October 2006 - Fractint - mailman.xmission.com

Re: 4D stuff
by jackoftradez＠comcast.net 06 Oct '06

06 Oct '06

""A bit rushed at the moment, I'll post some pars later. "" Hey Russ - post the complete pars for these things, like the revolution solid on your site. So I can render and tweak and maybe animate ....

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Re: whatever
by jackoftradez＠comcast.net 06 Oct '06

06 Oct '06

""I am so far behind the times that I consider the movies made in the 30's 40's and 50's to be better than most of the current day movies, which to me seem to be created for desensitized viewers with the intelligence of a flea and the attention span of a mosquito, and appear to be rated by the number of explosions and the computerized effects they con- tain. "" You and me both! Most of my (huge) DVD collection is sci-fi / horror classics from 60's -> early 90's. I just ordered a bunch of classic "B" movies from amazon - they're on DVD now! I never knew that.....

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Neo T-set
by Russell Walsmith 06 Oct '06

06 Oct '06

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FOTD 05-10-06 (Evaporated Fractal [7])
by Jim Muth 05 Oct '06

05 Oct '06

FOTD -- October 05, 2006 (Rating 7) Fractal visionaries and enthusiasts: Today's image is titled "Evaporated Fractal". An evaporated fractal is just that -- evaporated. Fractals will evaporate when all the exponents of Z in their formula are negative and the escape radius is raised to an extreme value such as the 10^100 of today's image. When fractals evaporate, their 'outside' parts shrink and eventually disappear completely, leaving a blank screen composed totally of 'inside' stuff. But certain inside fills such as the 'bof61' that I used in today's image can bring out the ghost of the fractal that has evaporated. Today's image is such a ghost. To see the un-evaporated version of the image, change the imag(p3) parameter to zero. The result is not quite as interesting as the evaporated version, but it is still worth a look. None of the other inside fills do much with this particular image. I rated today's image at a 7. I like something about the coloring more than would seem apparent at first glance. The render time of 1-3/4 minutes will pass almost instantly. If this does not happen, go to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view the image there. Gray morning fog led to midday sun here at New Fractal Central on Wednesday. The temperature reached 79F 26C. A very strong thunder-storm moved in at 5pm, turning day to night, but the fractal cats were more interested in the mouse hole than the outside weather -- that is until I plugged the hole, when they turned to me with a look of disappointment on their faces and went on to other diversions. Of course, plugging one hole will never keep the mice out. I am counting on the mouse that barely escaped warning the others about the dangerous cat situation. My day went as good as could be expected. And the fractal was not all that bad either. The next fractal will appear in 24 hours. Until then, take care, and ponder the imponderable. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Evaporated_Fractal { ; time=0:01:48.64--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip center-mag=+3.866706650767/+2.322479224495/12100.8\ 1/1/-20/3.62e-008 params=1/-1.5/0.333/-4.5/0/1e+100 float=y maxiter=2500 inside=bof61 periodicity=10 colors=000gVKiYMk_OmaQldRkgSjjSjlTioThrUhtUbsLYsD`\ mIcgNfaSiWXlQaoKfqFks9qu4wsAprFjpKdoQYmVSl_Mwmfxac\ yR`zFYz4WnYIbz5Wr6Pk6Ic6BX6GT8LP9F0AK0BUDD_9Ec5Fk1\ GjCKrMNjWQjeTjhWzm_zvzzzgzzzzzeOvdQpdOm_MjVKgQIeMG\ _JEUHCOEAIC8C9777E9IKBTRDcXFno7Rn6Vn5Ym4am3dk2aj2_\ h2Yg1Ve1Td1Rc1Pb3Vb5_a7ea9j`Bp`DudFrhGpkHnoJksKivL\ gtQerVcp_aod`jmVfuQfrPfpPfmPfkPfhPffPfdPjg_njjqlto\ mqmnoknliojgpgepecqbaq`elahhakdan_bqWbtSbwObrTemXg\ iaidek_inWnpRrrNvtel8bnC`oGZqJXrNVsRTuURvYPw`i4Il6\ Mn7Pp8Sr9VtAYvB`xCczDfrVZkkRnnOppMssKuuIcj_N`pMYmL\ VjKSgJPeIMbHJ_HGYBDMXMU5UC6QG6NJ6KM6HQ6ET6BW68ZG7_\ Q7__6`i6`r6`f5hV4pTGlSRiQafPlcOw`Pp_QjZRdZRZYSSXTM\ XUGWUAWWC`XEdYGiZIm_Kr`LveOpiQkmSfqV`uXWyZRu`OqbLm\ cIieFefCah9Yi6VgATeDRcGPaJM_NKYQIWTC6RGDYKJdNPkRVr\ U`y96WVWRotMimPdfR__TVTVPMXKFZF8`A1b92i83p73vC8sGD\ qLInPMlTRiYWga`dedbaf_000 } 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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Delicate lace pattern -- a zoom in Jim Muth's Oct 4, '06 FotD
by Hal Lane 05 Oct '06

05 Oct '06

########################################################## Here is a zoom and pan in Jim Muth's Oct 4,'06 FotD that creates a delicate lace pattern. Interestingly, one additional zoom is not supported by the floating point precision in my Intel chip. A muddy erratic image results. If you zoom out a few times from Jim's original image all you see is empty space. But I reached up to brush a speck of dust off my monitor and discovered that it was a lit pixel. When I zoomed on the pixel it went away. However, that was due to the solid guessing (g) method of rendering being used. (Solid guessing rendering appears to be the default value for the first entry on Fractint's 'X' page of modifiable parameters. I changed the 'g' to a '1' to get single pass rendering -- a method of rendering that won't drop pixels like solid guessing can.) When I changed to single pass rendering I was able to zoom and still see the pixel. That single pixel when zoomed in on expanded to this image. If the resolution you choose is too low, many points that make up the lace can be lost. 1024 x 768 works well. The lace pattern in my parameter file is not framed exactly the same way as my original .gif image is. No matter how many times I reload the original image and create its parameter file, the size of the parm file generated image seems to be about 10-15% smaller than my original .gif image. Anyone have any ideas about what's going on??? <---<< - Hal Lane ######################### # hallane(a)earthlink.net # ######################### START PARAMETER FILE======================================= Lace_C { ; Hal Lane Oct 04,'06 5:06 P400 1024x768 ; Zoom and pan in Jim Muth's Oct 4,'06 ; FotD. If you zoom once more floating ; point precision is lost. Nice lace. ; If the resolution you choose is too ; low, many points that make up the lace ; can be lost. 1024 x 768 works well. reset=2004 type=formula formulafile=_pastarc.frm formulaname=mandelbrotmix4 function=recip passes=1 center-mag=+3.49473090804890900/+1.14324392815559900/2.\ 360511e+012/0.9997/130.041983675011238/-0.0172431643752\ 262304 params=1/-1.5/0.333/-4.5/0/0 float=y maxiter=1000 inside=0 logmap=79 periodicity=10 sound=off colors=0000A0<3>0C9<2>AEFDFHHHJ<3>UPRXRT`TVcVYfX_iZa<3>\ mhiojkpmmroprrsttvuuzwuzxuzzuzzuzzuzxqzvnwukrshm<3>p_Up\ YQoWN<3>lOClMAhLD<3>UIPRHSNGVKGXdUfygpp0mgQo_oq<3>JkmFj\ lIdn<3>UItceI<3>MBJI4JJ8I<8>MaHNeGNhG<3>OuG<8>knhmmkpln\ <3>zjz<4>jVegRadOY<3>TCIYqm<2>KEE1kE9O8d0xlK8<2>O53pRec\ ISS9FnW0_cBQK6grAgrxIQ1<2>G72tD`_7JxZb1Ik6CWB6HGUD<2>G8\ 4gRZYIOP9DQFz<2>I4H4f_EYy<2>G9H_GX<2>L49n0xtldfXSTHFk9c\ W5L5uR9bIDKAA4mf0P<2>M07wVh<2>R8C5cz9ReDEMCib21h71UC1Gg\ 9KBjV7oV3sVOSdh0n<2>cFR<3>KIXFJZAJ_5Ka1KbUVNvd8<3>Q5SI0\ XU0Ve2T<3>m4qo4wxTrP0`K1JkaU<2>OA9PoEMZAJI65OOBCD80mB0Y\ E0IjQIVDA_nZQQI9GQCBIE6AB_VDOLFCBM0TK0MR6OO7L000 } 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======================================== ########################################################## -- No virus found in this outgoing message. Checked by AVG Free Edition. Version: 7.1.407 / Virus Database: 268.12.12/462 - Release Date: 10/3/06

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FOTD 04-10-06 (Dark Shadows [Not Rated])
by Jim Muth 04 Oct '06

04 Oct '06

FOTD -- October 04, 2006 (Not Rated) Fractal visionaries and enthusiasts: Today's image is named "Dark Shadows". This is no tribute to the old TV series that ended over 30 years ago. It describes my dark mood. When bad things happen to good people, it gets me mad. I start wondering why. Like most people, I do not like meaninglessness. And like quite a few others, I am becoming ever more disappointed with a material-based science that is helpless in the face of the big questions of life. At the same time, I am not so naive as to wonder why a God who is all-good etc. permits the bad things to happen. But I do wonder how it was possible for the human mind to evolve such an instinctive need for meaning if behind all the physical glitter there is nothing but a meaningless random accident. In recognition of my dark mood I have created a fractal that is almost entirely darkness. It resembles little more than a dew- sprinkled spider web glistening in the pre-dawn gloom, illumined by the rays of a distant street light. The image was created by combining Z^(-1.5) with Z^(-4.5) and adding (1/C). The somber color palette is an intentional creation. Since I intentionally made the image so gloomy, I gave it no rating. One bit of good news is that the render time of 1-1/2 minutes will try the patience of no one. And the task of rendering may be avoided entirely by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A temperature of 79F 26C and partly cloudy skies went unappreci- ated by the fractal cats, who, because the mouse failed to reappear, joined me in sulking. The evening treat of cheese and tuna only partly eased their disappointment. Except for the bad news on the TV, my day was fairly routine. If all goes well and tomorrow is a repeat, the next FOTD will appear in 24 hours. Until then, take care, and don't be a gloomster. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Dark_Shadows { ; time=0:01:36.12--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip center-mag=+3.494730910064264/+1.143243928066017/\ 7.666195e+011/1/120/0 params=1/-1.5/0.333/-4.5/0/0 float=y maxiter=1000 inside=0 logmap=79 periodicity=10 mathtolerance=0.05/1 colors=0000A00B20B40C70C93DB7DDAEFDFHHHJKJLNLNRNPU\ PRXRT`TVcVYfX_iZaj`ckcelegmhiojkpmmroprrsttvuuzwuz\ xuzzuzzuzzuzxqzvnwukrshmrehrccqaZp_UpYQoWNnUKnSImQ\ FlOClMAhLDdKGaJJYJMUIPRHSNGVKGXdUfygpp0mgQo_oqVnpR\ moNlnJkmFjlIdnLZpOTqRNsUItceIZYJVQJQJJMBJI4JJ8IJBI\ KFIKIIKLILPHLSHLVHMZHMaHNeGNhGNkGOoGOrGOuGRtKUsNWr\ QZrT`qWcpZfoahoeknhmmkplnslquktxjwzjzvfuscqp`mmYij\ VegRadOYaLUZIQWFMTCIYqmTcaPRQKEE1kE9O8d0xlK8cF6WA5\ O53pRecISS9FnW0_cBQK6grAgrxIQ1HJ2HD2G72tD`_7JxZb1I\ k6CWB6HGUDGMAGF7G84gRZYIOP9DQFzNBjL8WI4H4f_EYyFPjF\ HWG9H_GXVCPQ8HL49n0xtldfXSTHFk9cW5L5uR9bIDKAA4mf0P\ _0JT0DM07wVhlNYaGNR8C5cz9ReDEMCib21h71UC1Gg9KBjV7o\ V3sVOSdh0nf5fdAZcFRZGTUHUPHWKIXFJZAJ_5Ka1KbUVNvd8m\ WDeNIYENQ5SI0XU0Ve2Tg3_i3ek4km4qo4wxTrP0`K1JkaUcSN\ WJGOA9PoEMZAJI65OOBCD80mB0YE0IjQIVDA_nZQQI9GQCBIE6\ AB_VDOLFCBM0TK0MR6OO7L000 } 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 03-10-06 (Minibrot in Bloom [5])
by Jim Muth 03 Oct '06

03 Oct '06

FOTD -- October 03, 2006 (Rating 5) Fractal visionaries and enthusiasts: Yes, I know that today's FOTD is late. As often happens in my convenience-type business, an unexpected job came in on Monday morning, which the customer needed the same evening. The job was small, and was indeed finished by evening, but this left little time for fractals. Despite the rush I did find one fractal with a bit of interest. It appears as today's FOTD. The image is a scene with a mini- brot, in the parent fractal that results when negative portions of Z^(-1.6) and Z^(-4.7) are combined and (1/C) is added. I often use reciprocal C with fractals that contain negative exponents of Z. Such negative fractals are often inside-out. Reciprocal C turns these fractals inside-out again, which makes them rightside-out and easier to examine. I enhanced today's image by calculating it with the 'outside' set to 'tdis', but it is impossible to make much of little, so with little to start with, I could rate the result no greater than an average 5. I named the image "Minibrot in Bloom" for no particular reason. It is only fair that a merely average image be a fast one, and with its render time of only 3 minutes, today's image is fast enough. The only faster way of viewing the less-than-glorious scene is to take a virtual trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and to download the completed image from there. A morning with drifting patches of fog gave way to a sunny warm afternoon with a temperature of 70F 21C here at New Fractal Central on Monday. The fractal cats glanced out the window a few times, but spent most of the day waiting by the hole for the mouse to come out and play. They must play too rough, for the mouse never appeared. Their disappointment was eased in the evening by a generous treat of tuna and cheese. My day was unusually busy, but it looks like things will now be normal for a week or two. Unless I am wrong, which I sometimes am, the next FOTD will appear in around 15 hours. Until then, take care, and walk in this world with puzzlement and enjoyment. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Minibrot_in_Bloom { ; time=0:03:05.92--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip center-mag=-0.84928080821253190/-1.706583784520602\ 00/1.211013e+008/1/122.5/-5.73023364377339695e-005 params=-1/-1.6/-0.5/-4.7/0/0 float=y maxiter=1000 inside=0 outside=tdis periodicity=10 colors=000oVCoTBoQAoO9oM8oK7oI7jNCeRH`WMW_R7A8TkXN\ kWKiZIhaGgcDffBeh9ck6bn4ap2`s0_u2Zt4Zs6Zr7Zq9ZpBZo\ CZnEZmGZlIZkJZjLZiNZhOZhPajQclRenSgoTiqUksVmtWovXq\ xXsyYnwYjvYftYbsYZrYUpYQoYMnYIlYEkYAjXCkWDlVFmUGnT\ HnSJoRKpQMqPNqOOrNQsMRtMStKRrJRqIQoHQnGQmFPkEPjDPi\ COgBOfAOe9Nc8Nb7Na6J`6F_6BZ67Y63X60X72V84U86T98RAA\ QACPBEOCGMCILDKKEMJEOHFQGGSFGTEISDKRCMRBNQAPQ9RP8S\ P7VS8XV8ZY9``9cbAeeAghBikBkmBijAgg9fd9da8cZ8aW7_T6\ ZQ6XN5WK5UH4TF4ONBKVIFbPBiWBgYBfZBe`BcaBbbBadB_eBZ\ fBYhBWiBVkBUlBSmBRoBQpBPqMOnWNkfMhpMeqNcrNasN_sNYt\ NXuNVuNTvNRwNPxNOxNMyNKzNIzNHuQGqSKuUOhWEcYD__CVaC\ RcBMeAIgADi99k85m89kEDiJHgOLeTPcYTacX_h`YmdWrhUwX`\ qLgkAnfGrbAd9EcDIbGLaJP`MT`QW_T_ZWcYZfXajXenWhqVku\ UnxUqrRhlO`fMS`JKVGBQE3SF5UG7VG8XHAZIB_IDaJEcKGdKI\ fLJhMLiMMkNOlNPlLQlJRlHSlFSlETlCUlAUl8Vl6Wl5WPQQ1i\ KmjJngIneHncGnaFnZEnXDzWS } 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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Vigilant cats
by Jim Muth 02 Oct '06

02 Oct '06

I wrote: >>The duo [of cats] watched the hole for over an hour, but the mouse never >>re-appeared. When they finally lost interest, I praised them >>for their vigilance and gave them an extra treat. Hal Lane replied: >Are you sure that they don't think that you rewarded them for >*stopping* their watch at the mouse hole? Behavior re-enforcement >using rewards can be tricky... If they got the wrong idea, they seem to have forgotten it. The duo was back at the hole a good part of today. Jim Muth

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FOTD 02-10-06 (New Low Record [5])
by Jim Muth 02 Oct '06

02 Oct '06

FOTD -- October 02, 2006 (Rating 5) Fractal visionaries and enthusiasts: Today's image is more a curiosity than a work of art. The name "New Low Record" has nothing to do with the weather. It refers to the exponent of Z in today's fractal, 1.05, which is the new low record. I have never before found a midget in a Mandeloid of such a low order. And what do midgets in this range look like? As today's image shows, they look like little more than lopsided ovals centered in a splash of total but semi-orderly chaos. I chose a color palette with very narrow and sometimes clashing color bands to emphasize the confusion. The question might arise as to how I manage to find the midgets in such unpromising fractals as today's parent fractal. To see the difficulty, zoom out of today's image to a magnitude of 0.5 while keeping the same center coordinates, and see if any visible sign exists that a midget might lie at the center of the frame. Nothing is there but waves of chaos. But Fractint is very versatile, and has built into it a secret method of finding hard-to-find midgets. Take the hopeless outzoom with its waves of chaos, change the 'outside' option from 'iter' to 'fmod', with a proximity factor of 0.1, make sure the 'logmap' is off, and re-calculate the hopeless image. Surprise! The location of the hidden midget is now indicated by a bulls-eye. Simply continue zooming into the center of the bulls-eye until the midget is reached. The location of other hidden midgets lying nearby is also apparent. These 'fmod' bulls-eyes do not always lead to midgets, sometimes they lead to bottomless spirals, but they lead to midgets often enough to make the 'fmod' outside option one of the most useful. I must congratulate the one who thought of putting it into the program. The question arises of why I would want to find such chaotic midgets in such low-order Mandeloids. The reason is just for the fun of seeing how low I can go. My goal is to find a midget in a Mandeloid with an exponent of Z less than 1.01, but that might be impossible. I could rate today's image no higher than an average 5. It has no center of attraction and only a vague overall theme. The elements near the shoreline of the midget sub-divide so rapidly that they soon disintegrate into fractal sand. The render time of 13 minutes is a bit slow. But the image may be viewed in its completed form on the FOTD web site in almost no time. The FOTD web site may be found at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A partly cloudy and warmer day, with a temperature of 66F 19C, here at New Fractal Central on Sunday went un-noticed by the fractal cats, who spent most of the day staring and sniffing at the hole in the floor by the radiator pipe, waiting for the mouse to pop out again. Unfortunately for them, the mouse is now cat-wise, and is unlikely to show itself in such dangerous territory. When the evening treat time came, I wondered if the cat duo might have preferred mouseburgers. My day was as pleasant as things can be expected to be in this far from perfect world. The work is caught up, albeit temporar- ily, and the fractals are in no danger of running out. The next fractal will appear in 24 hours. Until then, take care, and the human eyes never see all that lies before us. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= New_Low_Record { ; time=0:13:06.91--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 center-mag=-0.2055129638\ 737225/-5.1312228660223/6.741629e+007/1/-117.5/0 params=1.05/0/-37/10000 float=y maxiter=10000 inside=0 periodicity=10 colors=000Pr1Pp1Oo1Nm1Mk1Mj1Lh1Kg1Je1Jc1Ib1H`1GZ1G\ Y1FW1EV1DT0CR0CQ0BO0AM09L09J08H07G06E06D05B0490380\ 360240130010bwb_r_XmXUiURdRO_OLWLIRIFNFCIC9D969634\ 3bZnaYl`Xk_WjZViYUgXUfWTeVSdURcTQaSP`RP_QOZQNYPMWO\ LVNKUMKTLJRKIQJHPIGOHFNGFLFEKEDJDCIDBHCAFBAEA9D98C\ 87A769658557446334223112001zYNoSJeMFVHBLB7A53nSclR\ bkQajQ`iP_hOZgOYfNXeNXdMWbLVaLU`KT_KSZJRYIQXIQWHPV\ HOTGNSFMRFLQEKPEKODJNCIMCHLBGJAFIAEH9DG9DF8CE7BD7A\ C69B68957846746635534423312211100sdSqbRoaQm_PkZOiY\ NgWMeVLdUKbSJ`RIZPHXOGVNFTLESKEQJDOHCMGBKFAID9GC8E\ A7D96B85964753542321110B_Q9VM8RJ6MG5ID4D9296143uRR\ TDDoDgmCekCciBbgB`eAZcAYa9W_9UY8TW8RU7QS7OQ6MP6LN5\ JL5HJ4GH4EF3DD3BB29928716514303101g7I`6FV5CP4AI37C\ 25612i8Fg7Ef7Ed7Dc7Db6C`6C_6BZ6BX5BW5AKYeJYfIWdHUb\ GT`FRZEQXDOVCNTCLRBKPAIN9HL8FJ7DH6CF6AD59B47936724\ 5133100011IR4Ty2Sw1Ru1Qt1 } 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 01-10-06 (Rectangle Apparition [7])
by Jim Muth 01 Oct '06

01 Oct '06

FOTD -- October 01, 2006 (Rating 7) Fractal visionaries and enthusiasts: Nobody's prefect. Not even myself. I was surprised when someone actually caught the intentional mis-spelling in my recent note. Fractalists are sharp indeed. It's what happens to those who think about numbers too many times. Today is October 01, the day quadratic midgets are permitted to reappear. And I wasted no time. The image for the day shows a midget in the East Valley area of the large midget on the main- stem complex of the Z^(2.003)+C Mandeloid. This is the area of the Julibrot where the curious Julia rectangle is located. The train-tracks that criss-cross the area are obvious. And if you look carefully around the midget, you will find eight tiny copies of the great Julia rectangle itself. At first glance the Mandelbrot rectangles seem to be perfect copies of the Julia rectangles, but a bit of experimenting shows a significant dif- ference in their interior structure. The Julia rectangles stay almost fixed in position as the value of C is changed, while they fill in and their shape undergoes rapid transformation. The Mandelbrot rectangles zoom out of sight off the screen with the slightest change in the value of Z, but when they are finally found, it is seen that they are still open and their shape has remained largely unchanged. The reason for this lies in the peculiar four-dimensional geome- try of the rectangles. I will not try to describe this geometry until I can actually visualize an entire tesseract in a single moment of time. I do not expect to be able to do this for quite a while yet. The rating of a 7 for today's image seems about right. The name "Rectangle Apparition" has the slight hint of the mystical that is suggested by the entire world of fractals. The render time of 17-1/2 minutes borders on slowness, but the result is worth the wait, and no waiting at all will be needed if the finished image is viewed on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A cool cloudy drizzly day with a temperature of 55F 13C here at New Fractal Central on Saturday kept the fractal cats confined indoors. But since they never go out anyway, they were uncon- cerned. They had one moment of excitement however, when a mouse popped out and scurried down the hallway. The would be mouse- catchers fell over each other in pursuit. The mouse got away through a hole by a radiator pipe, having learned its lesson. The duo watched the hole for over an hour, but the mouse never re-appeared. When they finally lost interest, I praised them for their vigilance and gave them an extra treat. My day was reasonably pleasant. The work is up-to-date, nothing big is in sight, and the fractals are going well enough. What else could a fractalist want, other than the answer to the ques- tion of the meaning of existence? The next FOTD will appear in 24 hours. Until then, take care, and does meaninglessness reign supreme? If it does, what is the meaning of it. Or is the very concept of meaning a creation of human thought processes? I wonder. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= RectangleAparition { ; time=0:17:35.23--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot4 center-mag=-0.000000312\ 87984841/-0.00000010697476267/5.35887e+011/1/20/\ 7.8241581935589721e-008 params=0/0/0/0/-1.7435/0/0\ /0/2.003/0 float=y maxiter=7600 inside=0 logmap=988 periodicity=10 mathtolerance=0.05/1 colors=000MBAODAQFASHAUJAWLAYNA_PAaRAcTAeVAgWAiXAk\ YAmZBm_AmaCmbEmdGmeInfKqhMtiOwkQznSzqUztWzwYzz_oYV\ mZXlZZkZ`jZbi_dh_fg_hf_je`ld`nc`pb`q`bnZclXdiWegUg\ eShbRi`PjZNlWzmUznRzoPzqNzrKzsIztGzsJzrMzqPzpSKoUM\ nXOm_PlbRkeSjgUijWhmXgpZfs_fuaetbetddtedtfdthctict\ kbtlbtmbtoatpatr`ts`tt`trdophkokgmoclr_jvWiySVXUO_\ WHbZAd`FeaJebNecRedVeeacigbmmaps`ty_wpbhhdU`fFdiLg\ lRjnXmqbpshsvnvxsoslioeck_YgTScMM_GLaBKb6Jc1NfLQid\ TkxXZ``NDZSCXWCV_CSYMPXWMVeJUo7lPFeUN_ZUUcXT`ZTZaT\ XcTUfTShTQjTO`0PxngfipPdxSUmUKcWAUU9RT9OS9LS9IV8FY\ 8C`89c51h86f0AzMAyAEqEIhFMdHQ_IUWJYSK`UJaWIbXHcZGd\ `FeaEfcDgk3ddDgYMiRVkKcmDlo3uy7uqAuiEubHuVLuOOuGRu\ 9_lGhcMqWSoUTmSUkQViOWgMXeKYnNagMWdOZbQa_SdYTfWUiT\ VlRWoDXrJYqPZqU_p_`peaojbopcnuenohjikgcncYq`StXMwU\ GzLHzOHzRIzdHzZHzUHzOBzLHzJNzITzHZzFdzEjzDpzCqz9qz\ 6qz4nz5kz6lzIlzLmzNmzQmzS } 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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