March 2004 - Fractint - mailman.xmission.com

Re: Quadratic midget? Is this one?
by Jim Muth 26 Mar '04

26 Mar '04

On Fri., March 26, 2004 Hiram Berry wrote: >Okay, Jim. But what does the "quadratic" part of "quadratic >midget" mean? By a quadratic midget, I mean any midget shaped like a miniature classic Mandelbrot set, which is created by the quadratic formula Z^2+C. In quadratic midgets the surrounding elements split in two as they approach the midget. When I mention cubic midgets, I refer to midgets with two main lobes, shaped like the Z^3+C Mandeloid. In these midgets, the elements triple in number at every split. The midget drawn by your parameter file is of the sixth order, (Is this order called hexic?), with five main lobes and elements that split into six smaller versions at every split. Jim M.

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FOTD 26-03-04 (What is it? [4])
by Jim Muth 26 Mar '04

26 Mar '04

FOTD -- March 26, 2004 (Rating 4) Fractal visionaries and enthusiasts: In today's image, things get stranger yet. Now, the midget itself has been infected by whatever is happening in this part of the fractal world. What we have in the image is a quadratic midget that has begun to morph into a midget of the sixth order. The five lobes of sixth-order midgets are already taking shape. The smaller satellite midgets however still retain the familiar Mandelbrot outline. Check the westernmost extremity of the large midget, on the X-axis where the stem branches out. You will find a perfect Mandelbrot bud there. Then check the smaller outlying midgets. Some of these are irregular holes with a decidedly non-critical appearance, but others are perfect mini-Mandelbrot sets. Finally, notice the 6,36,216... series of elements leading to the central midget -- a sure sign of an emerging sixth-order midget. What's happening here is crazy enough, but we have not yet seen the worst of it. Stay tuned over the next few days for even stranger fractal wonders. Since today's image has only limited artistic worth, I have rated it at a 4, which is a little below average, but not low enough to make the 1-1/4 minute render time too much to ask. Thanks to the short render time, the overall value registers an impressive 323. Perhaps the fastest way to see the image is to download it from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Fine early spring weather on Thursday made the fractal cats happy. The warm sun and temperature of 68F 20C was just what the duo was waiting for. They spent the entire afternoon in the yard, doing what old-age cats do best -- sleeping. When they came inside, the treat of tuna completed their day. This morning is starting even warmer. Another good day seems to be coming. I have several hours work to accomplish, then it's back to the fractal screen. Until next FOTD, take care, and who knows what is possible in the world of fractals? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ What_is_it { ; time=0:01:14.37--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-0.509759593836255/0/351.2859/1/180 params=1/3/0.355/4/0/0 float=y maxiter=900 inside=0 logmap=15 symmetry=xaxis periodicity=10 colors=000LB9L96L84OC6RF7UI9XLA_OBbRDeUEhYFk`HncIq\ fJtiLwlMzoNymKylIykGyjEyiCwgFvfIudLtcOsaQr`TqZWpYZ\ oWanVclYdj_dhadfcddedbgdaid_ldYndWpdUrdStdQvdPxdOw\ cNvcMubLubKtbJsaIraHr`Gq`Fr`Es_Dt_CuZBvZAwZAxbAyfA\ ziAzmAzqAzuAzxlztgzpczlbziczcdzYezSfzNgzQhzSizVjzX\ kz_lzamzdnzfozipzkqznrzpszltziuzfvzcwz`xzYyzUzz2zz\ FzzRzzbzzczzdzzezzfzzgzzhzzizzjzzkzzlzzmzzmzzlzziz\ zfzzczz`zzXzzUzzRzzOzzLzzIzzFzzCzz9zzAzzBzzBzzCzzC\ zzDzzEzzEzzFzzFzzGzzHzzHzzIzzIzzNzzSzzXzzazzVzzOzz\ HzzPzzWzzbzzjzzqzzxzzuzzrzzozzlzzjzzgzzdzzazzZzzXz\ zUzzRzzOzzMzzOzzPzzQzzRzzPzzNzzLzzJzzHzzFzzEzzCzzB\ zzAzz9zz7zz6zz5zz4zz3zz6zz8zzAzzCzzFzzHzzJzzLzzNzz\ QzzTzzWzzZzzazzczzfzzizzlzzozzqzzdzzSzzFzz3zz6zz8z\ zBzzDzzFzzIzzKzzMzzPzzRzzTzzXzz_zzbzzezzhzzkzzhzze\ zzbzz`zzVzzQzzUzzXzz_zzczzfzzizzmzzpzzszzozzkzzgzz\ dzz`zzXzzOzzLzzJzzGzzEzzB } 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 20.0 PAR-FORMULA FILE==================================

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FOTD 25-03-04 (Somber Snowflake [6])
by Jim Muth 26 Mar '04

26 Mar '04

FOTD -- March 25, 2004 (Rating 6) Fractal visionaries and enthusiasts: Today's fractal pictures a quadratic midget. There is nothing unusual in having a quadratic midget at the center of the screen. Most of my images have them. But this midget is strange indeed. By their nature, quadratic midgets are surrounded by symmetrically spaced elements that continually split in two as they approach the midget. The first indicator of a midget is the presence of two symmetrical elements that split into four similar but smaller elements. This splitting continues in the series 2,4,8,16,32... as the elements approach the midget. We now can see what is wrong with today's midget, which I have named "Somber Snowflake". I gave the image this name because the pattern surrounding the midget is shaped quite like a dark snowflake with a green aura. But snowflakes have six sides, and the number 6 is not part of the 2,4,8,16... series. Something has gone wrong. Some other series has infected the quadratic series, and this infection will become only worse as the exploration of the Z^3+x(Z^4) fractals continues in the days to come. Though it is on the dreary side, today's image rates a 6, which is just a little above average. The render time is a speedy 2-1/2 minutes, which results in an overall value of 233. The pre-rendered GIF image is available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> With sun and a temperature of 61F 16C, Wednesday was a rather pleasant day here at Fractal Central. Thomas, the oversized orange, spent several hours in the yard. Tippy, the lean wiry tabby, passed the day sleeping on his window shelf. Since 14-year-old cats do little but sleep, it was hard to tell if Tippy did not feel good. In the evening all appeared well when the tuna treat vanished as it should. This morning is starting with clearing skies and warmer temperatures. I expect a good day for the duo. As for me, being not quite as old on the human scale as the cats are on the cat scale, I still enjoy an occasional bit of the unusual, but it appears it will be another in a seemingly unending stream of normal days, with the exception of a new fractal at the end. Until tomorrow, take care, and fractals are never boring. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Somber_Snowflake { ; time=0:02:34.39--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-0.54195976260355410/+0.002250716455883\ 61/127978.5/1/-52/1.42828571886299827e-009 params=1/3/0.357/4/0/0 float=y maxiter=1000 inside=0 logmap=37 periodicity=10 colors=000NMfONgPOhQPiRQjSRkTSlSTmRUnRVmQWlPYkP_j`\ kf_mcZr`YvXWyUUzRTyOQtQNoSLjTIeVG`WCXT9TR6PP3LN0IL\ SXIrjFg_GYPHOEIE3JD9ICEHBJHBPGAUG9ZF9cFH`COZAVX7aU\ 5hS2oQ0lV6iZCfbIcfOajUenVjqXnuZrx_pubnrdlofjlhhijf\ fldcnb`p`Yr_UoZRmYNjXKhWHfVDcUAaU7_W9`YAa_BbaCcbDd\ dEefFfhHgjIhkJimKjoLkqMlsNmtOnpMhmKbjIYgHSdFMaDHZB\ BWA6YD5ZF5_H5`J5aM4cO4dQ4eS4fV3gX3iZ3j`3kc2le2mg2n\ i2jk9fmFboMZqSVsZRudX2hR3fM3eG3dB3cJA_QHXXOTdVQkaM\ rhJynGvqNttTrwZpudamfOcgQcbRcZScVTcRRcQQePPgOOiOMk\ NLmMKoLJqLcsJYuLSvNMwPHxREyRBzR8zR5zRlzujzmizfhz_f\ zTezMdzFcz8azD_zIYzMWzRUzWSz_Yzebzkgzqlzwszvyzvwzk\ uzaszSrzIjzUczegzfjzgmzgpzhszhgziWzjKzjUzkczlmzmvz\ mpzfkz`fzUazOXzHSzBNz5IzQEzjDzjDzjDzjDzjDzjIziNzgS\ zfXzeazdazeazfazgazgazhaziazjazjazkazlazl`zp_zsZzv\ YzyXztXzoXzkXzfXzaXzYXzTXzOXzKVzIUzHTzGSzFQzDPzCOz\ BNzALz8Kz7Jz6Iz5Hz4Iz9JzD } 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 20.0 PAR-FORMULA FILE==================================

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FOTD 24-03-04 (X-Y Mandel Fractal [5])
by Jim Muth 24 Mar '04

24 Mar '04

FOTD -- March 24, 2004 (Rating 5) Fractal visionaries and enthusiasts: In today's image things start to go wrong. The midget at the center is clearly of the quadratic variety, as are almost all midgets in fractals created by the MandelbrotMix* series of formulae. But the expected 2-4-8-16... series of elements leading toward the midget is not as well defined as it might be. The confusion is just starting to appear, but it is there, and from here on, the confusion will only increase. The parent fractal of today's image is virtually the same as the parent of yesterday's image -- a seemingly harmless mixture of Z^3 and Z^4 that would be expected to do little but create a routine combination fractal. In the world of fractals however, surprises are common, which is why I find fractals so fascina- ting. The surprises coming in the next few days are some of the greatest I have yet stumbled upon. I have named today's image "X-Y Mandel Fractal". Something about the image reminds me of pictures I have seen of the X and Y chromosomes that determine an individual's sex. I believe all individuals start as women, but half are mutated into men by an X-Y chromosome. If this is true, then half the population of earth consists of alien mutants bent on death and destruction. After watching the news, I guess it's true! Before getting sidetracked into politics, an ever-present danger, I must get back on the fractal track and admit that I could rate today's image no higher than an average 5. When the render time of 4 minutes is taken into consideration, the overall value jumps to 118. The best value of all is to download the GIF image file from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A warmer temperature of 48F 9C, lots of sun, and lighter winds gave the fractal cats a pleasant afternoon in the yard here at Fractal Central on Tuesday. Today is starting still warmer, but with clouds moving in, the duo might not be as happy. For me, it looks like another routine day of getting the work finished, then exploring in Fractal Land. So until next time, take care, and good fractals make unhappy cows give more milk. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ X-Y_Mandel_Fractal { ; time=0:04:13.92--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-0.52128983921205970/+0.000169467990356\ 02/988403.5/1/90/3.88578058618804789e-016 params=1/3/0.3555/4/0/0 float=y maxiter=1200 inside=0 logmap=78 periodicity=10 colors=000AGQAHR9IS9JT8KU8LV8LW7MX7MY6NZgzzTzxRzvV\ vsZrpbntfjwifzdZu_RqVJmz_KzUKzBKxI2uHCsGLpFVnEclI_\ jMWhQTfTPdzMbuIapFdkKffPicUk`YnYbpVgrSkqPhqSfqWcp_\ arcZvgXzkVg1ElHBqW9zj7zhBzfEzdHwbKt`OqZRnXUkWXhTZe\ Q`bNa_KcXHdUEfRBgOKjLSlI_noVopRpqNqrIrsEstAtu6trBn\ pFhnKblOXjTRhXMoi`lgWjeShdOfbKdaGbcCad9`e6_f3Zg0px\ _lx`hwadwb_wcWvdSveOvfhVdjSkkQqjR_jRJZOLNLMMQOMVQL\ _RLdTLiVKnWKsYKxZaHHWJKRKNMLQGNTBOW6PZCSbIUfNWjTYn\ Z_rcaveXtfSshOriJpkEolAneBmZBlSCkLCjEDi8DiGEhNFgVF\ faGeiHdpHcfQWYZOOgGFo8JkFNgMQdSU`ZYXe`UkZKlXAlW0lS\ 1mP2nM3oI4pF5qC5r9Jn6Xj4igHccUY`fSYsMVtQZtTatXdt_g\ i_j_`mQapGbsFcrEdqDepCfpBgoAhnAinOjZ`kJml4jm9hnEfo\ IcpNaqS_rWWsQTtKPuDMv7Jw1DxB8yK3zT9zXFz`LzdRzhXzlb\ zphztmzwjzrgzndzjaze_zaXzYUzTRzPPzLLzQIzVEzZBzc8zg\ 9zh9zhAziAziAzjBzjBzkCzkCzlCzlDzmDzmEznEznEznDzlDz\ jDzhCzfCzdCzbBz`BzZBzXAzV } 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 20.0 PAR-FORMULA FILE==================================

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FOTD 23-03-04 (Another New World [7])
by Jim Muth 23 Mar '04

23 Mar '04

FOTD -- March 23, 2004 (Rating 7) Fractal visionaries and enthusiasts: Today's image is the first glimpse into a new fractal world. This is why I named it "Another New World". New fractal worlds are no big deal. They can be created at will. But the world introduced by today's image is rather unusual, as the next several FOTD's will illustrate. On the surface, the image appears to be a routine quadratic midget in the fractal that is created when 0.355 parts of Z^4 are added to Z^3 before C is added. And this is indeed what it is. But in its heart lies a deep secret, which I will reveal in stages over the days to come. For now, enjoy today's image, which is already good enough to rate an above-average 7. The overall value is brought down to 25.5 by the render time of 27 minutes, but this value can be increased by avoiding the rendering entirely, which can be done by downloading the finished image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> With a high temperature of 37F 3C and brisk winds, Monday was far too harsh for the delicate paws of the fractal cats. They did manage an hour or so on the porch, but the clouds that kept obscuring the warm sun gave them no end of annoyance. Luckily, cats have short memories, and by the time they had finished their evening tuna, they had nearly forgotten their bad day. Today is sunny and warmer, and the wind has died. The duo is already thinking of going out. And I'm thinking of finishing the work that must be done so I can get to the fractals that are fun but not absolutely necessary to survival. Until the next wonderful image appears 24 hours from now, take care, and see you then. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Another_New_World { ; time=0:27:25.89--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-0.52321930545120110/-0.002589589762561\ 87/2.048744e+010/1/-54.9998285074083242/4.87322811\ 3853878e-005 params=1/3/0.355/4/0/0 float=y maxiter=10000 inside=0 periodicity=10 colors=000z06u39m8EeDKYGPPLU9ozCozCozCozCozCozCozC\ ozEozEozEoxEouElrEipEgmHdjHagHZeHWbHT_HRY00z00z00x\ 00p03j9Dbz0zj0z0J00L00L04L09O9EOMz0zz0xz0xz0uz0uz0\ uz0rz0rz0pz0pz0pz0mz3mz3jz5ju8jr8gpBgmBegDeeDebGb_\ GbYJ_SJ_PL_MLYKOY0oE0gK4aPCTU0iz0gu0dr0am0Zj0Xg4Tb\ CR_1Lz4Oz4Oz4Oz4Oz4Oz6Oz6Oz6Oz6Oz6Oz9Oz9Oz9Oz9Oz9O\ zCOzCOxCOuCOrPJrPGpPGjSGeSDbSDYSBUUBPzoMzoPxoUroYm\ g_gZbbTgYLjSDmP8pKJjERe9Z_4iU0oP0oK0oH0oK0oK0oK0oM\ 0oM0oM0oM0oP0oP0oP0oS0oSPoEMo1CoE1oP0o_0dm0Rx0Dz00\ z03z03z03z05z05z05z08z08z08z0Bz0Bz0Bx0Du4LU0Du0Dr0\ Dr0Gp0Gm0Gm0Jj1Jg4Jg6Le9Le9LbCO_EO_HOYz00z00z00z00\ z00z00z00z00z00z00z00z00z00z00x30u50r51m84j86gB9eD\ CbDE_GHUGKSJMPLPMLSKOUzo0zo0zo0zo0xo0uo0uo0ro0po0m\ o0jo0go0gl0ei1bg4_g6Yd9UaCUZESXKPXMMTPKRSHOU0op0om\ 0om0om0oj1oj1oj1og4og4og6oe6oe6oe9ob9sbCobCk_Cf_Ea\ _EXYHTYHRYz00zm0zg0zb0zX1 } 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 20.0 PAR-FORMULA FILE==================================

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FOTD 22-03-04 (First Fractal Flight [8])
by Jim Muth 22 Mar '04

22 Mar '04

FOTD -- March 22, 2004 (Rating 8) Fractal visionaries and enthusiasts: Today's image is still another view of the Julia rectangle in the Z^2.003 Julibrot. I should not call it a rectangle today however, for today's orientation has been rotated 0.63 degree, which is just far enough from the Julia direction that the rectangle has been stretched into a near perfect square. But the square is only a small part of today's image, which resembles some fantastic bird in flight. Having been shrunk to near insignificance, the square lies where the wings are attached to the body of the big bird. This resemblance of the entire image to a bird in flight inspired the name "First Fractal Flight". I rated the image, perhaps a bit over-enthusiastically, at an exceptional 8. When the render time of 13 minutes is figured in, its overall value rates a 60. This value may be increased by saving the time that would otherwise be spent rendering the image. And this may be done by downloading the finished image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Cold winds, only occasional sun, and a temperature of 41F 5C limited the cats' outdoor time to less than an hour on Sunday, but a generous treat of tuna in the evening kept their moods from becoming too sullen. This morning it is still windy and the temperature is down to 28F -2C. It looks like another less- than-ideal day for the fractal duo. I have near the normal amount of work to finish before retiring to fractal land. Today, I will bid a temporary 'good-bye' to the rectangle, and set out for unexplored territory. What I find there will appear as tomorrow's FOTD. Until then, take care, and float like a fractal, whatever that means. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ FirstFractalFlight { ; time=0:13:21.14--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=SliceJulibrot4 passes=1 center-mag=-0.000138176/-0.00692793/21.92537/1/-40\ /-5.05012698326368081e-014 params=90/90/89.27/90/\ -1.7435/0/0.00019/0.07388/2.003/0 float=y maxiter=60000 inside=0 logmap=29 periodicity=10 colors=000RASSATTAUUAVVAWWAXXAYYAZZA__A``AaaAbbAcc\ AddAeeAffAggAhhAiiAjjAkkAllAmmAnnAooAppAqqArrAssAt\ tAuv9vtCurEuqGtoJtnLslNskPriSrhUqfWqeZpc`pbbo`do_g\ nYinXkmVnmUplSrlPumRtlTskVrjWqjYpi_ohanhbmgdlfflfh\ keijdkidmhcogbpfbreatd`ud`sc_qc_oc_nc_lbZjbZibZgbZ\ ebZcaYbaY`aYZaYYaYW`XU`XS`XR`XP`XN_WM_WK_WI_WH_WIY\ UJXTKWSKVQLUPMTONSMNRLOQKPOIQNHQMGRLESKDTJCTIAUH9V\ G8TC8VF7XH7ZJ6_M6aO5cQ5dT4fV4hX3jZ3ka2mc2oe1ph1rj0\ tl0qn0kf7gZEiRLkJRmLSoNUqPVsRXuTYwVZyX`zZaz`czbdzd\ fzfgzhhzjjzlkznmzpnzrpztqzvrzrszoszlsziszeszbsz_sz\ XszUszUszUszUszUszUszUszUszUszUszUrzWqzYqz_pzapzco\ zeozgnzinzkmzmlzolzqkzskzujzwjzyizzizzhzzhzzhzzgzz\ gzzgzzfzzfzzfzzezzezzezzdzzdzzdzzczzczzczzazz`zz_z\ zZzzYzzXzzWzzVzzTzzSzzRzzQzzPzzOzzNzzMzzKzzJzzIzzH\ zzGzzFzzEzzDzzEzzEzzFzzFzzFzzGzzGzzHzzHzzHzzIzzIzz\ IzzJzzJzzKzzKzzKzzLzzLzzN } 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 20.0 PAR-FORMULA FILE==================================

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FOTD 21-03-04 (Correct version -- A Space Oddball [5])
by Jim Muth 21 Mar '04

21 Mar '04

FOTD -- March 21, 2004 (Rating 5) Fractal visionaries and enthusiasts: For today's adventure in fractal land we return to that rectangle in the Julia set of the Z^(2.003) Julibrot. But we do one thing very different. Instead of viewing it in the Julia direction, we turn our viewpoint 90 degrees and view it in the Oblate direction, which is determined by the real(Z) and imag(C) axes. Surprisingly, the rectangle is still a rectangle, though it is now quite squashed, and its top and bottom edges are no longer sharply defined, but have become fuzzy. When viewed from this direction, the scene has origin symmetry, the lateral elements being transformed into graceful swirls. With few more good features to tell of, the image could be rated no higher than a 5, which, with a 21-minute render time, equals an overall value of 24. Perhaps remembering that great film of 35 or so years ago, which was set in a future that is now 3 years in the past, I named the image "A Space Oddball". And I wonder why none of the things foreseen in that film have come true. I guess it's a plot of the evil space aliens to keep us helpless in preparation for the coming takeover and enslavememt. :-) The enlightened will avoid the aliens and save 20 minutes by downloading the finished image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Those who enjoy watching their fractals come to life will run the included parameter file. The first day of spring turned out to be very pleasant here at Fractal Central on Saturday. The fractal cats took full advantage of the sun and temperature of 59F 15C by spending most of the afternoon in the yard, checking the spring bulbs that are already showing. At sunset, they came inside for their evening treat without urging. Today is starting mostly sunny and mild, but it is quite windy, and the duo dislikes wind, which conceals the sound of danger. It remains to be seen what kind of day they will have. Regardless of the cats' day, my day will be pleasant, and the fractals will all be above average. Until next time, take care, and hang on to your fractals. Once you lose them, they are gone forever. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ A_Space_Oddball { ; time=0:20:55.04--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=SliceJulibrot4 passes=t center-mag=0/0/3303.206/0.0232/0/-77.7313946499058\ 517 params=0/0/90/0/-1.7435/0/0.00019/0.07388/\ 2.003/0 float=y maxiter=60000 bailout=9 inside=0 logmap=66 periodicity=10 colors=0008355450532654765877999AAABBCCDEDEFEFHFHI\ GIKHJMGLNFMPENREPSDQUCRVBSXBUZAV_9Wa8Yc8Zd7_f6ag5b\ i5ck4el3fn2gp2iq1js0kt0ls3is6gr9drCbqF`qIYpLWpOToR\ RoTPnUOmVOlVOkWOjWOiXNhYNgYNfZNeZNd_Nc_Mb`MaaM`aM_\ bMZbLYcLXcLWdLVeLUgLTiKSkKRmKUoK_qKatJcuJexJhyJhzJ\ hzKhxJevKbsLZsLUoMPnMKkNFiOFgOEePEePDdQDcRCcRCbSBb\ SBaTB`UA`UA_V9_V9ZW8YX8YX7XY7XY6WZ6V_5V_5U`4U`4Ta4\ Ta5Wc5Ye6_f6bh7di7fk8il8kn9mo9pqArrAtt8wvAvuBvtCvs\ DvrEvqFvpGvoHvnIvnJvmKvlLvkMvjNviOvhPvgQwfRwfSwdTw\ bTwaUw_UwYVwXVwVWwTWwSXwQYwOYwNZwLZwJ_xI_xG`xE`xDa\ xBaxAbxBcxCdxDexEexEfxFgxGhxHixIixIjyJkyKlyLmyMnyN\ oyOpyPqyQryRsyStyTuyUvyVwyVxyWyyXzzXzzYzzYzzZzz_zz\ `zzazzbzzczzdzzdzzezzfzzgzzhzzizzjzzjzzkzzlzzmzznz\ zozzpzzpzznzzlzzkzzizzhzzfzzezzczzFzzEzzEzzDzzCzzC\ zzBzzBzzAzzAzz9zz8zz8zz7zz7zz6zz5zz5zz4zz4zz3zz2zz\ 3zz3zz3zz3zz4zz4zz4zz4zz5 } 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 20.0 PAR-FORMULA FILE==================================

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FOTD 21-03-04 (A Space Oddball [5])
by Jim Muth 21 Mar '04

21 Mar '04

FOTD -- March 21, 2004 (Rating 5) Fractal visionaries and enthusiasts: For today's adventure in fractal land we return to that rectangle in the Julia set of the Z^(2.003) Julibrot. But we do one thing very different. Instead of viewing it in the Julia direction, we turn our viewpoint 90 degrees and view it in the Oblate direction, which is determined by the real(Z) and imag(C) axes. Surprisingly, the rectangle is still a rectangle, though it is now quite squashed, and its top and bottom edges are no longer sharply defined, but have become fuzzy. When viewed from this direction, the scene has origin symmetry, the lateral elements being transformed into graceful swirls. With few more good features to tell of, the image could be rated no higher than a 5, which, with a 21-minute render time, equals an overall value of 24. Perhaps remembering that great film of 35 or so years ago, which was set in a future that is now 3 years in the past, I named the image "A Space Oddball". And I wonder why none of the things foreseen in that film have come true. I guess it's a plot of the evil space aliens to keep us helpless in preparation for the coming takeover and enslavememt. :-) The enlightened will avoid the aliens and save 20 minutes by downloading the finished image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Those who enjoy watching their fractals come to life will run the included parameter file. The first day of spring turned out to be very pleasant here at Fractal Central on Saturday. The fractal cats took full advantage of the sun and temperature of 59F 15C by spending most of the afternoon in the yard, checking the spring bulbs that are already showing. At sunset, they came inside for their evening treat without urging. Today is starting mostly sunny and mild, but it is quite windy, and the duo dislikes wind, which conceals the sound of danger. It remains to be seen what kind of day they will have. Regardless of the cats' day, my day will be pleasant, and the fractals will all be above average. Until next time, take care, and hang on to your fractals. Once you lose them, they are gone forever. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ A_Space_Oddball { ; time=0:20:55.04--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=SliceJulibrot4 passes=t center-mag=0/0/3303.206/0.0232/0/-77.7313946499058\ 517 params=0/0/90/0/-1.7435/0/0.00019/0.07388/\ 2.003/0 float=y maxiter=60000 bailout=9 inside=0 logmap=66 periodicity=10 colors=0008355450532654765877999AAABBCCDEDEFEFHFHI\ GIKHJMGLNFMPENREPSDQUCRVBSXBUZAV_9Wa8Yc8Zd7_f6ag5b\ i5ck4el3fn2gp2iq1js0kt0ls3is6gr9drCbqF`qIYpLWpOToR\ RoTPnUOmVOlVOkWOjWOiXNhYNgYNfZNeZNd_Nc_Mb`MaaM`aM_\ bMZbLYcLXcLWdLVeLUgLTiKSkKRmKUoK_qKatJcuJexJhyJhzJ\ hzKhxJevKbsLZsLUoMPnMKkNFiOFgOEePEePDdQDcRCcRCbSBb\ SBaTB`UA`UA_V9_V9ZW8YX8YX7XY7XY6WZ6V_5V_5U`4U`4Ta4\ Ta5Wc5Ye6_f6bh7di7fk8il8kn9mo9pqArrAtt8wvAvuBvtCvs\ DvrEvqFvpGvoHvnIvnJvmKvlLvkMvjNviOvhPvgQwfRwfSwdTw\ bTwaUw_UwYVwXVwVWwTWwSXwQYwOYwNZwLZwJ_xI_xG`xE`xDa\ xBaxAbxBcxCdxDexEexEfxFgxGhxHixIixIjyJkyKlyLmyMnyN\ oyOpyPqyQryRsyStyTuyUvyVwyVxyWyyXzzXzzYzzYzzZzz_zz\ `zzazzbzzczzdzzdzzezzfzzgzzhzzizzjzzjzzkzzlzzmzznz\ zozzpzzpzznzzlzzkzzizzhzzfzzezzczzFzzEzzEzzDzzCzzC\ zzBzzBzzAzzAzz9zz8zz8zz7zz7zz6zz5zz5zz4zz4zz3zz2zz\ 3zz3zz3zz3zz4zz4zz4zz4zz5 } 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 20.0 PAR-FORMULA FILE==================================

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The Pseudo-Dragon Spacefilling Tree...
by Tony (Anthony) Hanmer 20 Mar '04

20 Mar '04

Here is an old L-system find of mine, which I have recently explored further. It started out as a speedup to one of my favourite discoveries, a curve which could be adjusted from being a spacefilling 1:sqrt2 rectangle to the TwinDragon, which is 2 Dragon Curves laid end to end. Then I discovered that this curve could also be transformed into Levy's Curve; and recently found its Dragon Curve version as well. This led me to a curve which seems to be halfway between the DC and TD! Other variations are possible: indeed, if one translates the curve into d version from f version, its Angles can be incremented to arbitrarily fine differences, making animations between the various curves possible. (This is the case with many L-systems...) Below, included with the curve, are many of the variations I have found. Paste the whole thing into a text editor, and call it pdsft.l Keep this file open, and Alt-Tab into Fractint. Here you can try all of the variations one at a time, by jumping back into the file in the text editor and removing the preceeding; semicolon from the string you wish to try, saving the file, and jumping back into Fractint. I have left it with the variation which is a half-DC, half-TD mix as default. One question: given 8 positions for an angle change, such as + or - (before and after each of f, x, f and x), and 8 possible changes of angle for Angle 8 (0, +, ++, +++, |, +++++, ++++++, -), what is the total number of permutations? (Some of these permutations will lead to a flat line or other redundant variations.) Tony Hanmer Tbilisi, Republic of Georgia (adh5306l {; Anthony Hanmer 7/3/2004 Angle 8 ; pdsft (Pseudo-Dragon SpaceFilling Tree) speedup, various variants Axiom x ; Choose any string by removing its preceeding ;semicolon ; (All possibilities: 1f1, 1x1, 1f1, 1x1 and ; 0, +, ++, +++, |, +++++, ++++++, -: = ...?) ;x=d[@iq2\90x]\180d[@iq2\90x]; rectangular sft ;x=f[@iq2++x]|f[@iq2++x]; rectangular sft ;x=f[@iq2+x]|f[@iq2+x]; TD ;f=f+@iq2f|f+++@q2; TD 4026, multiple-layer redundant (mlr) (needs Axiom f) ;f=f+++@iq2f|f+@q2; TD 4027 mlr (needs Axiom f) ;x=d[@iq2\45x]\180d[@iq2/45x]; DC 5306m ;x=f[@iq2+x]|f[@iq2-x]; DC 5306n; 1-string all-f DC eludes me so far! ;x=f[@iq2+x]f|[@iq2-x]; Fat DC, 13/3/2004 ;x=f[@iq2+x]|f[@iq2x-]; Halfway between DC & TD, 13/3/204 ;x=f[@iq2+x]f|[@iq2x-]; Halfway between DC & TD, 13/3/204 ;x=f[@iq2+x]-f[@iq2x]; Levy's Curve, 13/3/204 ;x=f[@iq2++x]|f[@iq2x]; Partway between DC & sft?, 13/3/2004 ;x=f[@iq2++x]|f[@iq2+x]; Partway between DC & sft?, 13/3/2004 ;x=f[@iq2++x]|f[@iq2-x]; Partway between DC & sft?, 13/3/2004 ;x=f[@iq2+x]f[@iq2+x]; TD tree ;x=f[@iq2+x]f[@iq2-x]; Levy's Curve, 12/3/2004 x=f[@iq2+x]|f[@iq2x]; *Halfway BETWEEN* DC & TD! - 8/3/2004 ;x=d[@iq2\45x]\180d[@iq2x]; *BETWEEN* DC & TD!, d-version - 9/3/2004 ;x=d[@iq2\45x]\180d[@iq2/15x]; *BETWEEN* DC & TD!, Angle 8 - 9/3/2004 ;x=d[@iq2\45x]\180d[@iq2/30x]; *BETWEEN* DC & TD!, Angle 8 - 9/3/2004 ;x=d[@iq2\45x]\180d[@iq2/40x]; *BETWEEN* DC & TD!, Angle 8 - 9/3/2004 ;x=d[@iq2\45x]\180d[@iq2\15x]; *BETWEEN* DC & TD!, Angle 8 - 9/3/2004 ;x=d[@iq2\45x]\180d[@iq2\30x]; *BETWEEN* DC & TD!, Angle 8 - 9/3/2004 ;x=d[@iq2\45x]\180d[@iq2\40x]; *BETWEEN* DC & TD!, Angle 8 - 9/3/2004 ;x=d[@iq2\30x]\180d[@iq2x]; Just playing - 9/3/2004 ;x=d[@iq2\60x]\180d[@iq2x]; Just playing - 9/3/2004 ;x=d[@iq2\15x]\180d[@iq2x]; Just playing - 9/3/2004 ;x=d[@iq2\75x]\180d[@iq2x]; Just playing - 9/3/2004 ;x=d[@iq2\90x]\180d[@iq2x]; Just playing - 9/3/2004 ;x=f[@iq2+x]|f[@iq2+!+x]; Just playing - 9/3/2004 ;x=f[@iq2-!x]|f[@iq2++!x]; Just playing - 9/3/2004 ;x=f[@iq2-x]|!f[@iq2+!x]; TD - 9/3/2004 ;x=f[@iq2|!x]-!f[@iq2+!x]; sft - 9/3/2004 ;x=f[@iq2-!+!x]+f[@iq2+!x]; Just playing - 9/3/2004 ;x=f[@iq2-!+!x]|!f[@iq2+!x]; Just playing - 9/3/2004 ;x=f[@iq2-!--x]|!f[@iq2+!x]; Rt Triangle - 9/3/2004 ;x=f[@iq2---x]|!f[@iq2+!x]; Rt Triangle - 9/3/2004 ;x=f[@iq2---x]+++f[@iq2+!x]; Just playing - 9/3/2004 ;x=f[@iq2---x]+++f[@iq2|x]; Nice new DC - 9/3/2004 ;x=f[@iq2+x]-f[@iq2+x]; playing, 12/3/2004 ;x=f[@iq2x]f[@iq2-x]; playing, 12/3/2004 } _________________________________________________________________ MSN 8 helps eliminate e-mail viruses. Get 2 months FREE*. http://join.msn.com/?page=features/virus

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FOTD 20-03-04 (Discombobulated [5])
by Jim Muth 20 Mar '04

20 Mar '04

FOTD -- March 20, 2004 (Rating 5) Fractal visionaries and enthusiasts: In today's image we once again visit the Z^(2.003)+C Mandeloid, and examine the area just east of the East Valley of the large midget on the negative X-axis. The large midget cannot be said to lie on the main stem. There is no main stem in this Mandeloid. The stem has broken into fractal dust, and as for the large midget -- it has been distorted into a monstrous thing that must be seen to be believed. When I say that today's scene is located just east of this monstrous midget's East Valley area, I am not actually speaking correctly. The midget has no East Valley. What once was East Valley has broadened into an area that can better be described as East Plateau. The top of this plateau consists of newly created features that do not exist in the traditional Mandelbrot set. There are newly created bays and valleys here, with sub- features unlike any found in the M-set. The strange Julia rectangle lies in this area, along with the figures of overweight people raising their arms in praise of something. And of course there are midgets. Today's image illustrates one of the smaller midgets in the area. Its dis- organization is typical of the entire area, and has inspired the name "Discombobulated". To add to the interest I rendered the image with the outside set to 'tdis'. It seems to have worked too well. The disorganiza- tion actually goes a bit too far, spoiling the overall artistic worth and cutting the rating to a merely average 5. The rather slow render time of over 1/2 hour further cuts the overall value to a lowly but not disgraceful 15. For tomorrow's FOTD I might remain in the same area or I might move on. It all depends on my mood when fractal time arrives this evening. Meanwhile, up to 1/2 hour of precious time may be saved by visiting Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and downloading the completed GIF image from there, thereby avoiding the rendering entirely. The weather slowly improved through the day Friday here at Fractal Central, until at 3pm, with full sunlight, the tempera- ture reached a high of 48F 9C. The fractal cats must have approved, for they went outside just after 2pm and did not return indoors until 5pm. At one time I saw Tippy perched several feet up one of the holly trees, but he climbed down without incident. Today is starting sunny, and it is due to be warmer. This bodes well for the fractal duo. As for me, I've got a bit of work to finish, and then who knows . . . anything could happen. Until next FOTD, take care, and wait with bated breath . . . you might catch a great fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Discombobulated { ; time=0:33:28.30--SF5 on a P200 reset=2003 type=formula formulafile=slices.frm formulaname=MandelbrotN passes=1 center-mag=-1.74350051908036900/+0.000000081693461\ 53/1.972472e+011/1/-20/-4.43607331641199254e-005 params=2.003/0/0/0/0/0 float=y maxiter=18000 inside=0 outside=tdis periodicity=10 colors=000NfYKi_IkaGmcEoeGkcIgaKd_M`YOYWQUURRTTNRV\ JPXGNZCL`9Jb5Hc2Gb4Ia5Ka7M`8O`AP_BRZDTZEVYGXYHYWOX\ VUXT`WSfWQcYO`_MZ`KWbJUcHReFOfDMhBJiAHk8El6Bn49o26\ q14r28l2Bf2E`2IW2LQ2OK2RF3UE4WE5YE6`E7bE7dE8gE9iEA\ kEBnECpECrEDnGEjIFfKGbLHZNIVPJRRKNSLJUMFWMCXQITUNQ\ YTNaYKebHihEmmBpr8grEZrJQrPEIO9DK48G97JE7LJ7OO7QT7\ SY7Vb7Xg7_l7aq7cp9RpBFpC3oE5nG7mH9lJBkKCjMEjNGiPIh\ QJgSLfTNeVPeWQbbY_hdXolVusSklQaeOTZMJSKAMDGL6MK0SK\ 9UNIWPRYRZZUg`WpbYxc_u_asXcqUeoRgmOikLkzZzgFoxCqc9\ re8nf8kg7gi7dj6ak6Ym5Vn5Ro4Oq4Lr3Hs3Eu2Av27w24r65m\ A6iD7dBE`AKW9RS8XO6cJ5iF4pB3vHFjNQ_T`OZkDdv2cr7cnB\ bkFbgJadNa`S`XW`U__Qc_NgbPddQbfS_hTYjUVlWTnXQpYOnb\ SlfVjjZhoafseewhhubjzYmqTopNzzItlDvz8plFkmLenS`nYV\ odQpjLppIqjGqdEqZBqT9qN7qH5qB6mF7jJ8gN8dR9zVAZZBWb\ BTfEJNDFNCCNIJKOQITWGZbDchBio9nu7tfUcTpmWnrZlw`kwc\ ivfguhftkdtnbspars_RbTPdW } frm:MandelbrotN {; Jim Muth b=p1, z=p2, c=p3+pixel: z=z^(b)+c, |z| <= 16 } END 20.0 PAR-FORMULA FILE==================================

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