gQ_hNZhLYhKui\ ItiHtjGtjFtkEtkDtlBslAsm9sm8sn7sn6soUWoq9peJpvYqv_\ qvarvbruast`ts_us_vrZwqYxpXypXzoWznVznVzmUzlTzkSzk\ SzjRz_GziQziQzhPzgOzfNzfN } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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FOTD 22-01-08 (Minibrot Minibrot [7])
by Jim Muth 21 Jan '08

21 Jan '08

FOTD -- January 22, 2008 (Rating 7) Fractal visionaries and enthusiasts: Today's image shows the outline of a large twisted minibrot in East Valley of the Mandelbrot set, which in itself is nothing unusual. But inside this East Valley minibrot lies a smaller minibrot from Seahorse Valley, which at first is quite puzzling. The puzzle is solved when we see that the image was created by the type=hypercomplex formula, which draws four-dimensional Mandeloids consisting of two overlapping classic M-sets. By changing the cj and ck parameters, the two sets may be made to overlap at any two points chosen. Today's parent fractal was drawn with East Valley overlapping Seahorse Valley in such a way that a small Seahorse Valley minibrot shows through a larger minibrot in East valley. (The c and ci parameters of the formula are fixed to the screen and cannot be changed, but the z, zi, zj, zk axes are all perpen- dicular to the screen. It would be nice to have a way to perturb the images in these four directions, and also to rotate the orientation of the images through the entire 4-D Mandeloid.) Since it took a bit of effort to find the overlapping midgets, I decided to add an extra point to the rating in recognition of my effort. The image itself is perhaps a bit above average, though similar images have been seen in some earlier FOTD's. The name "Minibrot Minibrot" accurately describes the image. The rather slow calculation time of 5-3/4 minutes is due to the maxiter of 14400, but it was needed to get full definition inside the outer minibrot. And all but a minute or so of this time may be saved by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Full sun could not offset a temperature of only 25F -4C here at Fractal Central on Monday. The fractal cats avoided the more drafty windows to keep warm on their shelf by the window over the radiator. My M.L.K. holiday was reasonably slow. The next FOTD will come from nowhere in 24 hours. Until then, take care, and if free will is but an illusion, why is it such a convincing one? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Minibrot_Minibrot { ; time=0:05:43.45-SF5 on P4-2000 reset=2004 type=hypercomplex function=sqr passes=1 center-mag=-0.2434276956/+0.0177325261/24493.47/1/\ -162.5/0 params=0/0/0.020008/0.505996 float=y maxiter=14400 inside=0 logmap=86 periodicity=0 colors=000ZUXWUXSUXOUXKUXGUXCUX9UX8UX7Ua6Ua6Ua8UaA\ UaCUaGUaKUaOUaSUaWUbZUbZUcZUcZUdZUdZUe_Ud_Ub`Ub`U`\ aU_aUYbVXbVVcWUcWSdWRdXPeYNe_Mf`KfbJgcHgeGhfEhhDii\ BijAggBfdBebBd_BcXBaVB`SB_QBZOBYMBWKCVICUGCTECSCCQ\ 9CP7CO5CN2CM0CR10L0CF0O9KZCKXFKVIKTLKROKPRKOUKMXKK\ ZKIYKGXJ8WI6VH4UG3TF4SE5RD6QA7Q88Q98QA9QB9QCAQDAQE\ BQFBQGCQHDQIDQJEQKEQLFQMFQNGQOGOJCIE9CA56520103306\ 51872B93EA4GC5JE6MG7OH8RJ9ULAWNBZOCaQDcSEfUFhVFfWG\ eXHcYIbYJ`ZK__LY`MX`NVaOUcPShQRlRVpS_pTduUiuViuWnu\ XruXvuVzzzzzzzzzzzzzzzPFfQFfRFfQFfQFfQFfQFfPEePDdP\ DcPDbPDaOD`OD_OCZOBYOAXN9WN8VN7TN6RN5RM4RM3RM2SM1S\ M0SN1TN1UO1VO1WP2X`NZ`MXaKVaITbHRbFShDzhCziAziAzxA\ zyAzzAzuAzvAzvAzwAzrAzmAzdAz_AzWKoSKkNKfQKaVKa_Uad\ U_iUYnUWrUUvZRvcPvhNvmLvr7vvJvzVvzevzcvzhvzmvzrvzv\ vzzvzzvzzvzzvzzvzzvzzvzzvzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } END PARAMETER FILE=========================================

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FOTD 21-01-08 (Not too Deep [5])
by Jim Muth 21 Jan '08

21 Jan '08

FOTD -- January 21, 2008 (Rating 5) Fractal visionaries and enthusiasts: I was kept so busy watching TV on Sunday that I had no time for a proper FOTD. But that old warhorse, the Mandelbrot set, bailed me out by producing an instant image of average quality. The image is a scene on the northeast shore line of the large period-2 bud of the M-set, lying at the border of Seahorse Valley. It's nothing we haven't seen before, so I rated it at an average 5. The name "Not too Deep" indicates that the image does indeed lie in the valley, but not very deep. The magnitude was great enough to require the mathtolerance entry. The calculation time of one minute is more an estimate than a true record. The completed image may be seen at any time on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Cold and colder conditions prevailed here at Fractal Central on Sunday, with lots of sun but a frigid temperature of 14F -10C. The fractal cats sampled the chilly draft by the window and retired to the radiator, while I finished some important work in front of the TV. The next FOTD will appear in 24 hours. Until then, take care, and if I have free will, I will refuse to do what God, who can see the future, has told me I will do. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Not_too_Deep { ; time=0:01:00.00-SF5 on P4-2000 reset=2004 type=mandel passes=1 float=y inside=0 center-mag=-0.80359866207152790/+0.164616502313286\ 80/1.152001e+011/1/-35/0 params=0/0 maxiter=5500 logmap=1443 periodicity=10 mathtolerance=0.05/1 colors=00000WrMVqOXoRZnT`lVbkYdj_ehaggdiefkdhmckok\ mqrostruytwzvxzwwvwvrwumwuhwtcwsZwrUxrPxqKxpFxo9xo\ 6xn4xm2xm4to6qq8msAjuCfwEcyF`zE_wE_tE_qE_nEZkEZhEZ\ eEZbEZ_DYXDYUDYRDYODYLDXIDXFDXCDX9DX6FY8GZ9I_AJ`BL\ aCMbDOcEPdGReHSfIUgJVhKXiLYjM_kO`lPbmQcnReoSfpTgqU\ fpWeoXenYdm_dl`ckackbbjdbieahfagh`fi`ej_ek_dmZcnZb\ oYaqY`rX_sX_tujusdsr_qqVooPmnKkmFilAgmDemFdnHbnJao\ L_oNZpPXpRWqTUqVTqXSr_QraPscNseMtgKtiJukHumGvoEvqD\ vsCfmERgGCbHDdIEeIEfJFgJFhKGjKGkLHlLImLInMJpMJqNKr\ NKsOLtOLuO`jao_omaplbqjdqierggsfhsdjtcktalu`nvZovY\ qwWrwVtxTuySwyQxzPyzQxuQxpQwkRwfRvaRvYUsVWqTYnQ_lO\ bjLdgJfeGzbUk`BmZ9oW6qU4sS2rR3qQ4pQ5oP6oP6nO7mO8lN\ 9lN9lO6lP4jO5iO5gN5fN5eM6cM6bL6`L6_K7ZK7XJ7WJ7VI8T\ I8SH8QH8PG9OG9MF9LF93FJ2AH1AF4cH6cJ8cLAcNCcPEcRGcT\ IcVKcXMcZOc`QcbShdUmfWrhYviUzeRzbOzZLzWIzTFzPCzM9z\ J9zO9zU9zZZzc_ze`zfazgbzi } END PARAMETER FILE=========================================

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FOTD 19-01-08 (Cave of the Dragon [8])
by Jim Muth 19 Jan '08

19 Jan '08

FOTD -- January 19, 2008 (Rating 8) Fractal visionaries and enthusiasts: Today's image is a near-Julia set of the mouth of the valley leading to the large period-3 bud on the northeast shore of the main bay of the (-Z)^(1.5)+C Mandeloid, which is actually a rather interesting fractal. The outer outlined shape is very close to the Julia set of the point where the two branches of the valley would reach their limit. The pinkish wedges are a grossly magnified view of the two branches of the Mandelbrot aspect of the valley itself. The cobweb-like elements are added attractions brought about by the odd angle of the slice. The name "Cave of the Dragon" came about when I fantasized a dragon lying just inside the mouth of its cave-lair, guarding its treasure trove and watching for approaching dragon-slaying knights. The rating of an 8 indicates that I consider the image quite a bit of an improvement over yesterday's image. The calculation time of 1-3/4 minutes is brief enough to make no one impatient. And the image may be seen even more conveni- ently by viewing it on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> An un-midwinter-like temperature of 43F 6C and strong sunshine here at Fractal Central on Friday got rid of the little snow that fell on Thursday. But a cold wave is due in a day or so, so we'll see how it goes from here on. The fractal cats are still sulking at each other. But only they know why. My day was moderately busy. Luckily, the snow on the sidewalk melted before I needed to clear it away. And best of all, the next FOTD will be posted to these same lists in 24 hours. Until then, take care, and even if we do not have free will, we still have the freedon to think about it. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Cave_of_the_Dragon { ; time=0:01:45.84-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=EvenMoreSlices passes=t center-mag=-0.0312989/0.169102/0.9082652/1/52.5/0 params=1.5/0/0.05/0/0.5187656/0.3853761/0.2/0 float=y maxiter=6000 inside=0 logmap=3 symmetry=none periodicity=10 colors=000LHIMIINJIPKIRLITMIVNIXOIZPI_RIaSIcUIgVIl\ XIqXIv`IweIxkIyqJzuKzwYztXzqWznVykUxhTweSvcRvaQvaP\ u`Ou_Nu_MuZLuZLuYKuXJuXIuWHtVGtVFtUEtTDtTCtSBtRAtR\ 9tQ8UarX_mZZiaYecX`fWXhVTkUPmTKpSGrRCk`el_cl_blZam\ Z_mYZmYYnYXnXVnXUoWToWSoWQpVPpVOpUNqULqUKqTJrTIrSG\ rSFsSEsRDsRBtQAtQ9EF3JH4NI4RJ5WK5_L6cM6hN7lO7pP8Mx\ fQtbUpZYlVahRedNi`JmXFqTB6_V8ZUAZTBZSDYSEYRGYQIXPJ\ XPLXOMWNOWNQWMRVLTVKUVKWVJYUIdMNcMObNQ`NR_OTZOUYOV\ aQTdSRhUPkWNoYLr_JvaHycFxbExaExaEx`Dx`Dw_Dw_DwZCwZ\ CwYCvYCvXBvXBvWBvVAuVAuUAsQAuUAuT9uT9tS9uS9vR8wR8x\ Q8yz5zw6zu6zs6zq6zo6zl7zj7zh7zf7zd7zb7z_8zY8zW8zU8\ zS8zbgzaez`cz`az__zZZzZXzYVzXTzXRzWQzVOzVMzUKzTIzT\ HzSFzRDzRBzQ9zzPzkGzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzz\ UzzngzihzeizakzYmzUoznwzmuzlszkzzjzzizzhzzgzzfzzez\ zdzzczzbzzazz`zz_zzZzzYzzXzzWzzVzzUzzTzzSzzRzzQzzJ\ zzKzzKzzKzzKzzLzzLzzLzzLz } frm:EvenMoreSlices {; Jim Muth ; P1--exponent, P2--angle, ; P3--M center, P4--J center, z=pixel+(p4), c=p3+(pixel*p2): z=(-z)^(p1)+c, |z| < 16 } END PARAMETER FILE=========================================

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FOTD 18-01-08 (Something Valley [No Rating])
by Jim Muth 18 Jan '08

18 Jan '08

FOTD -- January 18, 2008 (No Rating) Fractal visionaries and enthusiasts: Today's fractal is named "Something Valley". I gave it this name because I'm not sure which type of valley it lies in. It's parent valley is kind of like a Seahorse Valley, but it's on the east side of the parent fractal's main bay. And it's kind of like an East Valley, but there are two of it. But regardless of what one calls the parent valley, the minibrot in the image betrays the fact that the exponent of Z is between 2 and 3. In fact, the exponent is 2.5, and to make matters even more confusing, it is not Z being iterated, but negative Z. With so much confusion floating around, I could hardly give the image a proper rating. And the calculation time is a frustrat- ingly slow 18-1/4 minutes even on the P4-2000mhz fireball. With all this in mind, I recommend that all interested fractal fans exercise their free will by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the moderately impressive finished product there. As for the problem of free will, I doubt that God's image can be much damaged by the lack of or existence of human free will. To me, the paradoxes raised by God's assumed nature merely show how insufficient are the God-images created by the infinitesimal imaginations of puzzled theologians, which reduce the creating power to the status of a glorified human being. Light snow fell all day Thursday here at Fractal Central in central Pennsylvania, but the temperature remained just above freezing and the snow melted on the pavement. Only on the grass did a measly 1-inch (2.5cm) pile up. The fractal cats were fas- cinated for a time by the big sloppy flakes, but soon grew bored with the show and started chasing each other up and down the long F.C. hallway. My work-day was pleasingly average, as average as the day's fractal. And the next fractal, hopefully considerably above average, will be posted to this very same list in a short 24 hours. Until then, take care, and exercise your free will. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Something_Valley { ; time=0:18:16.24-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=EvenMoreSlices center-mag=+0.162919462\ 1248572/+0.2821811066023142/8.109735e+008/1/-135/0 params=2.5/0/1/0/0/0/0/0 float=y maxiter=32767 inside=0 periodicity=10 colors=000_Rv3fm7diAbfEacH_`LYYOXUSVRVTOZSLaQIdPFa\ TIZWLW_NUbQReSOiVMlYJp_GsbEvdoXBjVAfU9bT8ZS8VR7QP6\ MO5IN5EM4AL36K3CN4IQ4OT4TW4ZY4d`4ic4of4uf4xh4sd6o`\ 7eZ8XW9QSAINBBGC43D8AIBHMEOQHVUKaYUgaZiacjahlammar\ oavpazrazsaruamvahqfdljkjyghndgd`fUYeKVdAUcFUbJUaN\ U`RU_WUZ_UYcUXgR`jUXkXUk_QlbNleKlZYiSjf`fILwdNvgOu\ iQtlRsnTrqUqsWpvXpxeXanDFkCIhCLfBNcBQ`ATZAVW9YT9`R\ 8bO8eL6hM8gNAfOCfPEeQFePHcOJbOLaNN`NP_MRZMTYLVXMWT\ LXWKXZJXaIXdHXgGYjFYmEYpDYsE_yDYuCWrCUnBSkBRgAPdAN\ `9LY8JU8IR7GN7EK6CG3A76BD8CIACNCDSFDYHEbJEgLFlNFqT\ IdZLTdOGiQ4qh3xz2vt5uo7tjAseCr_FqVHpQKoLMnFPmARl5U\ k0Wj3Vi6Uh9TgCSfFReIQdLPcOObRNaUMbXP`XMZXKXXIVXFTX\ DP_9RXBSVCTTEVRFWPHXMIZKK_IL`GNbEOcBQd9Rf7Tg5Uh3Ve\ 4Yb4`_4bY4eV4hS4jP4mN4oJJqFYs7nwCltGkqKinOhlSfiWef\ _cccbag`Zk_WoYTuVSsXRrYQq_Pp`OobNncMmeLlfKkhJjiIij\ HhiKghNfgQefTdeWddZccabbd } frm:EvenMoreSlices {; Jim Muth ; P1--exponent, P2--angle, ; P3--M center, P4--J center, z=pixel+(p4), c=p3+(pixel*p2): z=(-z)^(p1)+c, |z| < 16 } END PARAMETER FILE=========================================

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FOTD 16-01-08 (Pipefish Valley [6.5])
by Jim Muth 17 Jan '08

17 Jan '08

FOTD -- January 16, 2008 (Rating 6.5) Fractal visionaries and enthusiasts: We have another new formula today, so be sure to copy it into one of your formula files. The formula draws oblique slices of (-Z)^n Julibrots. I named the image "Pipefish Valley". A pipefish is a kind of seahorse without the curly tail, and today's image is a near- Julia set of the large valley of the (-Z)^(1.125)+C Mandeloid. This valley cannot honestly be called a Seahorse Valley, since it has no curly-tailed seahorses, but it is interesting nonethe- less, and especially so in its near-Julia aspects. The pure Julia set of the valley is a rather drab empty figure-8 shaped figure, but by centering the view on the inside of the upper arm of the valley and rotating the view 2-1/2 degrees toward the Mandelbrot orientation, I managed to make a rather interesting image of it. A good part of the scene consists of 'inside' stuff made visible by the 'bof61' inside fill. The coloring adds an unusual textured smoothness to the scene. I credited myself the usual 1/2 point for the coloring, and rated the image at a 6-1/2. The image is a slow one, taking over 41 minutes on the fast machine, so I recommend viewing it on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A typical midwinter day prevailed here at Fractal central on Tuesday, with cold winds, lots of gray clouds and a temperature of 34F 1C. And the forecast is for things to become even more winterish over the next several days. The fractal cats were too busy sulking at each other to notice the weather. My day was about average. The next FOTD will appear in 24 hours. Until then, take care, and if God, who is never wrong, tells me the future, will I still have the free will to avoid the things he tells me will happen? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Pipefish_Valley { ; time=0:41:38.66-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot5 passes=1 center-mag=-0.344371/0.0122124/1.180338 params=87.5/87.5/87.5/87.5/-0.7362027083/0.04/0/0/\ 1.125/0 float=y maxiter=30000 inside=bof61 outside=tdis logmap=12 periodicity=10 colors=000YT0WTBWSAVSAURAUR9TQ9SQ9SQ9RP8QP8QO8QO7P\ O7PN7ON7NM6NM6MM6LL5LL5KK5JK5JK4IJ4HO4GM3HJ4IF4IH4\ JI4JK4KL5KN5LO5MQ5MR5NT5NU6OW6OX6PZ6Q_6Qa7Rb7Rd7Se\ 7Sg7Th7Uj8Uk8Vm8Vn8Wp8Wq8UnDTlHRjLQhQOfUNdYLabK_fI\ YjHWoFUsESwFPvFNuFLtFJtFHsFFrFDqFBqF9pF7oE4qF5oG5m\ G5kH5iI5gI5eJ6cJ6aK6_L6YL6WM6UM7SN7QO7OO7MP7KO6GP7\ IP7JP7KQ7LQ7MQ7NR7OR7PR8QR8RS8SS8TS8UT8VT8WT8XT9YU\ 9ZU9_U9`V9aV9bV9cW9dWAeWAfYAgZAhcAihAjmAkrAnvBqzMt\ zUwzUzwXzrNzmBzjByf9wcAtaBq`CnZClYDiYEfXEdWFaWG_VH\ ZVHXUIVTIVTHUSHTRHTRHSQGQQGPPGPOGOOINNKNMMLMNJLPIL\ RGKSEJUDJVBIW9HW8HX6GY4GY3FZ4KZ5PZ6UZ7ZZ8cZ9hZAmZB\ rZBvZCzZDzZEzZFzZGz_Hz_Iz_Jz_Jz_Kz_Lz_Mz_Nz_Oz_P9_\ Q8_R8_R8_S8_T7`U7`V7`W7`X6`Y6`Z6wZ5w_5w`5wa5wb4wc4\ wd4we5wf4we4we4we4we4we4we4wemwzmwzmwzmwzmwzmwzmwz\ mwzmwzmwzmwzmwzmwzmwzmwzmwzmzzmzzmzzmzzmzzmzzmzzmz\ zmzzmzzmzzmzzmzzmzzmzzmzz } frm:SliceJulibrot5 {; draws slices of (-Z)^n Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=(-z)^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

6 5

FOTD 17-01-08 (The Tenth Valley [5])
by Jim Muth 17 Jan '08

17 Jan '08

FOTD -- January 17, 2008 (Rating 5) Fractal visionaries and enthusiasts: Today brings another trip to a Seahorse Valley, this time to one of the 9 Seahorse Valleys of the (-Z)^10+C Mandeloid. The valley I chose is naturally the one centered on the negative X-axis, which is by far the easiest to work with. Another new formula was required to do the job, so another new formula was created. The formula is included at the bottom of today's parameter file. It does the same job as the 'More Slices' formula, but can calculate any power of negative-Z. I chose (-Z) instead of (+Z) because the fractals created when it is raised to powers between 1 and 2 are far more interesting, and the images drawn by the integer powers of (-Z) are identical to those drawn by the customary (+Z). In today's image I chose a near-Julia set of a Seahorse Valley of the (-Z)^10+C Mandeloid. A grossly magnified but reasonably undistorted image of the valley fills the inside of the order-10 Julia set. I named the image "The Tenth Valley" for obvious reasons. Then I rated the whole thing at a rather boring 5. I really cannot find too much to get excited about in the image. The calculation time of 6-1/2 minutes does border on the tire- some side. But perhaps the best news of the day is that the finished image is or soon will be posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A fairly typical midwinter day prevailed here at Fractal Central on Wednesday, with a temperature of 36F 2C and partial sunshine. The fractal cats, who remained in bad moods, paid no attention to the outside conditions. My day was a little busy but still under control. The next trip to a seahorse-type valley will appear in 24 hours. Until then, take care, and live a life of fractal joy. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Tenth_Valley { ; time=0:06:37.28-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=EvenMoreSlices passes=t center-mag=0.2845/0/0.93 params=10/0/1.5e-005/0/-0.851698/0.00144/-0.2845/0 float=y maxiter=5200 inside=0 outside=tdis logmap=yes periodicity=10 colors=000XEZskFrgGrcIr_JqWKqSLqONpKOpGPpCQp8RoCSn\ FSnISmLSmOSlRTlUTkYTUdGUYGQRGKHGGUKO_NWeRckUkqXmnU\ olRqjOsgLueIwcFxaDYaM7aU8`U9`UA`UB`UC`UD`UD`UH_GK_\ 3S`C_aLgbUocbwcjsalo_mkYngWocUq_SrWQsSPtWkbViZVgVU\ fRUdNTcJTaFT`CVlWWwn`qhdlbhfXmaRqWLuRFyM9oRIeVRX_Z\ NcgEgoAjf7lY4nP5iS6eU7`W7XYDZUJ`QPaMVcI`eEffAbgGZg\ MVhRShXOhbkFclOXnXRoeKpmERZD1LCAMGJNJSOM`OQiPTrQWz\ QZrOWkMUdKSYIPRGNKFLJRTIa_HlgHwnCiW7XECOUHGhOOaVWW\ acQhkKosEvbsdTmOKh7Bc6G`5KY5PW4TT4YR3aO3eMBm_JulQm\ kWekaYkgQjmIjsBjOr6ThHX_SaQbeHmdJlcKlbMlaNl`Ok_QkZ\ RkYSkZRi_Rh_Rg`Re`RdaQcWXDTcDSfEShESkFRmFRpGRrGRtG\ WqE_oCdlAhj80nC69hJKdWU`hdXtnUuiRvePw`NwXLxSJyOHzJ\ FzFDmb_cYZUUYKPYALX0HXlNfoRarVXuZSwaNk`L`_KPZIEYH3\ YGDRRMKaVDlYCk_CibBheAgg9ej8dl8ceKb_WbTgaNraLnbKjb\ JgbIcbH`bGXbFUbEQbDNbCJbBGbACb99b85b72b84V86O88H8A\ A8C37D77DB7DF7DJ7DN7DR7DV } frm:EvenMoreSlices {; Jim Muth ; P1--exponent, P2--angle, ; P3--M center, P4--J center, z=pixel+(p4), c=p3+(pixel*p2): z=(-z)^(p1)+c, |z| < 16 } END PARAMETER FILE=========================================

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FOTD 15-01-08 (Festive Julia Set [7.5])
by Jim Muth 14 Jan '08

14 Jan '08

FOTD -- January 15, 2008 (Rating 7.5) Fractal visionaries and enthusiasts: Who knows what absurdities lurk in the heart of Seahorse Valley? (No one but The Shadow knows, and I don't see him around here!) I certainly never expected anything like the indescribable mass that fills the almost-Julia set of Seahorse Valley in today's image. The image is centered at the same point as yesterday's image, though the orientation of the slice, as well as the generating formula, is totally different. I named the image "Festive Julia Set" and rated it at a 7-1/2. Actually, the extra half-point is a bit liberal, since the color palette came about through the efforts of the Fractint program- mer who decided that striking the 'enter' key while in color cycling mode would create a totally new and random palette. One quick click produced the colors. The orientation of today's slice is rotated 0.01 of one degree toward a 90-degree rotation of the Mandelbrot set. This is a very small rotation indeed, but small rotations produce big changes this close to the Julia direction. There is nothing unusual about the calculation time, which at 2-3/4 minutes is close to the FOTD average. But as always, the most convenient way to see the image is to view it on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The forecasted snowfall failed to materialize here at Fractal Central on Monday, not that the fractal cats were bothered by the busted forecast. But the cloudy day with occasional light rain and a temperature of 43F 6C, kept things still a bit on the unpleasant side. My day was busy enough to keep boredom at bay. The next FOTD in the Seahorse Valley series will appear in 24 hours. Until then, take care, and keep alert. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Festive_Julia_Set { ; time=0:02:43.51-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot2 center-mag=0/0/0.87 params=89.99/89.99/89.99/90/-0.7500101/0.004/0/0 float=y maxiter=250000 inside=0 periodicity=10 colors=000JGl5HjJOjWUjeWjkXgpYcsVYrSSqOMqKGpIMpHSp\ GYsFbvLTyPKzSBtO9iJ7ZD5R63A01Y6c_8g`AkbCncDqeFtfHw\ hJxiKy5K58JCBJIEIPHIVKHaNHgQGnSGtOmYNgTMaOLWJKQFJK\ AIE5Y4iidOVOCXjhUc`RYUPRNMLFJE8FzTGsPGlMGeIGZFHSBH\ L8HE4N87L85K84I828KfAI_BGTDEMECFGA8sSokOdcKVWGLOCB\ pB6kA5gA4b94Z93U92Q82L81UU26lg9aXCSMFIBAuSDdJFOAdw\ oaphZjbWcWTYQQRKNLDKE75mua4HbwrZniVe`SYSOPJKGANEvL\ CjKBZJAOI9C9kICYCFL6GM6HK5HI4HG3HE3HC2HA1ZwOQYCjfT\ 9QiDHNDBaEAXEASF9OF9JG9EG8AH85MNHKJDJF9IB5W7BT89Q8\ 7N85K83zTgcIMytnpjdg`VZRLQHBC3cF6KDmNEdIFXEGO9HG5u\ fNn`JgVF`PCUJ8ND4O2DM4AK57I743_GAphCh`DaUEUNFNFGF8\ KLcJIXJGRIEKICEHA7OffM_YLTQJMHIF9WgWUbSSZOQUKOQGML\ CKH8IC4DcDFO7eWn`SeXOYTKQPGHLC9zpJtjGndEh_CcUAYO7S\ J5MD3bfCg90MUc3nG8_BDM6ofTfYMYPFPG8HMJHJFHGBHD8HA4\ _68W76T75Q74N83K82HZiHVbHRXHNQHJKHFDHB7n6bg7V`7NU8\ GN88z`ClY9bR6TO3UK8FDHYFn } frm:SliceJulibrot2 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END PARAMETER FILE=========================================

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AOTD
by JackOfTradeZ＠comcast.net 14 Jan '08

14 Jan '08

. Animation of Jim Muth's FOTD -- January 02, 2008 (Rating 9.5) "Aurora Fractalis" is posted: http://www.fractal-animation.net/vid/aurorafractalis.zip WMV, 640x480, 52 sec, 8.5 Meg .

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FOTD 14-01-08 (New View of Seahorse [7])
by Jim Muth 14 Jan '08

14 Jan '08

FOTD -- January 14, 2008 (Rating 7) Fractal visionaries and enthusiasts: Today we introduce a new formula, which draws the slices of the Julibrot that are missed by the other odd-slice and oblique- slice formulas. This formula draws only the oblique slices in which there is no annoying stretching or skewing that must be unstretched to be properly seen. I named the image "New View of Seahorse", and indeed, this is what it is. In the image we see the entire Julia set of Seahorse Valley as well as an enlarged view of a deep part of the valley itself in the same frame. And don't miss the peanut holes where the vertical valley meets the edges of the Julia parts of the image. The blank outer shape is immediately recognizable as one of the Julia sets of Seahorse Valley, while the colorful vertical inner stripe is a grossly enlarged but unstretched view of Seahorse Valley as it appears at a depth of y=0.004. The sides of the valley are parallel not because it is stretched, but because it is sliced at a depth where its sides actually are parallel. The inner part of the image is enlarged for the same reason that a 2-D slice of a circular cylinder can appear as anything from a circle to a stripe with straight and parallel edges. A cross- section of a similar 4-D cylinder is a sphere, and the cylinder can be sliced by a 2-D plane in a direction that stretches the projection equally in 2 dimensions. Such a two-dimensional stretching appears as a simple magnification. I rated the image at a nominal 7, a fair rating for an image with a rather slow calculation time of around 22 minutes. But why not forget about calculating by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the image there? Sunday turned out pleasant but a bit colder here at Fractal Central. The clouds that moved in during the afternoon held the temperature to 43F 6C and led to a cold rain mixed with snow after nightfall. The fractal cats and myself as well spent most of the day taking it easy in front of the TV. The next FOTD will appear in 24 hours. Until then, take care, and I wonder what happened to all the wonder I once felt as I read those early books about the wonders of science and the physical world. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= NewViewOf_Seahorse { ; time=0:21:58.54-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MoreSlices passes=t center-mag=0/0/0.86 params=-0.7500101/0.004/0.00014/0/0/0 float=y maxiter=40000 inside=0 outside=tdis logmap=yes symmetry=none periodicity=10 colors=000LQmKPjJNhIMeHKbGJ_FHX8FXCIWFLVJOU_LnaNld\ PjXdTVbVS`XQZZNX`LVbNWcOXcPXcQYcRZdSZdT_dU_dV`eWae\ XaeYbeZbeYcbXc`XcZWcXWcVVdTVdRUdPUdNTdLTdJSbNR`QQZ\ UPXXOV`NTcMRfLPjKNmJLqIJtIHwHJtHLrGNpGPmFRkFTiEVgE\ XdDZbD``DbZEZaEWcETeFPgFMiFJkGFmGCoG9qEDrDGrBKrANs\ 8Qs7Us5Xs4_t2ct1ft0itBblMWdXPYgIQrBJnAMj9Pf9Sb8VZ8\ YV7`R7cN6fJ5iF5lB4o74r33u03x5At9HpDOlHVhLadPgaNcVL\ _OJYHHSAFk4DmcHc`K8YNBVQESTHPWKMZNJaQGdTDgWAjY7nbB\ rgFzmJvfLvaMvXUvScvNmvJmuKmuLmuMmuMmuNmtOrtOvtPztQ\ ztQzsRzsSzsSzsTzsUzsUztSzuQzvOtwMrxKqyIpyHouKpqMqn\ OrjQrgSscUt`WtXYuT_vQavMcwJexFgxCiy8kz5mz7Zz9YzAXz\ BWzDVzEUzFTzGSzISzJRzKQzLPzNOzONzPMzQMzOOzNQzMRzKT\ zJUzIWzGXzFZzE_zCazBbzAdz9ezCbzF_zIYzLVzOTzRQzUOlX\ Lj_IhbGfeDdhBbk8`n6_oDYoJWpPUpVTq`RqfPrlNrrMkmKdiJ\ ZeISaHLXFFTE8PD2LC6JGAHJDGMHEQLCTOBWS9_W7bZ6eb4if2\ li1okBgmL_oVSqdKO_vNYsMXp } frm:MoreSlices {; Jim Muth ; P1 -- M-center of slice ; P2 -- angle of slice ; P3 -- J-center of slice z=pixel+(p3), c=p1+(pixel*p2): z=sqr(z)+c, |z| < 16 } END PARAMETER FILE=========================================

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FOTD 13-01-08 (Misfits [3])
by Jim Muth 13 Jan '08

13 Jan '08

FOTD -- January 13, 2008 (Rating 3) Fractal visionaries and enthusiasts: After a 10-rated fractal winner such as we had yesterday on January 12, all we could dredge up for today was a fractal loser, rating a measly 3, which is well below the FOTD average between 6 and 7. The image is a view of one of the Julia sets of the Quaternion Mandelbrot set, which, as far as I can see, is the 3-dimensional figure that the classic Mandelbrot set would trace out if it were rotated around its X-axis. The Julia set in today's image has obvious Seahorse Valley characteristics, but it comes in 3 sepatated parts, which is a sign that its associated Mandelbrot point lies outside the quaternion M-set itself. The name "Misfits" came about when I could think of nothing better. Luckily, today's calculation time is as brief as yester- day's was long. Today's image calculates in 4-1/2 seconds. As always, the finished image is available for instant viewing on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A perfectly average midwinter day prevailed here at Fractal Central on Saturday, with partly cloudy skies and a temperature of 39F 4C. The fractal cats, who enjoy smooth-running, routine things, took little notice of the weather. My day was occupied with clearing up odds and ends. The next FOTD will appear in 24 hours. Until then, take care, and take heed. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Misfits { ; time=0:00:04.29-SF5 on P4-2000 reset=2004 type=quatjul center-mag=0/0/1.1086 params=-0.75/0.1/0/0/0.2/0 float=y maxiter=5000 inside=0 periodicity=0 colors=000IIAIIAIIAIHAIHAIHAIHAHHAHHAHGAHGAHGAHFAH\ FAGFAGEAFEAEEADDACDABDAADAACAABAAAAAAAAAAAAAAAAAAA\ AAAKNlMOkQPjURiYTgaVfeWeh_bjb_lfXniUqmRspOutLwwJvx\ OuxStxWsx`rxdqxhpxmoxqnxunxykvwiuufssdrqapo_omYmkV\ liTjgQieOgcMfbPaXSYSVUNXQIcUGiYEpaCvdAqeDmeFieHeeJ\ `eLXeNTePPeROdUNdXMc_LcbLbeKbhJakIanH`qH`sH_rH_rG_\ rG_rG_rG_rG_rF_rFZrFZrFZrEZrEZrEZrEZrEZrDYrDYrDYrD\ YrCYrCYrCYrCXqBXqBXqBXqBXqBXqAXqAXqAWqAWq9Wq9Wq9Wq\ 9Wq9Wq8Wq8Vq8Vq8Vq7Vq7Vq7Vq7Vq7Vq8Up8Uo8Un8Tn8Tm8T\ l8Tl9Sk9Sj9Sj9Ri9Rh9Rh9RgAQfAQfAQeAPdAPdAPcAPbBOaB\ OaBO`BN_BN_BNZBNYCMYCMXCMWCLWCLVCLUCLUDKTDKSDKSDJR\ DJQDJQDJPEIOEINEINGDBEHMEHLEHLEHKFGJFGJFGIFFHFFHFF\ GFFFGEFGEEGEDGDDGDCGDBQ__PZZPZZPZYPYYPYYPYXPXXOXXO\ XWOWWOWWOWVOVVOVVNVUNUUNUUNUTNTTNTTNTSMSSMSSMSRMSR\ MRQMRQMRQLQPLQPLQPLPOLPOLPOLONLONKONKNMKNMKNMKMLKM\ LKMLJLKJLKJLKJKJJKJJKIJKI } END PARAMETER FILE=========================================

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FOTD 12-01-08 (Ultra-Extremism [10])
by Jim Muth 12 Jan '08

12 Jan '08

FOTD -- January 12, 2008 (Rating 10) Fractal visionaries and enthusiasts: Today's image rates a 10. This is no mistake. To find it, I went as deep as possible into Seahorse Valley to highlight one of the things there that I call peanut holes. I named the image "Ultra-Extremism" because it takes everything to the extreme. To start, the maxiter of 2,147,483,647 is the program's limit, and even with this maxiter there are open holes in the image. Next, the magnitude of 1.7*10^13 is at the limit of the conventional math routine, and finally, the calculation time of almost 7 hours is the limit of practicality. (Arbitrary precision math would finish the image in about 700 hours, or one month.) Since the image sets a new record in so many aspects and also is artistically pretty good, I decided to give it a rating of a 10, the highest possible rating, very rarely achieved. Perhaps the most interesting thing in the image is its lack of resemblance to anything that might be expected in a typical Seahorse Valley image. The net-like features, for one thing, are nowhere in evidence in the normally explored parts of the valley. I strongly advise against calculating the image yourself. The calculation time of almost 7 hours on my fastest machine will stretch into days on anything slower. The way to view the image is to go to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where I have already sent the image for rapid posting. Friday started with heavy low clouds and rain here at Fractal Central, but at noon the rain ended and the sky cleared, leading to a most pleasant afternoon with a temperature of 48F 9C. The fractal cats celebrated by sleeping. My day was rather busy during the 7 hours the fractal cooked. But the wait was worth it. The next FOTD, probably not as good as today's but still worthwhile, will be posted in 24 hours. Until then, take care, and be thankful. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Ultra-Extremism { ; time=6:57:45.09-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-0.75000000009776880/+0.000007999957639\ 72/1.702597e+013/1/15/0 params=0/0 float=y maxiter=2147483647 bailout=9 inside=255 periodicity=10 mathtolerance=0.05/1 colors=0000If0Gf0Ef0Cf0Af08f06h04h02h00h00h00h00f0\ 0d00a00Z00W00T00Q00O00N00N00N00P00R00T00W00Z00a00c\ 00d00d00d00d00d00d00d01d02d03d04d05d06d07d08d09d0A\ d0Bf0Cg0Dh0Ei0Fj0Gk0Hl0Im0Jn0Ko0Lp0Mq0Nr0Os0Pt0Qu0\ Rv0Sw0Tx0Uy0Vz0Wz0Xz0Yz0Zz0_z0`z0az0bz0cz0dz0ez0fz\ 0gz0hz0gz0ez0cz0az0_z0Yz0Wz0Uz0Sz0Qy0Ov0Ms0Ks0Is0G\ s0Eq0Cn0Ak08h06f04d02b00_00Y02Y04_06Y08W0AT0CR0EP0\ GN0IK0KI0MG0OG0QE0SC0UW0ZW0cT0hT0qT0yR0vR0vR0sR0sP\ 0qP0qP0qN0nN0nN0kK0kK0hK0hI0fI0fI0dG0dG0bG0bE0bE0_\ E0_C0YC0YC0WC0WA0TA0TA0R80R80P80P60P60N60N40K40K40\ I20I20G20G10E10E10N00I00E10A208404601800A00C00G00I\ 00K00N00P00R00T00Y00W00W00W10W40WA2WE8WKCWPIWTPW_W\ WdbWkhWqqWvvWzzWzzfzzszzzzzzzzzzzzzzzzzzzzzzzszzfz\ zWzzWzzWzzWzuWzpYzkYzfYzaYzaYzfYxkYwp_uu_sz_qz_oz_\ mz_kz_izbgzcezhczmazw_zzYzzWzzUzzSzvQzrOymMshKnfIk\ dGfdEddC_dAWd8Td6Qd0Nd0Kf } END PARAMETER FILE=========================================

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FOTD 11-01-08 (Gateway to Infinity [No rating])
by Jim Muth 10 Jan '08

10 Jan '08

FOTD -- January 11, 2008 (No Rating) Fractal visionaries and enthusiasts: Today's trip to Seahorse Valley reveals an entirely new aspect of the valley. The slice is centered at C=-0.75+0.095i Z=0,0 and is sliced in an orientation double rotated 15 degrees from the Julia direction toward the Parabolic direction. Double rotation is another of the seemingly absurd things that are simple in four-dimensional space. It has no analog in 3-D space. The closeness to the Julia orientation is evident in the open top half of the image, which bears an unmistakable relation to the well-known Julia sets of Seahorse Valley. But the lower half of the image is a different story. Here we are apparently skimming through the buds of the valley, which have been stretched to infinity in the horizontal direction and appear as mere slits. Don't try to figure out which buds we are skimming through. I tried to deduce it and ended up totally mentally congested. It's just not possible for we beings of limited visualizing ability to mentally picture four-dimensional things. One of the more interesting aspects of the image is the ghostly transparent yellowish rings that are projected on the venitian- blind background of the bud slits. But strangely enough, when stretched in the proper direction, these ghostly rings prove to be quite ordinary Seahorse Valley elements. I named the image "Gateway to Infinity". The open background inspired the name. I gave the image no rating, since it is almost solely of mathematical interest. The calculation time however is very reasonable. The 24 seconds required to complete the calculation should try the patience of no one. The finished image is available as always on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> With variable clouds and a temperature of 48F 9C, Thursday proved to be an ordinary day here at Fractal Central. The fractal cats must have agreed. They became so bored that they got into an overheated tussle and mouthed some disgraceful cat words at each other. My day was moderately busy, which means the day's work was up to schedule by 3pm. The next FOTD will be posted in 24 hours. Who knows what havoc we will wreak on Seahorse Valley at that time. Until then, take care, and I assume the objective world must be real because every time I open my eyes, I experience in my mind consistent visual, auditory and tactile mental images of an inde- pendently existing outer world. But what would I experience if I could directly know the thing or things that are causing those mental images to be generated? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= GatewayTo_Infinity { ; time=0:00:24.61-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot2 passes=t center-mag=0/0/0.862069/1/0/6.08852815419518389 params=75/75/90/90/-0.75/0.095/0/0 float=y maxiter=6000 inside=0 logmap=yes periodicity=10 colors=000HCUIDUJEUKFULGULHUMIUOJUPKUQLUSMUSNUTOUV\ PUWQUYRUZSUYTUXUUWVUVWUUXUSWURWUQWUPWUOWUNWTMWSKWS\ JWRIWQHXPGXOFXNEXMDYMEYOEZQE_RF`TFaUFcWGdXGeZGf_Gg\ aHicHjdHkfIlgImiIojJplJqmJroJspJrqJqqJpqJpqJorJnrJ\ nrJmrJlrJlsJksJjsJisJisJhtJgtJgtJftJeuJeuJduJcuJbu\ JbvKavL`vM`vN_vOZwPZwQYwRXwSVxTXwUZvV`vWbuXduYftZh\ t_js`ksamrborcqqdsqeupfwpgyohzoiynjymkxllxkmxjnwiq\ whtwgwvfzvezvdzuczubzubztazt`zt_zsZzsYzsXzrWzrVzrU\ zqTzqSzqRzpQzpQzpPzoOzoNzoMznLznKznJzmIzmHzmGzlFzl\ EzmCzlEvkFrjHmjIhiKchLZhMUgOPfPLfRNeSOdTPcVRa_S_cU\ YhVWmWUrYSwZQz_OzaMzbKzdMzeOzfQzhSziWzjYzj_zkazkcz\ kezlgzlizmkzmmzmoznqznszotzouzpvzpwzpxzqyzqzzrzzrz\ zszzrzzqzzqzzpzzpzzozznzznzzmzzlzzmzzmzzmzzmzznzzn\ zznzznzzozzozzozzozzpzzpzzpzzpzzqzzqzzqzzqzzrzzrzz\ rzzrzzszzszzszzszzszzrzzrzzrzzrzzrzzrzzrzzrzzrzzrz\ zrzzrzzrzzrzzrzzqzzqzzqzz } frm:SliceJulibrot2 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 09-01-08 (In a Hidden Valley [7])
by Jim Muth 10 Jan '08

10 Jan '08

FOTD -- January 09, 2008 (Rating 7) Fractal visionaries and enthusiasts: In keeping with the January theme, today's fractal takes us to a valley of the Mandelbrot set. It is not Seahorse Valley, but rather the inside of the east branch of the valley enclosing the large southern period-3 bud. This valley has a name, though at the moment I cannot remember the name. The image has a maxiter of 200,000, and a logmap value of minus 31,250, but thanks to the speeded-up type=mandel formula and the efficiency with which the P2000 unit handles the speeded-up for- mula, today's image calculates in just a few seconds more than a minute. Coloring today's image presented a bit of a problem. With the logmap turned off, the image was too chaotic to be useful, while with a positive logmap value, the iteration bands were squeezed too far toward the low end. The negative value works reasonably well however, though even in this case, the bands are squeezed a bit too far toward the high end. With nothing of exceptional interest in the image, I rated it at a 7. The name "In a Hidden Valley" is not only poetic but describes the location of the image. The calculation time of just over one minute on my fireball computer is quite reason- able, but could easily leap to an hour or more on an older machine. All problems may be avoided however by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Incredibly spring-like weather in midwinter continued here at Fractal Central on Tuesday as the temperature reached 70F 21C along with bright sun and gentle breezes. The fractal cats noticed the pleasant conditions, then rolled over and went back to sleep. My day was busier than expected, but nowhere near hectic. The next FOTD will be posted in 24 hours. Until then, take care, and science assumes that the physical world is real, and science works very well, so why then do philosophers keep discussing the nature of reality? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= In_a_Hidden_Valley { ; time=0:01:11.30-SF5 on P4-2000 reset=2004 type=mandel center-mag=-0.1197639246212\ 321/-0.6496272393531843/3.787523e+010/1/168.5/0 params=0/0 float=y maxiter=200000 inside=0 logmap=-31250 periodicity=10 colors=000_Yzj9MhANgAOfAPeAQdARcASbBSacz`cz_BVZBWY\ BXXBXZmz_IX`LXbOX000dUXfXXUWXhcXjfXk`XllXnoXorXpzX\ nrZmo`klbjjchgegdgebhd_jbXlaVm_SoZPqYNrXJiWFaVCTU8\ LT5Dl0yoAtrJouSkvPlvMmvJnwGowDowApx7qq4rt1rqChjT_c\ XRXZIzzUvwAmpAdlAZgBTaBTYBTVCURCUOCUKDUHDVDDVAEV6E\ V3EW4GX5HY6JZ7K_8M`9NaAPbBQcCSdKTeUVfUWgUYg_Zh_XiU\ WiUVjDUjCTkBSkARl9Pl8Om7Nr6Mv5Lz4Kz3Jz2Iv5Jr7Jm9Kh\ CKcEL_GLXJLULMSNMPQNMSNKUNPWJUXGYZDb_9ga6kb3la7l`A\ l_El_HlZKlYOlXRmXVmWYmV`mUdmUgmTkmSnmSq_`hMi_8qSFm\ TMiTSfUZcUecUkcVrcVxcVscYnc_icadcc_cfVchQcjLclGcnI\ coJcoKcpLhpNmqOrqPwrQxrRyrxzCtzDpzElzEizFezGazGZzH\ VzHRzIOzJKzJGzKDzKCzJCzIBzHBzGBzGPzaazvbzvazt`zs`z\ q_zpZznZzmWzlUzlRzlPzlMzlKzlHzdFzYDzRBzK9zDNzF_zHl\ zJyzLxzKxzKxzKxzKxzKxzKxzKwzKwzKwzKwzKwzKwzKwzKwzK\ pzHizEbzBWz8Pz5Iz2ezvcztazs`zrRzfHzW7zL8zR9zW9z`Az\ eAzjHzeNzaTzY_zTezPjzQjzO } END PARAMETER FILE=========================================

5 5

FOTD 10-01-08 (Faster Than Light [No Rating])
by Jim Muth 10 Jan '08

10 Jan '08

FOTD -- January 10, 2008 (No Rating) Fractal visionaries and enthusiasts: Today we take a brief break from the Seahorse Valley theme of January to focus on the north bud of the M-set. The fractal is actually faster than light, calculating as it does in less than 3 seconds, in fact in less time than it takes the video to switch to 600x480x256. This is obviously why I named it "faster Than Light". The image is a scene near a larger minibrot in a spiral on the southwest shore of the large period-3 north bud of the Mandel- brot set. I found it in utmost haste, and for this reason I could not give it a rating. But it's kind of something new in the conventional math range of the type=mandel formula, and worth the couple seconds required to run the included parameter file. The image may be seen by running the parameter file or by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where it is or soon will be posted. High winds up to 60mph, 90kph raked the Fractal Central area Wednesday morning, but passed over with no damage. The wind kept the fractal cats a bit skittish until it died down in the afternoon. Otherwise it was a pleasantly sunny day with a temperature of 54F 12C. My day was busy. Thankfully, the fractal is the fastest in many days. The next FOTD fractal will appear here in 24 hours. Until then, take care, and of course the world is real . . . I think . . . Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Faster_Than_Light { ; time=0:00:02.93-SF5 on P4-2000 reset=2004 type=mandel center-mag=-0.2030651182443\ 4/+0.676851836106241/7.8e+010/1/-108.5/0 params=0/0 float=y maxiter=3000 bailout=9 inside=0 logmap=671 colors=000cUZcU_cU_cU_cUZcUZcUZcV_dW`fXahYZjZXl_Un\ _Sp`QraOtaLvbIxcFycDwaEu_FsYGrWGpUHnSIlQJkPJgNLdMM\ aLNZKOVIPSHQPGRMFSIDTFGUCJV9MWHPXPSXXVX_YTb`PddMgg\ IjdEl`BoX7rT3tQ0sN1rL2qJ2pH3oF3nD4mB4l95k75j76iK6i\ MKiMZgQaeSdcUgaWjZYhW_fTZdQYbNX_KYYH`WV`UX`OXbIacC\ de6gf0gh2ei4cj6ak7_m9YnBWoCUpESrGQsHOtJMuLKvMMwNOw\ NQwNSwOUwOWwOXwPZwP`wPbwQdwQfwQgwQhrOhmNhhMhcLh_Kh\ VIhQHhLGhGFhCEiFGiIIjLKjOMkRNkUPlWRlZTmaUmdWngYnj_\ nl`qhYseVubSwZPvUNuPKtKNsFPrASq5Up7So8Qm9OjAMgCLdD\ JaEHZFFWGKTIPQJSNKVKLYIM`NOcSQfUSi_UlcTraUq`SnYQkW\ NhTMdQM`NMXLLUIKQFJMCFIAAF9BM8JT8R_7Zf7am7nfz9AzO9\ za85o8DpCKqGSrKZsOftSmuWzzUnqSooQzzPpkNpiLqgKqeIrc\ GrbFmcGhhHcmI_rJdvAiz2IzYUzPdzGezNezUez`ezfXzXPzOH\ zE9z5Ez9JzDNzHSzLXzP`zTezXjz`nzctzfozdjzcfzaaz`YzZ\ TzYPzXKzYFzY6zSAzZizFdzI_zKVzNQzPLzSGzUBzXRzeLzcGz\ aBz_OzkJzgFzdAzauzvGzWEzY } END PARAMETER FILE=========================================

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FOTD 06-01-08 (This is not a Julia Set [No Rating])
by Jim Muth 08 Jan '08

08 Jan '08

FOTD -- January 06, 2008 (No Rating) Fractal visionaries and enthusiasts: The FOTD is late today because I was volunteered for a trip to view old junk at a remote antique mall on Saturday. Today's image is a scene in Seahorse Valley. But it is not a miniature Julia set. Nor is it a miniature Mandelbrot set, nor an Elliptic set, nor a Rectangular set, nor a Parabolic set. It does come within 1-tenth of a degree of being a miniature Oblate set however. (There are six independent kinds of sets in the Julibrot because in four-dimensional space there are six mutu- ally perpendicular planes through a single point.) Also, the Seahorse Valley in which today's image lies is not the main one of the M-set. It is the Seahorse Valley of the large minibrot at -1.75 on the negative X-axis of the M-set. An Oblate set is a slice through the four-dimensional Z^2+C Julibrot figure in the plane determined by the imag(c) and real(z) axes. The miniatures in Oblate sets can be shaped like anything but miniature Mandelbrot sets. They often take the form of Julia sets, but just as often do entirely their own thing, making figures that could never be found in a Julia set or the classic Mandelbrot set, (though I have seen Oblate-type miniatures in perturbed Mandelbrot sets). To visualize the location of today's image, start at the point at -1.768... of the M-set as being centered on the screen. This is the point where the two branches of Seahorse Valley meet. Then imagine the entire 4-D Julibrot in which the valley lies as being rotated so that the real(z) axis is perpendicular to the screen. The object in today's image then lies about 6 inches behind the point on the screen and is being viewed from the left. The object in question is not artistically very attractive, but it does show that Seahorse Valley, the FOTD theme for January, has more potential than can even be imagined. I gave the image no rating, though I did name it "This is not a Julia Set", a fact that is immediately apparent. The calculation time of 36 seconds is brief enough to inconven- ience no one. And as always, those who would rather download than render may do so at the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the completed image is or soon will be posted. Milder temperatures arrived here at Fractal Central on Saturday, but so did clouds, and in the evening, rain. The fractal cats made the best of conditionss by sleeping most of the day, while FL and I spent most of the day down in Dillsburg. The next FOTD will appear in 8 hours. Until then, take care and stay with it. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= ThisIsNotAJuliaSet { ; time=0:00:36.44-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot2 passes=1 center-mag=-0.00210532115066575/+0.525784551738717\ 90/121.4231/2.0567/90/3.88578058618804789e-016 params=0.1/90/0/90/-1.76852957968/0/0/0 float=y maxiter=10000 inside=0 logmap=11 periodicity=10 colors=000JGCHDBGB9E98D77G89I9BKADNBFPCHRDJUELWFNY\ FO_IN`LNbONcRNeUNfXMh_MibMkeMlhMojKmkMlkOklQjlRilT\ hmVfmXenYdn_cnacobcodcpfcphcpicqkcrmcspctncsmcslcr\ kcqjcoicmhckgcifcgecedccccbccacc`bc_acZ`cY_cXYaWW`\ WX_WXZVXYUXXTXWSXVRXVQXUPWTOVSNURNTQMSPKROIQOGPNGP\ MFOLFNKFMJFLIFKLFKNFKPFMRFOSEPUDQWCRYASZ8T`6Ub4Vd2\ We0Xb3Y`5ZZ7_X9`UBaSDbQFcOHdLKeJMfHOgFQhCSiAUj8Wk6\ Yl1Tl4_m6em9lmBrmGpjLohQnfPhpSkjVmdYoZ`qTcsOdpRdnT\ dlVdiXdgZde`dcbd`cdZcdXcdUcdScdQcdOcdLcdJcdHcdFcfG\ cgHciIcjKclLbmN_oNWqPSsQNuSJwUFyVBzY5zW6yV7xU8wS8v\ Q9uNAtLBsJBrICqHDpGDoEEnDFmCGlBGkAHj8Ii7Jh6Jg5Kf4L\ e4Hd3Kc3Kb3Ka3K`3K_3KZ2KY2KX2KW2KV2KU0KT2KV4KX6KZ8\ K_AKaCKcEKeGKfIKhKKjMKlOKmQKoSKqUKrUKrUKrUKrUKrUKo\ TKmRKjOKhMJeKIcIE`GAZE7MPQ6Yi9_gB`fEaeGbdJdbLeaOf`\ Hb_Me_Qg_Ui_Zk_bm_fo_ltajq_hoZgmXejWchUbfT`dSZaQY_\ PWYNVWMTTLRRJQPIOMGMKFLIE } frm:SliceJulibrot2 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 08-01-08 (The Center of it All [8])
by Jim Muth 07 Jan '08

07 Jan '08

FOTD -- January 08, 2008 (Rating 8) Fractal visionaries and enthusiasts: Today's agonizingly slow fractal is a dive down to the minibrot lurking invisibly at the center of yesterday's image. Today's image might or might not be worth the effort of calculating it, but it is certainly worth the effort of visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the image is posted already rendered for hedonistic instant gratification. The rating of an 8 might have been an 8-1/2 if I had given a little more attention to the colors instead of enjoying the good weather. The name "The Center of it All" needs no explanation. The slowness of the image is due to its extreme magnitude, which requires the much slower arbitrary precision math, and also the fact that the single-pass method must be used to avoid missing a good part of the fine details surrounding the circular central mass of color. ---------------------------------------------------------------- A record-setting temperature of 68F 20C accompanied by full sun made Monday a day to be remembered here at Fractal Central. The fractal cats must have agreed, for they forsook their heat sources and spent the day by the window, which was open for the first time in months to save fuel by letting the warm air inside. My day was notably lazy. The next FOTD is due in 24 hours, and with any luck at all it will appear on schedule. Until then, take care, and how long must we wait before the much-ballyhooed theory of (almost) everything is finally ready for consumption by the eager public? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= TheCenterOf_It_All { ; time=2:01:55.29-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=0.321914508767132354909185/-0.035213130\ 684051331828963/2.098351e+019/1/80/1.4033219031261\ 9787e-013 params=0/0 float=y maxiter=32767 inside=0 logmap=5693 periodicity=10 colors=000G6JISHB_ClwQkpWkiajbgjWmkXokXpkXrkYskYuk\ YvkYwfUubQtE6NIBRLFUOKYSO`VTdYXgSYdNZaHZ_C_X6`U1`S\ 9aNGbIScEafOkiXtkeynnzpwxmvtjvkgvgdvZbvY`pTZjTXdOV\ _OTUOROOPIONDPPEQRFRSFSUGTWHUXHVZIV_IUcPTfWSjbRmiQ\ poTlkWhgYdc``_bXX`RW_MWZHWXBVW6VV1VT9WSGXQNYPVZNa_\ Mh`LoaPmdSlgWkjZjlbhoegrifulewk`skWpjRljNiiIfiDbh8\ _h4Xe4Wb4VRTIGq6HnHIlSIjbJhmJfxLbqNZjOVdQRYRNSZkZ7\ _RWYfsWuS76LF4FM38T22_1KOBaCLr0Uj7YcEaXKePRhIXlBcp\ 4is9cjEYbJSVOMNSHFOMGLRHIWHF`ICeJ9jJ8iL7iM6iN6mOD`\ LKTIRKFYCCw4AfCIiJQlQXoXdrclujsir1dj6`bBWVGSNKJJlH\ GkGEjFCiE9hD7gC5fB3eJBcQIaZR_fZYogWztU_SU000oQz4A0\ 6IU8JZAOmCXzEezFkzEXWDSAxhl`XUEMCHTKJ_SMf_OmfUkY_i\ Pzgareejefjeceec_eFXeHUeJReKV2DAoBEfLHZVLRcOJmRBvU\ InXOf_U_b`SefKglD`kMVkUPjaJjiGzgEzfCzdAzc8zb9ze9zg\ AziAzkAzmBzoBzqBzsezr_zoUzlPzjJzgEze8zb3z`CzbKzcTz\ d`zfizgqzhozamzWkzQizKPzN } END PARAMETER FILE=========================================

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FOTD 06-01-08 (The Center of it All [8])
by Jim Muth 07 Jan '08

07 Jan '08

FOTD -- January 08, 2008 (Rating 8) Fractal visionaries and enthusiasts: Today's agonizingly slow fractal is a dive down to the minibrot lurking invisibly at the center of yesterday's image. Today's image might or might not be worth the effort of calculating it, but it is certainly worth the effort of visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the image is posted already rendered for hedonistic instant gratification. The rating of an 8 might have been an 8-1/2 if I had given a little more attention to the colors instead of enjoying the good weather. The name "The Center of it All" needs no explanation. The slowness of the image is due to its extreme magnitude, which requires the much slower arbitrary precision math, and also the fact that the single-pass method must be used to avoid missing a good part of the fine details surrounding the circular central mass of color. ---------------------------------------------------------------- A record-setting temperature of 68F 20C accompanied by full sun made Monday a day to be remembered here at Fractal Central. The fractal cats must have agreed, for they forsook their heat sources and spent the day by the window, which was open for the first time in months to save fuel by letting the warm air inside. My day was notably lazy. The next FOTD is due in 24 hours, and with any luck at all it will appear on schedule. Until then, take care, and how long must we wait before the much-ballyhooed theory of (almost) everything is finally ready for consumption by the eager public? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= TheCenterOf_It_All { ; time=2:01:55.29-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=0.321914508767132354909185/-0.035213130\ 684051331828963/2.098351e+019/1/80/1.4033219031261\ 9787e-013 params=0/0 float=y maxiter=32767 inside=0 logmap=5693 periodicity=10 colors=000G6JISHB_ClwQkpWkiajbgjWmkXokXpkXrkYskYuk\ YvkYwfUubQtE6NIBRLFUOKYSO`VTdYXgSYdNZaHZ_C_X6`U1`S\ 9aNGbIScEafOkiXtkeynnzpwxmvtjvkgvgdvZbvY`pTZjTXdOV\ _OTUOROOPIONDPPEQRFRSFSUGTWHUXHVZIV_IUcPTfWSjbRmiQ\ poTlkWhgYdc``_bXX`RW_MWZHWXBVW6VV1VT9WSGXQNYPVZNa_\ Mh`LoaPmdSlgWkjZjlbhoegrifulewk`skWpjRljNiiIfiDbh8\ _h4Xe4Wb4VRTIGq6HnHIlSIjbJhmJfxLbqNZjOVdQRYRNSZkZ7\ _RWYfsWuS76LF4FM38T22_1KOBaCLr0Uj7YcEaXKePRhIXlBcp\ 4is9cjEYbJSVOMNSHFOMGLRHIWHF`ICeJ9jJ8iL7iM6iN6mOD`\ LKTIRKFYCCw4AfCIiJQlQXoXdrclujsir1dj6`bBWVGSNKJJlH\ GkGEjFCiE9hD7gC5fB3eJBcQIaZR_fZYogWztU_SU000oQz4A0\ 6IU8JZAOmCXzEezFkzEXWDSAxhl`XUEMCHTKJ_SMf_OmfUkY_i\ Pzgareejefjeceec_eFXeHUeJReKV2DAoBEfLHZVLRcOJmRBvU\ InXOf_U_b`SefKglD`kMVkUPjaJjiGzgEzfCzdAzc8zb9ze9zg\ AziAzkAzmBzoBzqBzsezr_zoUzlPzjJzgEze8zb3z`CzbKzcTz\ d`zfizgqzhozamzWkzQizKPzN } END PARAMETER FILE=========================================

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FOTD 07-01-08 (Web of Iterations [6.5])
by Jim Muth 07 Jan '08

07 Jan '08

FOTD -- January 07, 2008 (Rating 6.5) Fractal visionaries and enthusiasts: Today's discussion will be as brief as the calculation time of the image is long. The image is located in the Seahorse Valley of a minibrot lying in the star of the period-11 bud on the southern shore of East Valley of the Mandelbrot set. With nothing better to do, I named the image "Web of Iterations" and rated it at a 6, with an extra half point added for my coloring. The image's calculation time of over 46 minutes makes the trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> by far the better choice. Sunday turned cloudy here at Fractal Central, but a temperature of 50F 10C and dry weather made it pleasant despite the clouds. The local fractal cats enjoyed the pleasant weather from the comfort of their window shelf, while I enjoyed it from outdoors. The next FOTD will be posted on schedule in 24 hours. Until then, take care, and ponder deeply. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Web_of_Iterations { ; time=0:46:24.11-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=0.3219145087671323544/-0.03521313068405\ 13645/2.315541e+014/1/30/0 params=0/0 float=y maxiter=7500 inside=0 logmap=2180 periodicity=10 colors=000G6JPdFLbGH_GDYH9VH2UG6TH9SICRJFQKIPLLOMP\ NNSMOVLPYKQ`JRlHJcIRVJZMKfAacDKmA0zG3vL5sQ7pW9m`Ci\ eEfkGcpI`uKYtNVsPTrRRqUPpWNpYLo_JnbHmdFlfDjf7lhBmi\ EnjIplLqmPrnStpWuqZvrasn`pk`mh`je`gb`dZ`aW`ZT`WQ`T\ N`WFeQK`KOWFTS9XN4`J6WT7Sa8Oj9KsAKrBKqBKqCKpCKpDKo\ CIpDKoDMoEOoEQoFSoFUoGWoGYoH_oD`qHaoLanPamSalWak_b\ jbbifbhjbgji`mbfpWkrPpqOiqNbqNWpMPpLIpLCnMBlNBjOAh\ PAfQAdR9bR9`S8ZT8XU8YV7ZW7_W5`W7aY8c_9e`AgbBidCkeD\ mgEoiFqkGslHunIwpJytHpqKhoN`lQTjTLgWBgWDeYEdZFc_Hb\ `IaaJgbKmcMmeNmfOmgPmhRmiShiTciUZiVUgVKeVAcV0bV0aW\ 0aW0aW0cW0cZ0aa0Zd0Wf0Td0QX0NX0KbOczebzKwzvbzkgYak\ QSoIIsJLpKNnLPlLSjMUgNWeNYcO`aPb_QdXQgVRnTStRSzPEk\ mIenL`cOWURRKUMKXHK_CK_5Ub7cn9mhAqoCozEmtEmzXlmGlz\ YkzRkcJk`wjYLjVMjSciOOiLmiImhFRh5NkCRhJUeQXbX_`cbY\ jeVqhSyjRwzQuzPszzqzzozzmzzzzzzzzzzzzzzzzzbsz`tzZu\ zYuzWszVqITpLSnOQmRXiETgF } END PARAMETER FILE=========================================

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FOTD for Jan. 07, 2008
by JimMuth＠aol.com 07 Jan '08

07 Jan '08

1 0

FOTD 05-01-08 (Simply Too Much [No Rating])
by Jim Muth 05 Jan '08

05 Jan '08

FOTD -- January 05, 2008 (No Rating) Fractal visionaries and enthusiasts: Today's image has a plethora of goodies. It has too much of everything -- too much detail, too many colors, too many themes, and it takes too much time to calculate. With all this stuff to consider, I could not decide on an honest rating. I finally let it go un-rated. The name "Simply Too Much" tells it all. The image is actually a scene in the Seahorse Valley of a mini- brot deep in an elephant trunk in East Valley of the Mandelbrot set. The elephant stuff in the image is quite obvious, though it takes a bit longer to spot the seahorse stuff. The image gave me quite a fight as I tried to color it. I tried nearly every option at thumbnail size before deciding on a straight palette. The calculation time of 38-1/4 minutes is far too slow for an unrated image. Try viewing it instead on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Friday turned warmer here at Fractal Central, but a high temperature of freezing is hardly balmy. And when the sun vanished behind clouds in the afternoon and a wind sprang up from the east, it felt every bit as cold as Thursday. The fractal cats passed the day lounging by the heat. My day was rather busy, which left too little time for the fractal. Tomorrow promises to be slow, so the fractal will likely be better. Until then, take care, and if common sense tells you it's true, common sense might be leading you astray. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Simply_Too_Much { ; time=0:38:15.01-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=0.3439483463116016330630741/-0.05608209\ 31295550270018991/4.983e+019/1/-142.5/3.8857805861\ 8804789e-016 params=0/0 float=y maxiter=5000 bailout=6 inside=255 periodicity=10 colors=000zCWzESzFPzHMzIJzIGzIDzJGzKIzLKvMMsNOpOQl\ PSiQVfRXbSZ_T`XUbTVdQWfMbbN_eNXhNUjNRmNPpNMrNJuNGx\ JBzNEzQGzTIyWKyZNxaPxdRwgTwjWvmYvp_utbvsausatr`sr`\ rq_qq_pq_ppZopZnoYmoYlnXknXloXmqXosXquXswXuyXwzWyv\ _xocvhguaksWorTqoQsmOtkLviIxfGydDzbBz`IybOvdUse_pg\ emikjjqglwemvfhufctgZsgUyc7weEufKsgQqiWojamkgklmRz\ zPzzOzzNzzMzzLzyKzxIyxHxwGxvFwvEvuDutByzCwwCutDrqD\ onElkEihFfeFccGa`G_YHZVHYSIWPIUMJSJIQ5JNBJKHKFMKAS\ LAYLAbMAhzzzzzzzzyzzxzxwzuvzrwzoxzlyzjzzgzzdzzazzZ\ zxWvvVruUrwUtyUxwXzvZyu`wtbtsdrqgopimokjnmhmoekrcj\ t`ivZhxWhyRgzUgxXfvZfsaepdemfejicgladn_aoYZpWWrUTt\ SQvRMxGIzHDvHEqIFmJGiJHdKF`LDXLASMAOHANJAMLALMAKOA\ JQFIRIIUHHXGG_FFbEEeDDhC6eD9bDB_DDXDFUDHTDJQDMNDOL\ DQIDSFDURBRVBUABVDDWFEWIGWKHWNIWPKWSLWUNXXOXZPXaRX\ cZXfhXhrXzzOtrTjhX`ZaPVkRIhSLeTPbUS_VWXWZUXbRYeOZi\ L_lI`oFVi7UbmaZghUbpQXxLR } END PARAMETER FILE=========================================

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FOTD 04-01-08 (Watered Elephants [7])
by Jim Muth 03 Jan '08

03 Jan '08

FOTD -- January 04, 2008 (Rating 7) Fractal visionaries and enthusiasts: A visionary is one who concerns himself with imaginary things; imaginary things exist only as images in the mind, and are there- fore not real. A fractal visionary is one who concerns himself with fractals. Since fractals are imaginary things, they are not real. Only the seriously disturbed confuse imaginary things with real things, therefore one who concerns himself with fractals is out of touch with reality, and in need of help. But it sure is a lot of fun living in a world where the unreal can become real at the touch of a computer button. There must be different kinds of reality surrounding us. Now as for Santa Claus . . . Today's fractal might or might not be real, but regardless, it rates an honorable 7. It is a scene near the same minibrot that held yesterday's image. But today, instead of checking the mini- brot's Seahorse Valley, we check its East Valley. What we find there is a typical East Valley scene filled with Seahorse Valley elements. I'm sorry pachyderm fans, but I could find no obvious elephants in the image. I guess they all sank in the seahorse water. For this reason I named the image "Watered Elephants". Being in the same area of the M-set as yesterday's image, today's image is nearly as fast. But why bother with the calculation speed? It's just as simple and nearly as fast to view the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Lots of sun but frigid temperatures around 19F -7C prevailed here at Fractal Central on Thursday. The fractal cats hugged the heat most of the day, while I waited for the first work of the new year to come in. The next FOTD will appear seemingly from nowhere in 24 hours, and return to nothingness as soon as the computer is shut off. Until then, take care, and are frac- tals animal, vegetable, or mineral? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Watered_Elephants { ; time=0:00:19.53-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-0.7418\ 527152462948/+0.143746626232636/9.536791e+012/1/\ -35.5/0 params=0/0 float=y maxiter=6400 bailout=36 inside=0 logmap=-1300 mathtolerance=0.05/1 colors=000HEKPbgO`hO_iOZiP`iQaiRbiSdiVeiciimmzvrzz\ yzzzzzzzzzzzvvzrmzmezhd9zY8zUBzVDzWFzXHzYJzZLz_Nw`\ PraRwbTwcVwdXwdVrbUmaTh_ScZQZXPUWOPUNKTLFSKAQJAPIA\ NGAMFAKEAJDAIJFGOJFTNEZRDcVBhZAnb9sf8xj7xeAz`CvVEr\ RHrMJpHLoDNkEMhFLdGKaHJ_HIXHHUGGRGFOFEMEDJDCGEBDGA\ BM9FQCJWEMaGQfJUkLXoN_kOagOdcOf_OhWOkSPmOPpKPrGPtD\ PnPLi_HdjD_uATiMNZYHOiBDtAMlASdAQYARQARJBWICRICRID\ RIDWIEWIEVIFZIFZIGZIGZIHZIH_IJZHLZGNZFPYFRWESVDUTC\ WSCYRB_PA`O9bM9dL8fJ7hI6iH6lKCnMIpONrQTtSZvUcxWizY\ nZRM`TOaUQbVRcWTdXVeYWfZYg__h``iabjbdkceldgmehdcgX\ afO_eGYeJWcMVaPT_SSYVRXXSWYTW_TV`UVaVVcVUdWUeXUgXT\ hYTiYTgaWedZch`akc_oeYrhWujYph_kfafdbabdX`fSZhNXiI\ WmCPq6JfIHXUFMeDCpBGkEKfHOaKSYNWTQ_OTcJWfFZ6kJCbTH\ VbMNlRFuaQmk`eujZp_RkQJgGChFHhEMhDQiCViB_iBceJYaQT\ Kfg3vvBsrJpoRmlYjiegfmdcta`7DrCGmHIhMKcRMZWOU`QPeS\ LkXXq`gvdrXOH_NObNUDQfBYa } END PARAMETER FILE=========================================

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FOTD 03-01-08 (Diamond Seahorse [8.5])
by Jim Muth 03 Jan '08

03 Jan '08

FOTD -- January 03, 2008 (Rating 8.5) Fractal visionaries and enthusiasts: In today's image we view Seahorse Valley from the Mandelbrot ori- entation, and check the Seahorse Valley of a minibrot that lies deep in the parent Seahorse Valley. The result is a very attrac- tive fractal with double seahorse features, which lies right at the limit of conventional math, making the mathtolerance entry necessary. The name I gave the image, "Diamond Seahorse", fully explains itself. The rating of an 8-1/2 credits me with 1/2 point for the coloring. The colors are good because things are slow around F.C. today, and it's always easier to create good colors when there is extra time to work on them. The calculation time of 5-1/2 seconds is no mistake. This is how fast the P4-2000mhz machine runs the speeded-up type=mandel formula. Today's image is one of the few FOTD images that calculates in less time than it takes to stop at the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view the finished image there. But the calculation time does not include the time required to set up the parameter file for calculation, so in the end, it is still both faster and simpler to visit the web site. Wednesday was sunny but cold here at Fractal Central, with an afternoon temperature of 26F -3C and a biting wind from the northwest. The fractal cats put their noses to the window, then decided it was best to stretch out on their broad warm shelf over the radiator. My day was slow, which permitted the extra work on the colors of today's FOTD. The next fractal in the near-endless series will be posted in 24 hours. Until then, take care, and where do we go from here? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Diamond_Seahorse { ; time=0:00:05.34-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-0.7418\ 546457524966/+0.143748516797246/6.5e+012/1/-7/0 params=0/0 float=y maxiter=6500 bailout=36 inside=1 logmap=1580 periodicity=10 mathtolerance=0.05/1 colors=000hendbi`_eXYaUVYQSTMQPINLFKHBIC7F83C40A05\ 93A95F97K99P8CU8EZ8Gb8IcBJdDKeFLeHLfJMgLNgNOhPOiRP\ iTQjVRkXRkZSl`TmbUmdUneXofZpgaphcqifrihsjkskmtlpum\ rvnuvnwsmuqlsokrmjpjinhhmfgkdfibeh_dfYcdWbcUaaSa`Q\ bZOcYMdWLdVJeTHfSFgQEgPChNAiMAiL9hLCeJFbII_GKWFNTE\ QQCSNBVJAYG8`D7b96e64h33j02i17i2Ch3Hh4Lg5Qg6Vf7_f8\ ce9heAmdBrdBveArfAogAkh9hi9ej9ak8Zl8Vm8Sn7Po7Lp7Iz\ 5Hq7Fi9DaBBTD9LF73C7DH6NM6WR5eW5n`5oWDoRLoMToH`oCh\ o7pnBmnFknJinNgmQdmUbmY`maZldWlhUllSlpQkxLlsOloRlk\ TlgWlcZrZ`vVdzRgzNjzJouFrmDrhCr`BrXArT9rQ8rM6rI5mE\ 4hA3c62Z31U53P74K95FB6AD7AE9AGAAIBAKCAMDFKFHKEJKDK\ LCLMBMNANO9OP8PQ7QR6RS5SU4TW5NY6Ic7Cg77jB6gF6cJ5`M\ 5XQ4UU4cY4m`3zd3zh2vl6roAmpFmpKmqPhqUjrZcrchrhmsmr\ srvtvzwzzzzvzzszzozzlzzizzevzawzZvzWuzTtzQszNrzJqz\ KpzLozMnzNmzNmzOmzPmzQmzQmzVwzZwzcwzgwz_wzTwzXmz`m\ zdmzhmzlmzpmztmzxmzwmzvmz } END PARAMETER FILE=========================================

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