February 2004 - Fractint - mailman.xmission.com

FOTD 25-02-04 (Bite the Bullet [2])
by Jim Muth 25 Feb '04

25 Feb '04

FOTD -- February 25, 2004 (Rating 2) Fractal visionaries and enthusiasts: I am brimming over with philosophy today, both scientific and political, but unfortunately, or perhaps fortunately, because of the general turmoil, I have no time to write it. So instead of blathering, we will go directly to the abbreviated discussion of the image. Today's image is a different view of the same scene that appeared in yesterday's image. The magnitude and maxiter are the same, but, using a different formula, the render time has jumped from 9 minutes to 95 minutes. This is a fine demonstra- tion of the efficiency of the Fractint Mandel formula, which was used to calculate yesterday's image. Yesterday's Mandelbrot image showed the real(c) and imag(c) axes of the scene. Today's image shows the imag(c) and imag(z) axes. I call this orientation the 'Rectangular' because the slice through the origin of the Julibrot in this direction is shaped quite like a rectangle. When seen from this particular direction, the hole that appeared as a midget in yesterday's image is shaped more like a bullet. In recognition of this fact, and considering the plight of the local school teachers, I have named the miserable picture "Bite the Bullet". Since today's image is basically a repeat of yesterday's, complete with the same color palette, I could rate it no higher than a 2, which, combined with the render time of 95 minutes, gives an overall value of a pathetic 2, perhaps the all-time lowest value. At times like this it is best to avoid needless frustration by giving Paul a chance to render and post the image, then download- ing it from his FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The weather was cold and rainy here at Fractal Central on Tuesday. The temperature of 36F 2C, while not quite cold enough for snow, was certainly cold enough to chill the whiskers and ears of the cats, who passed the day sleeping by the heat and glancing at the birds flying past. Today is starting sunny and cold, but promises to turn warmer. The cats have yet to make their judgement on the weather. For me, I've got quite a load of work to accomplish and the local agitation, (the fractal lady is involved in the school situation), is helping none at all. I'll try to have a fractal ready by post time tomorrow, but there is no promise. Until next time, take care. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Bite_the_Bullet { ; time=1:35:29.99--SF5 on a P200 reset=2003 type=formula formulafile=slices.frm formulaname=Rectangular passes=1 center-mag=0/0/2.171274e+008/0.002123/-0.035408778\ 9311406873/-89.8977468907879 params=-0.12942475461\ 27244/0.6495253624666402/-0.1294247546127244/0.649\ 5253624666402 float=y maxiter=100000 inside=0 logmap=5777 periodicity=10 colors=000NotLnuKmwJlxLkuMjsOipPhnRglSgiUfgVeeXdbY\ c`ZcZUcbPceKciGclEcbCcTBcJ9c98c0OcORcVTcaJcSFcWBc_\ 8cc7he7eg7ch7`j6Zl6Wm6Uo6Rp5Pr5Mt5Ku5Hw5Fx8LlBQ`FM\ cIJeMGgPDiSAlW7nZ4pa1rd4of7liAikDfmFcpI`rLYuOVwRSy\ TQcSXIRcNSfRTiVUkZUncVqgWskXvoXxlWviVugUtdTrbSq_Rp\ YQnVPmTOlQNjOMiLLhJKfGJeEIdHObJTaLZ_OcZQiXSnWUsVZH\ K_ML`QMaUNbYNcaOdePeiQfmQgqRhuShySbrQYkOSdNNYLHRKC\ KI7EHKKDWQ9gW5s`1jV8bPEUJLMDRD7Y52cD6YKATREOZIJeME\ lP9mNBgMCcLDmJFnIGnHHnFJnEKoDLoBNoAOo9PeGOWNNNUNUZ\ H`bBgf5nj0og0pd0qa0rZ0sX0tU0tR0uO0vL0wJ0xG0yD0zA0z\ 80rY1tI2qN2nS3lW3iZ6fX8dYAaYC_YEXZGUZIS_KP_MN_OPYM\ RWKTUIVTGXREYPC_NAaM8cK6eI4gG2hF1gF1gF1fG1fG1eH1eH\ 1dI1JEQJFPKGOKHNLIMLJMMKLMLKNMJNOINQIOSHOUGPWFPYEP\ _DQaDQcDReCRgBSiASk9Tm9Tm8UmAUm6Vm5Vm5Wm4Wm3Xm2Xm1\ FlAGk9Hj9Hi9Ii8Ih8Jg8Jf8Kf7Le7Ld7Mc6Mc6Nb6Na6O`5O`\ 5P_5QZ4QY4RY4RX4SW3PipOlr } frm:Rectangular {; Jim Muth imag(z),imag(c) z=flip(real(pixel))+p1, c=flip(imag(pixel))+p2: z=sqr(z)+c, |z| <= 16 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 23-02-04 (The Fractal Hill [7])
by Jim Muth 23 Feb '04

23 Feb '04

FOTD -- February 23, 2004 (Rating 7) Fractal visionaries and enthusiasts: Though today's image might not be the most beautiful scene ever discovered in the Z^2+C Julibrot, it must be one of the most unusual. Viewing the image, we once again find ourselves in the East Valley area, but what has happened to the valley we know so well? Where are the elephants? In today's image there is not the slightest sign of the ponderous pachyderms that live in the vicinity. Don't panic. The elephants have not stampeded off. They have simply been squashed beyond recognition, leaving us with some- thing that resembles a surrealistic mathematical hill standing on an alien planet, under a very earthly blue sky, complete with a haze layer near the horizon. Nothing beyond the basic equal-iteration bands has been used to render the scene. The only extraordinary aspect of the image is the fact that it has been stretched in the vertical direction almost 100000 times. Things become quite squashed as we near the tip of East Valley and view it from the unimaginable direc- tion of today's image. The stretching I did on the image was necessary so that it would consist of more than a straight, featureless razor-edge. I named the image "The Fractal Hill". It does rather resemble a hill, and it most certainly is a fractal. I put some extra effort into coloring the scene, which raises its rating to a 7. When the render time of over 10 minutes is considered, the overall value comes in at a 67. And when the pre-rendered image is downloaded from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> the value increases several-fold. With lots of sun and a temperature of 50F 10C, Sunday was fair enough here at Fractal Central. The cats must have thought so also, because they spent over three hours lounging in the yard, and when they came in, only a small bit of tuna was needed to keep their moods up. Today is starting sunny and pleasant once again. We shall see how the cats' day goes. For me, it will be another relatively uneventful day -- that is unless finding a great fractal can be considered a big event. Regardless of what happens, the next FOTD will appear in 24 hours. Until then, take care, and there's a hill beyond the hill beyond the hill . . . Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ The_Fractal_Hill { ; time=0:10:23.02--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=SliceJulibrot2 passes=1 center-mag=+0.25009805052166050/+0.519661012667224\ 50/28984.82/9.451e-005/90/3.64113739159677152e-011 params=45/90/0/0/0/1e-006/0/0 float=y maxiter=100000 inside=255 logmap=297 periodicity=10 colors=000PNzQOzRPzSQzTRzUSzVTzWUzXVzYWzZXz_Yz`Zza\ _zb`zcazdbzeczfdzgezhfzigzjhzkizljzmkzmlzmmzmmzmmz\ mmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmm\ zmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzm\ mzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmzmmz\ mmzmmzlmzlmzkmzkmzkmzjmzjmzimzimzimzhmzhmzhmzgmzgm\ zfmzfmzfmzemzUmLUmMUkLUjLUiLUgLUfLUeLUdLUbLYaLZ`M_\ ZOZYQYXSXWUWUWVTYUS_TQaSPcROhQNrPLkOKbNJZKHSKGSKFS\ KESKCSKBSKASK8SK7QK6OK5MK3KK2IK1IK0IKANKKSPUXUbaZa\ aiaacaaUaaUaaA`aB`aB`aC`aC`aDcaE_aE_aF_aF_aG_aHWaH\ ZaIZaIZaJZaJZaKYaLYaLYaMYaMYaNXaOXaOXaPXaPXaQXaRWa\ RWaSWaSWaTWaUVaUVaVVaVVaWVaWVaXWbXWbYWbYWbYWbZWbZW\ b_Wb_Wb_Xb`Xb`XbaXbaXbaXbbXbbXbcXbcYbcYbdYbdYbeYbe\ YbeYbfYbfYbgZbgZbgZbhZbhZbiZbiZbiZbjZbj_bk_bk_bk_b\ l_bl_bm_bm_bn`cm_bm_bm_bm`em`emaemaembembdmcdmcdmc\ dmccmccmccmccmcbmcbmcbmcb } 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 20.0 PAR-FORMULA FILE==================================

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FOTD 22-02-04 (Where are the Elephants [3])
by Jim Muth 22 Feb '04

22 Feb '04

FOTD -- February 22, 2004 (Rating 3) Fractal visionaries and enthusiasts: Today's image is not particularly attractive. I warned that the odd planes of the Julibrot can sometimes be stressful to look at. But it is still an interesting view of what happens to the elephants in East Valley when the angle of view is changed to something totally new. In today's image we have stationed ourselves at the origin of the Julibrot, which is also the origin of the Mandelbrot set, and we are looking east toward East Valley. The four- dimensional Julibrot figure is oriented in our 3-D space so that the X-axis of the image is the imag(z) axis of the Julibrot and the Y-axis is the imag(c) axis. What we see looking east has been stretched 250 times in the vertical direction. If this had not been done, the image would have consisted of nothing but a few horizontal lines and bars. And after stretching the scene, what do we see? East Valley is sometimes called Elephant Valley because the features there resemble elephants. The name is well earned. The East Valley features resemble elephants more closely than the Seahorse Valley features resemble seahorses. But here we are in East Valley, and "Where are the Elephants"? The elephants are all around us, but only bits and pieces of them are recognizable. Look closely and you will see parts of trunks here and there, half-elephants touching trunks, and disembodied parts of bodies scattered about in a totally disorganized manner. The elephants are here indeed, but we have missed them, for, though they lie very near, they are in the fourth dimension, leaving us only hints of their true nature. After careful consideration, I decided today's image was worth no more than a rating of a below-average 3. This rating combines with the render time of 2-1/2 minutes to give an overall value of 119. The finished image has been posted to Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> from where it may be conveniently downloaded. The Saturday temperature of 50F 10C was fair enough here at Fractal Central, but the wind, which gusted to over 40mph 64kph was far too much for the cats, who spent most of the day sitting on their shelf by the window, watching the trees blowing and the birds flying by. An extra treat of tuna in the evening restored their good spirits. With nothing much to do for the rest of today, I am going to do nothing much. Sometime this evening I'll see what I can find in the Julibrot that will rate higher than today's 3. Until next time, take care, and there are more wonders in the fourth dimension than can be imagined by the mind of man. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ WheresTheElephants { ; time=0:02:31.05--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=SliceJulibrot2 passes=1 center-mag=-0.00704999421812261/+0.295991068831446\ 40/742.8395/0.004019/90/1.912220382038754e-013 params=90/90/0/90/0.27555/0/0/0 float=y maxiter=10000 bailout=9 inside=0 periodicity=10 colors=000GsLJnNLjPOfQQbSTZUVVVYRX_NYZJ`ZGbZDdYAfY\ 7hY4jY1lS8cNEWHLNCRF7X7A_ECbLFeSHhYJkdMnkOqrQsxNmr\ KhlIcfFZ`CUVAPP7KJ5FEDLHLRJSXM_bOfhRnnTutVtfQsULrG\ Gq3C`3IK3OTBY`IfhPoZTcQWSHZG8a5CdCGgJKjQOmXSpbQoVO\ nONnGLm9Km2QdJVW__OpZSqYWrX_sWbtVfuUjvTnwSqxPiyMby\ JVyHOyEGyB9y92yB1vC1sD1qF0nG0kH0iI4mI8pICsIGvIKyAU\ u2cr3`q4Yq4Vp5Sp5Po6Mo6Ko9IkCGgFFcID_KBXNATQ8PT6LV\ 5IU9OTCUSGZRJdQNjPQoSTkUVhWYeY_a_bZbdWdgSfiPhlMjnI\ mqFosCqv8sx5uz2qx5nv7ju9gsBdqD`pGYnIVlKRkMOiOLhQIj\ TGlWEmZCoaAqd8rg6tj4vm2wpFniSebdXWpPPtdOwsNsrLprJm\ rHjrFgrDdrBar9Zr7o1Yk7_hCaeIcbNe_TgWYiTckQhmNnoKsq\ GokDkeAh_7dU4aOLhGao9rv2mt5is7dr9`qBWoDSnFNmHJlJEj\ LAiN5hP1gR4eV7dYAc`DbcGafJ`iM_lPZoSYrUXuTVtSUtRTsQ\ SsPRsOQrNPrMOrLMqKLqJKpIJpHIpGHoFGoFFoEKqDOrCSsBWt\ A`v9dw8hx7ly6pz9lyBiyDeyFbyI_yKWyMTxOPxRMxTJxVFxXC\ xZ9xUCxPExKGxeOf_WaTcWMkQ } 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 20.0 PAR-FORMULA FILE==================================

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FOTD 21-02-04 (That's the Way It Is [5])
by Jim Muth 21 Feb '04

21 Feb '04

FOTD -- February 21, 2004 (Rating 5) Fractal visionaries and enthusiasts: Today's image is a simple view of the Julia set of Seahorse Valley. If this is doubted, start the included parameter file, then bring up the X screen, drop the maxiter to 100 and restart the image. After a few seconds, the screen will show a near- perfect Julia set with the inside colored a brilliant orange. Why then did I choose this very-familiar Julia set to be the FOTD for today? The answer is obvious when the maxiter is raised to 1000000. The Julia set turns out to be not a Julia set after all, but rather a slice of the Julibrot that has been double-rotated 1/10 of 1 degree from the Julia orientation. (Double rotation is a new motion, not possible in 3-D space.) This slight rotation has made a great change in the resulting almost-Julia fractal, which is now magically filled with curious detail. The detail filling the Julia set is actually a greatly magnified image of the Oblate aspect of Seahorse Valley. It has been magnified 573, or tan(89.9), times in fact. (The Oblate aspect is what appears on the screen when the real(z) and imag(c) axes of the Julibrot are pictured.) To see the unmagnified oblate aspect of Seahorse Valley, change the real(p1) and real(p2) parameters to zero. This can be done in equal increments to make things more interesting. Now, to prove that it is actually Seahorse Valley we are investigating, drop the maxiter to 1000 and change the imag(p1) and imag(p2) parameters to zero, while leaving the real(p1 and p2) parameters at zero. If this is done in equal increments, you will see the Mandelbrot set gradually take shape and rotate into its proper position, with Seahorse Valley at the center of the screen. It has been Seahorse Valley we have been investiga- ting all along. This magnification of the Mandelbrot aspect as the Julia orientation is approached is one of the most puzzling things in the Julibrot. I am reasonably certain of what is happening here, but a visualization is totally beyond me. In fact, I cannot even come close. All I can do is sit back and say "That's the Way It Is", which is the name I gave the image. The rating of a 5, when adjusted for a slow render time of almost an hour, gives an overall value of 8.5. The hour wait for the parameter file to run may be cut drastic- ally by visiting Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and downloading the completed image from there. A very pleasant Friday here at Fractal Central made for very happy cats. The temperature reached only 52F 11C, but the wind was light and the sun, which is just now clearing the holly trees in the afternoons, was warm, making the cats' time in the yard very pleasant. At the end of the day no treat was needed. For me, the work is heavier than usual for a Saturday. But it is nothing that cannot be finished in time to find a fractal. Until next FOTD, take care, and do fractals exist on the planet Pluto? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ ThatsThe_Way_It_Is { ; time=0:58:58.38--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=SliceJulibrot2 passes=1 center-mag=-4.44089e-016/3.33067e-016/0.8503401 params=89.9/90/89.9/90/-0.75/0/0/0 float=y maxiter=1000000 inside=255 logmap=yes periodicity=0 colors=000A0EB0GC0ID0KE4MD7OCAQCDSBGUBIWALY9O_9Ra8\ Uc8We7Zg6ai6dk5gm5in7km9lmAmmComDpmFqmGrm8oj9lhAii\ AfdBc_C`VCYRFVQISPLPPOMORJNYINRJgZKmhIjiHgjFdkEalD\ ZmBWnATo8Qp7Nq6Kp7Lp8Mp8Mp9NpANpAOpBOpCPpCQpDQpERp\ ERpFSpFSgIW_L_SOcKRgCUjEWiGXhIZgK_fM`eNbePcdRdcTfb\ VgaWhaYj`_k_amZcnYeoXfqXhrWjsVluUnvTowTmsSkpSjmRhj\ RggQedQcaQbZP`VP_SOYPOWMOVJNTGNSDMQAMP7MNHOLZQJcRH\ hTGiUIgWKeXLcYNaZO_`QYaRWbTUcVSdWQfYOgZMh`KiaKkcKl\ eKmfKnhKoiKqkJrlOsnRtoUuoXvo_vpbwpewphwqkxqnxqqyrt\ yrwzryzrwznuzjrzgozcmz`kzXizUgzQeyNcyJaxG_xHYwIWuI\ UsJSqJQoKOmKMkLKiLIgMHeMIcNKaNL_ONYOOWPQUPRSQQQRPO\ SOMTOKUNLVMLWLMXLMYKMZJN_IN`INaHObGOcFOcFOTEFIE7KH\ 8LJ9MMANOBORCPTDQVERYFS_GTbGUdHVgIWiJXkKYnLZpM_sN`\ uOawOdpRfiUhcXkX_mRboKerEht7kv1mt3nr4np5nn6nl8nj9o\ hAofBodDobEo`FoZGpXHpVJpTKpRLpPMqNOqLPqJQqHRqGSqIV\ kKXeM__NaUPdORfITiCUk6zl7 } 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 20.0 PAR-FORMULA FILE==================================

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FOTD 20-02-04 (Seahorse Lake [6])
by Jim Muth 20 Feb '04

20 Feb '04

FOTD -- February 20, 2004 (Rating 6) Fractal visionaries and enthusiasts: Last evening I got into a discussion with the fractal lady, who is of the opinion that I am spending too much time concerning myself with such useless things as fractals and fantasies of the fourth dimension. She seemed to think that this is something only little boys do before they grow up and learn to think like sensible, practical men. When such discussions arise, I totally agree with her opinion, leaving nothing to disagree about, but to myself I often wonder how useless the fourth dimension actually is. One thing the fourth dimension most definitely is good for is fun. And if Einstein had thought it childish to consider the fourth dimension, what kind of world would we live in today? Perhaps we would not have developed computers and discovered fractals, and today's image would not exist. Today's scene reminds me of a lake with reflections shimmering off the wave tops, but it is actually a view of Seahorse Valley sliced in an unimaginable direction. These reflections needed no special formula to bring them to life. They are an actual part of the Julibrot itself. Perhaps this area should be known as "Seahorse Lake", which is the name I gave the image. Due to time limitations, I am unable to write a description of the orientation of today's image, but I will go into the curiosities of four-dimensional geometry in future FOTD's. For now, enjoy the image. It is a very fast one. I have rated today's image at a 6, which combines with the render time of just over one minute to give an overall value of 508. The image may also be viewed by going to Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A very pleasant and sunny late-winter day with a high temperature of 56F 13C here at Fractal Central on Thursday gave the intrepid cats a long, pleasant afternoon in the yard. When evening came, they settled down without complaint. The best news is that today looks to be a repeat. For me, the work is rather heavy, but it is under control, and will be finished in plenty time for another trip to the fourth dimension to find another fractal. The fractal I find will appear as tomorrow's FOTD. Until then, take care, and the everyday world we live in is four-dimensional, so what's the fuss about? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Seahorse_Lake { ; time=0:01:11.01--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=SliceJulibrot2 passes=1 periodicity=10 center-mag=-0.0812181/5.55112e-016/3.045118/0.62/9\ 0/3.885780586188e-016 params=45/90/0/90/-0.75/0/0/0 float=y maxiter=50000 inside=0 logmap=yes colors=000dAjcAibAhaAg`Af_AeZAdYAcXAbWAaVA`UA_TAZS\ AYRAXQ9WP9VO9TN9SM9QL9OK9MJ9KH9IB9GA9EMMMQQQSUUX__\ beelpouyxntvgot`jsVeqO`oHWnARl4Nk5Pj6Qi7Rh7Tg8Ug9V\ fAWeAYdBZdC_cC`bDbaEc`Fd`Ff_GgZHhYIiYIkXJlWKmVKnVH\ gNEeFBc7Ca8D_8EY9FW9GU9GUAHUAIUBJUBKUBKUCLUCMUCNUD\ OUDOUEPUEQUERUFSUFSUFTXHTZJU`LUbMVdOVfQWhSWjTXlVXn\ XXpYTqWPoVLmUHkTDiSCgQBeOBcNAaLA_K9YI9WH8UF8WEAYGC\ ZHE_JG`KIaLKbNLcONdPPeRRfSTgUVhVWiWYjY_kZal_cmaenb\ focdqaer`gsZitYkuWmvVowUquSstRurQwqPzoNwnMumLskKqj\ IohHmgGkfFidDgcCeaBc`Aa_9_`CY`EW`GUaJSaLSaNTbQVbSW\ bUXbWYcVZdU_dT`eSafSbfRcgQdhPehPfiOfiNgjMhkLikLjlK\ kmJlmImnInoHooGppFppFnqImqKlrNjrPisRhsUftWetYdu`cu\ bavd`vg_wiYwkXxnWxpVxrWvqXtqYrqZpq_nq`lqajpbhpcfpd\ dpebpe`pfZogXohVoiTojRokPolNnmLnnJnoHnpFnpEnmDlkDk\ iDjgDieDhcDgaDf_DeYDdAKUWDcq7pp6lp6ho5eo5ao4Yn4VZT\ c_Re`QfaOgbMhcLidJjeIlfGm } 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 20.0 PAR-FORMULA FILE==================================

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FOTD 14-02-04 (Unwhisked Whiskbroom [5])
by Vortex Swirling 20 Feb '04

20 Feb '04

Jonathan, Thanks. Looks like Fractint once again has more flexibility than I can imagine. By changing the 3rd setting from the bottom from 1 to 2 it achieved what I was trying to do. --- Outgoing mail is certified Virus Free. Checked by AVG anti-virus system (http://www.grisoft.com) Version: 6.0.590 / Virus Database: 373 - Release Date: 2/16/2004

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FOTD 14-02-04 (Unwhisked Whiskbroom [5])
by Vortex Swirling 20 Feb '04

20 Feb '04

Edwin, I'll take note of that map, I find those color transitions quite nice. I tried rotating the "test par" image and found it to have a very cool effect, a sort of strobe with changing colors moving up slowly. General question. For coloring, is there a way to force the (for a lack of a better word) pool color to not change? What I noticed during the color rotation cycle is that the background goes through the color progressions. I've always accepted that it is this way, but it might be nice to be able to lock that background into a single color. I would have liked that to remain black all through the color rotation. I don't think it can do that. Now more specifically for Edwin, is this to say that there is something Fractint can't do? That you had to write a separate program (that I being an XP head can't run)? I know a Mandelbrot can be converted into a Julia as it is. This would seem to mean that if there were an option to only rotate by a few degrees (if I've been understanding Jim Muth's talks on this) it might be able to do this. While rotating into these other planes it might even be fast enough to do it as a movie? Or at least make a movie of it by collecting snapshots quite quickly. Just some thoughts here, I'll let the experts have at it if they want. --- Outgoing mail is certified Virus Free. Checked by AVG anti-virus system (http://www.grisoft.com) Version: 6.0.588 / Virus Database: 372 - Release Date: 2/13/2004

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Re: FOTD 19-02-04 (The Golden M [5])
by Jim Muth 19 Feb '04

19 Feb '04

At 01:50 PM 2/19/04 -0600, Paul Lee wrote: >But, this [outage] has only affected one of my websites at >AT&T. The actual webpage for today's FOTD by Jim Muth may >be viewed by going directly to the following URL: > > http://home.att.net/~Fractals_3/FotD_04-02-19.html > >Hopefully, service will be restored shortly. :-) I could save a few steps for those who pick up the FOTD's from Paul's web page by from now on listing the URL that will take the viewer directly to the FOTD of that day. It would be easy to adjust the year-month-day part of the address, but I would need to know when the ~Fractals_3 part of the URL changes. Jim M.

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FOTD 19-02-04 (The Golden M [5])
by Jim Muth 19 Feb '04

19 Feb '04

FOTD -- February 19, 2004 (Rating 5) Fractal visionaries and enthusiasts: With an unexpected load of work to get out, I have time for only a short discussion of today's image. The image is a scene in Seahorse Valley. It looks nothing like the familiar valley because it is sliced through the Julibrot in a new direction. To visualize the direction, imagine the Seahorse Valley area of the M-set extending as a 3-D figure in front of and behind the screen as it would when the real and imaginary parts of Z are perturbed equally. Then imagine a horizontal slice through this 3-D figure cut 0.05 above the X-axis. And then imagine yourself looking down on this slice from above. Or better, forget the imagination. From this angle, Seahorse Valley appears as a 'bridge' spanning the width of the Julibrot. The impossibly straight edges are typical of scenes in the odd planes. There is an explanation for why this is so, but it will have to wait until I have more time to write it. Until then, enjoy Seahorse Valley as you have never seen it before. I named the image "The Golden M". The reason for the name is obvious when the image is seen. The rating of an average 5 combines with the render time of 16 minutes to give an overall value of 31. The value may be increased by downloading the finished GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The sun shone and the temperature rose to 46F 8C on Wednesday here at Fractal Central. The cats enjoyed the pleasant conditions to the best of their ability, and when the sun went down, came inside without complaint. Only a small treat was needed to satisfy their meager desires. Today is starting cloudy, but it is still mild. It will be another good day for the cats. For me, it remains to be seen how the trip into the fourth dimension will go. But however it goes, whatever I find there will appear as the next FOTD. Until then, take care, and keep your feet on the ground and your head in the clouds. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ The_Golden_M { ; time=0:16:10.54--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=SliceJulibrot2 passes=t logmap=yes center-mag=-0.00128325508607199/-0.000000000000004\ 55/159.0018/0.01505/90/-5.05012698326368081e-014 params=45/90/0/0/-0.75/0.05/0/0 float=y maxiter=100000 inside=0 outside=summ periodicity=10 colors=000NuPNrQOpSOmTPkVPhWQfYQcZR``RZaSWcSUdTRfT\ PgUMiUKjWJiXIiZHh_GhaFgbEgcEgeDffCfhBeiAek9dl8dm8d\ bIaTRZJ`W9iTDeVHbWL_XPXYTUZXR_`OadLbhIclFdpCet9fw6\ gqHdlRbg`_hjYmqWmoTmmQmkNmiJmgFmeBmd8meAmfCriAml9m\ n7uq6xr5uo4sk4qh4qe4pc4oa4n_4mZ3mY3nX3oW3pV3qU3rZ3\ rV3rT7mRBhOFcMIZJMUHQPFUKFXEH`8Id7Kh6Mk5No4Ps3Rw3S\ z8XrD`kIddNhYSmRXqKauDfy6bu9_qCXmFTjIQfKYbNJ_QGWTD\ SV9PYaL`mHmcEeUHrcKmcMcmKccScEUcHXcJZcLacfdhQfmSim\ VlmXnmZqm`smZpmYmmWmmVmmTmmSmmQmmOmmNmmLcmacmZQmXO\ mUMmRKmPImMGoKEpGGqDHrAJr7Ks4Ls8NtCOtGPtKRtOStSTtW\ Vt_WtcXtgZtk_to`tsbtwctzdtxfqvgouhmsjmqkmplmnmmlon\ kpoiqphrqfqrepsdotcnubmvalw`kxblycmzdnzfozgpzhqzir\ zkszltzmuzovzpwzqxzryzpzzozzmzzlzzjzzizzhzzfzzezzc\ zzbzz`zz_zzZzzbzzezzhzzkzznzzozzpzzpzzqzzqzzrzzszz\ szztzztzzuzzvzzvzzwzzwzztzzrzzozzmzzjzzhzzfzzczzaz\ z_zzYzzWzzUzzSzzQzzOzzMzz } 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 20.0 PAR-FORMULA FILE==================================

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-32767 limit on zoom-out demo.
by SherLok Merfy 19 Feb '04

19 Feb '04

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