May 2002 - Fractint - mailman.xmission.com

FOTD 15-05-02 (Mandelia [6])
by Jim Muth 22 May '02

22 May '02

FOTD -- May 15, 2002 (Rating 6) Fractal visionaries and enthusiasts: As has been obvious for some time, I am fascinated by things that cannot be comprehended by the human mind. When these things are irrational, some on the philofractal list feel that I am indulging in fantasy, but none can dispute that the Mandelbrot set and its associated Julia sets comprise a single four-dimensional object that in a sense most certainly does exist, yet cannot be comprehended by the human mind. This 4-dimensional object is sometimes called the Julibrot figure. Depending on the direction and location in which this 4-D figure is sliced, either Julia sets or perturbed Mandelbrot sets will appear. But in addition to producing Julia and Mandelbrot sets, the Julibrot can be sliced in other directions which produce hybrid sets that are neither Julia nor Mandelbrot sets, but combine the features of both. Today's image is one of these hybrid sets. I could have named the image "Julibrot", but that word has become hackneyed, so I named the image "Mandelia", a name which combines the names of both families of sets and also has a nice sound to it. I rated the image a 6. To produce today's image, I began with the Julia set of Seahorse Valley, which normally appears as a chain of empty bays, but I did not slice the Julibrot in exactly the Julia direction. Instead, I double rotated the slice 1/100 degree and 1 degree from the Julia direction. This tiny rotation produces a tremendous difference in the resulting image. (Curiously, the values of the rotation are quite critical this close to the Julia direction.) The overall shape of the fractal is that of the Julia set of Seahorse Valley. But the chain of bays is no longer empty. Instead of a dull, blank inside, we see an inside filled with detail quite unlike any normally seen in Julia or Mandelbrot sets. The valley itself appears at the exact center of the image, and the great spirals that lie in the area are also in evidence, appearing where the many unadorned valleys of the pure Julia set would normally lie. I have tilted the image to give it a more dynamic feeling, and colored it with the basic equal-iteration-band method. I used the basic coloring method to assure that the unusual effects in the image are actually a part of the fractal and not a result of a fancy coloring system that distorts and sometimes totally hides the original fractal. Due to the unusually high maxiter and the periodicity setting of 15, both of which are necessary, the parameter file is a rather slow one, taking 25 minutes on my machine. But Paul and Scott are here to save such frustration, and will soon have the completed GIF image file posted to their web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> from where it may be downloaded with ease. The fractal weather Tuesday was chilly (64F 18C) and very windy, with heavy threatening clouds that finally released a damaging rain squall at 7pm. When the squall passed, a glorious double rainbow appeared. (All rainbows are double, but the second bow, which lies outside the main bow, is usually too faint to be seen.) Then the sun set peacefully. The dynamic duo, who were still shell-shocked from the hailstorms of Sunday and Monday, dashed for cover when the wind started roaring and things started flying around again, and didn't reappear for several hours. Due to a power failure Sunday evening, I am a bit behind on the FOTD CD. But a half-hour extra work today will make up the shortfall. And it's now time to get busy. Until next time, take care, and it all depends on which direction you view your fractals. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ Mandelia { ; time=0:25:37.91--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=multirot-XY-ZW-new function=flip/ident passes=t center-mag=3.19189e-016/6.66134e-016/0.99\ 3388/1/55/3.88578058618804789e-016 params=89/89.99\ /2/0/0/0/-0.75/0 float=y maxiter=75000 logmap=yes inside=0 periodicity=15 colors=000N7PL8SL9SKGSJ9TI\ CUHDVGEWEFXCGYAH_8L_6P_4Wa2_a0ca0ha0nc3tc9ycDzcFzf\ HzfJzfLzfNzfPzfRzfUzfWzfUz_UzUUzNRzHRzBRz5_z0fv0mn\ 0tf0zY0zR0zJ0zD0zH0tL0fN0RR1FWB3YJ7cFBjBDn9Hv5Jz3N\ z0Pz0Uz0Wz0Yz0Yz5YzB_zJ_yP_tWrnBzj0zh0zz0zz0zz0zz3\ zv7zrBzmFzhJzcNz_RzWWzR_zNczJfzHhzHhzHhzHhzHjzHjzH\ jyHjvHmtHmrHmnHmmDjjBhj7fh5ch3af0_f0_c0Ya0Wa0U_0R_\ 0PY0NY0Nj5YyUhzttzzzzzyzzrzzjzzcvzYrzRmzchzlcyjlwj\ tvjyumzsnzqrznrzktzitzfvycvtaymayh_za_zY_z__aa_Hc_\ 0f_0hY0jW0mU0nT0rS9tRJvQUyPPzOLzRHzUDzXBz_7vb3re0n\ h0jk0fn0cq0_t0Ww0Uz0Nz0Hy0Dv07t01r00n00m00j00h00f0\ 0c00a00_00YLYWzWUyURrRPmWPhYPc_P_aPWfRUhRPjRLmRHrU\ FtUBvU7yU3zU1nW3fY3YY3P_3Ha39a3J_FUYPcWanUmyRyfYvR\ cvBjt0rt0yr0zr0nh0ea1gUBhNNhHYc9jU3vK0zA9z0Jz0Uz3c\ zDnz9mz5mtAmjHmaLmWOjNRjFUj9Xj1_j0bh0eh0hh0kh0nh0q\ j0tm0wn0zr0zt0zv0zy0zz0zz0zz0zz0zz0zt0zm0zf3zf3zf } frm:multirot-XY-ZW-new {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p3, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4: z=z^(p2)+c, |z| <= 36 } END 20.0 PAR-FORMULA FILE==================================

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Re: [Fractint] At it again...
by Andrew Coppin 22 May '02

22 May '02

>From: "Morgan L. Owens" <packrat(a)nznet.gen.nz> >Reply-To: fractint(a)mailman.xmission.com >To: fractint(a)mailman.xmission.com, fractint(a)mailman.xmission.com >Subject: Re: [Fractint] At it again... >Date: Tue, 21 May 2002 10:25:27 +1200 > >At 00:14 21/05/2002, Franktal Gallery wrote: >>>From: "Morgan L. Owens" <packrat(a)nznet.gen.nz> >>> >>>I think it's probably more likely due to the difficulty of manufacturing >>>optics, mirrored spheres, and CCDs/film emulsions to the required >>>precision/resolution. >> >>No, what I meant was, if you build a physical mirror >>ball stack, with a physical camera mounted inside >>(no matter how precise/small), the resultant picture >>would be modified by the infinite reflections of the >>camera itself. So, you'd need a virtual camera to >>make sure there's no perturbation introduced. > >Oh, right; very true - the same situation in Andrew's case, of >course, where his own head would keep getting in the way of his view of >the infinite corridor. But there's no "uncertainty principle" here. > >Morgan L. Owens >"'Cos right before my eye" Yes, it does take a lot of effort to find a spot where I can SEE infinite reflections of myself (my head is small, but my hair is not). It also attracts unwanted attention from the other shoppers for that matter... Andrew "Well, what else is a guy do to when forced to go shopping with mum? :S" _________________________________________________________________ Chat with friends online, try MSN Messenger: http://messenger.msn.com

2 1

homemade watch
by Guy Marson 21 May '02

21 May '02

Hi fractinters, homeworkers.. although the numbers are not correctly positioned, zhis is dedicated to my daughter.. watch-1 { ; Version 2002 Patchlevel 3 reset=2002 type=formula formulafile=uhr-mand.frm formulaname=uhr-mand center-mag=-0.10261656595166480/+0.94415252797943690/757.5809/1/7.999999\ 99999890132/9.29110954839273973e-013 float=y maxiter=250 inside=0 logmap=old colors=000w02<5>d0Aa0CZ0D<3>M0II0KG0I<3>708506303000<2>01612913B14D14F<6\ >39V3AX3BZ<2>4De5Eh4Kg4Of3Sd<3>2ba2e`1g`<3>1oZ0pY0rY0tX0vW0vX<12>0TG0RF0\ PE<3>0F80C70A6<2>032000202<3>B0CD0FG0HI0K<4>Z0Da0Ce0A<2>o05s04w01y00<3>y\ N0zS0zY0<3>zt0yy0zu0<3>zZ0zT0zN0<3>z00<6>d0Aa0CZ0D<3>M0II0KG0H<3>5063030\ 00<3>11A11C21F<2>31L31O42Q42T42V<3>63d63g63i69i5Gh4Mf<3>2Zb2ab2ca<3>1k_1\ mZ0oZ0qY0rX0tX0vX0vX<12>6TK7RJ7PI<3>9FE9CDAAC<2>B39C08C09<3>G0GH0II0KL0J\ O0HS2GV0E<3>h08l06o05<2>z00<4>zT0zY0zc0<2>zt0yy0zu0<9>z00 } watch-3 { ; Version 2002 Patchlevel 3 reset=2002 type=formula formulafile=uhr-mand.frm formulaname=uhr-mand center-mag=-0.10285122098288750/+0.94403293733755530/1.08674e+009/1/2.99\ 99988845146679/-0.000451242073825117163 float=y maxiter=28460 inside=0 logmap=2846 colors=0002jS<7>6TK7RJ7PI<3>9FE9CDAAC<2>B39C08C09<3>G0GH0II0KL0JO0HS2GV0\ E<3>h08l06o05<2>z00<4>zT0zY0zc0<2>zt0yy0zu0<3>zZ0zT0zN0<3>z00<5>g09d0Aa0\ C<3>P0HM0II0K<3>90B708506303000<2>01612913B14D14F<6>39V3AX3BZ<2>4De5Eh4K\ g4Of3Sd<3>2ba2e`1g`<3>1oZ0pY0rY0tX0vW0vX<12>0TG0RF0PE<3>0F80C70A6<2>0320\ 00202<3>B0CD0FG0HI0K<4>Z0Da0Ce0A<2>o05s04w01y00<3>yN0zS0zY0<3>zt0yy0zu0<\ 3>zZ0zT0zN0<3>z00<5>g09d0Aa0C<3>P0HM0II0K<3>809506303000<4>11C21F21H31J3\ 1L<3>42V52Y53_<3>63i69i5Gh4Mf<3>2Zb2ab2ca<3>1k_1mZ0oZ0qY0rX0tX0vX0vX<3>2\ mT } frm:uhr-mand { ; ; 'periodicity=0' and 'passes=1' recommended x=real(scrnpix)/real(scrnmax), y=(imag(scrnmax)-imag(scrnpix))/(rea\ l(scrnmax)*0.75), z=x+flip(y) x1=1.5*x chr11 = y<x1+0.245&&y>x1+0.23094&&y>-x/1.5+1.26333||(x>0.48491&&x<0\ .49271) x2=2.5*x chr22 = abs(cabs(z+(-0.51266,-0.95305))-0.01305)<0.0039&&(y>0.95305\ ||y>-x/1.22571+1.3713)||(y<1.22571*x+0.31021&&y>1.22571*x+0.29787&&\ y<-x/1.22571+1.3713)||y<0.9178&&x>0.49571&&x<0.52961 test1 = chr11||chr22&&y>0.91&&y<0.97 chr13 = y<x1+0.252&&y>x1+0.23794&&y>-x/1.5+1.24867||(x>0.47491&&x<0\ .48271) chr24 = abs(cabs(z+(-0.50266,-0.94505))-0.01305)<0.0039&&(y>0.94505\ ||y>-x/1.22571+1.35515)||(y<1.22571*x+0.31446&&y>1.22571*x+0.30213&\ &y<-x/1.22571+1.35515)||y<0.9098&&x>0.48571&&x<0.51961 test2 = chr13||chr24&&y>0.902&&y<0.962 chr15 = y<x1+0.46&&y>x1+0.44594&&y>-x/1.5+1.06667||(x>0.29491&&x<0.\ 30271) chr16 = y<x1+0.42144&&y>x1+0.40738&&y>-x/1.5+1.08381||(x>0.32062&&x\ <0.32842) test3 = chr15||chr16&&y>0.84&&y<0.9 chr17 = y<x1+0.4635&&y>x1+0.44944&&y>-x/1.5+1.055||(x>0.28791&&x<0.\ 29571) chr18 = y<x1+0.42494&&y>x1+0.41088&&y>-x/1.5+1.07214||(x>0.31362&&x\ <0.32142) test4 = chr17||chr18&&y>0.833&&y<0.893 chr19 = y<x1-0.11&&y>x1-0.12406&&y>-x/1.5+1.32||(x>0.67491&&x<0.682\ 71) test5 = chr19&&y>0.84&&y<0.9 chr110 = y<x1-0.1065&&y>x1-0.12056&&y>-x/1.5+1.30833||(x>0.66791&&x\ <0.67571) test6 = chr110&&y>0.833&&y<0.893 chr111 = y<x1+0.485&&y>x1+0.47094&&y>-x/1.5+0.81||(x>0.16491&&x<0.1\ 7271) chr012 = abs(cabs(z+(-0.19266,-0.71305))-0.01305)<0.0039&&y>0.71305\ ||(abs(cabs(z+(-0.19266,-0.68695))-0.01305)<0.0039&&y<0.68695)||(((\ x>0.17571&&x<0.18351)||(x>0.20181&&x<0.20961))&&y>0.68695&&y<0.7130\ 5) test7 = chr111||chr012&&y>0.67&&y<0.73 chr113 = y<x1+0.4885&&y>x1+0.47444&&y>-x/1.5+0.79833||(x>0.15791&&x\ <0.16571) chr014 = abs(cabs(z+(-0.18566,-0.70605))-0.01305)<0.0039&&y>0.70605\ ||(abs(cabs(z+(-0.18566,-0.67995))-0.01305)<0.0039&&y<0.67995)||(((\ x>0.16871&&x<0.17651)||(x>0.19481&&x<0.20261))&&y>0.67995&&y<0.7060\ 5) test8 = chr113||chr014&&y>0.663&&y<0.723 chr215 = abs(cabs(z+(-0.80695,-0.71305))-0.01305)<0.0039&&(y>0.7130\ 5||y>-x/1.22571+1.3714)||(y<1.22571*x-0.29051&&y>1.22571*x-0.30285&\ &y<-x/1.22571+1.3714)||y<0.6778&&x>0.79&&x<0.8239 test9 = chr215&&y>0.67&&y<0.73 chr216 = abs(cabs(z+(-0.79995,-0.70605))-0.01305)<0.0039&&(y>0.7060\ 5||y>-x/1.22571+1.35869)||(y<1.22571*x-0.28893&&y>1.22571*x-0.30127\ &&y<-x/1.22571+1.35869)||y<0.6708&&x>0.783&&x<0.8169 test10 = chr216&&y>0.663&&y<0.723 chr917 = abs(cabs(z+(-0.15695,-0.47695))-0.01305)<0.0039&&y<0.47695\ ||abs(cabs(z+(-0.15695,-0.50305))-0.01305)<0.0039||(x>0.1661&&x<0.1\ 739&&y>0.47695&&y<0.50305) test11 = chr917&&y>0.46&&y<0.52 chr918 = abs(cabs(z+(-0.14695,-0.46695))-0.01305)<0.0039&&y<0.46695\ ||abs(cabs(z+(-0.14695,-0.49305))-0.01305)<0.0039||(x>0.1561&&x<0.1\ 639&&y>0.46695&&y<0.49305) test12 = chr918&&y>0.45&&y<0.51 x3=0.7*x chr319 = abs(cabs(z+(-0.83389,-0.47695))-0.01305)<0.0039||abs(cabs(\ z+(-0.83389,-0.50305))-0.01305)<0.0039&&(y>-x3+1.08677||y<x3-0.1067\ 7||x>0.83389) test13 = chr319&&y>0.46&&y<0.52 chr320 = abs(cabs(z+(-0.82389,-0.46695))-0.01305)<0.0039||abs(cabs(\ z+(-0.82389,-0.49305))-0.01305)<0.0039&&(y>-x3+1.06977||y<x3-0.1097\ 7||x>0.82389) test14 = chr320&&y>0.45&&y<0.51 chr821 = abs(cabs(z+(-0.19695,-0.26695))-0.01305)<0.0039||abs(cabs(\ z+(-0.19695,-0.29305))-0.01305)<0.0039 test15 = chr821&&y>0.25&&y<0.31 chr822 = abs(cabs(z+(-0.18995,-0.25995))-0.01305)<0.0039||abs(cabs(\ z+(-0.18995,-0.28605))-0.01305)<0.0039 test16 = chr822&&y>0.243&&y<0.303 x4=1.8*x chr423 = y<x4-1.134&&y>x4-1.15006&&y>0.27||(x>0.80335&&x<0.81115)||\ (y>0.2622&&y<0.27&&x>0.78&&x<0.81715) test17 = chr423&&y>0.25&&y<0.31 chr424 = y<x4-1.1284&&y>x4-1.14446&&y>0.263||(x>0.79635&&x<0.80415)\ ||(y>0.2552&&y<0.263&&x>0.773&&x<0.81015) test18 = chr424&&y>0.243&&y<0.303 x7=2.75*x chr725 = y<x7-0.74743&&y>x7-0.77025||y>0.1422&&x>0.3&&x<0.3318 test19 = chr725&&y>0.09&&y<0.15 chr726 = y<x7-0.73518&&y>x7-0.758||y>0.1352&&x>0.293&&x<0.3248 test20 = chr726&&y>0.083&&y<0.143 chr527 = abs(cabs(z+(-0.6789,-0.1089))-0.015)<0.0039&&(y<0.1089||x>\ 0.6789)||(x>0.66&&y>0.12&&x<0.6978&&(x<0.6678||y>0.1422||(y<0.1278&\ &x<0.6789))) test21 = chr527&&y>0.09&&y<0.15 chr528 = abs(cabs(z+(-0.6719,-0.1019))-0.015)<0.0039&&(y<0.1019||x>\ 0.6719)||(x>0.653&&y>0.113&&x<0.6908&&(x<0.6608||y>0.1352||(y<0.120\ 8&&x<0.6719))) test22 = chr528&&y>0.083&&y<0.143 chr629 = abs(cabs(z+(-0.50695,-0.07305))-0.01305)<0.0039&&y>0.07305\ ||abs(cabs(z+(-0.50695,-0.04695))-0.01305)<0.0039||(x>0.49&&x<0.497\ 8&&y>0.04695&&y<0.07305) test23 = chr629&&y>0.03&&y<0.09 chr630 = abs(cabs(z+(-0.50695,-0.06605))-0.01305)<0.0039&&y>0.06605\ ||abs(cabs(z+(-0.50695,-0.03995))-0.01305)<0.0039||(x>0.49&&x<0.497\ 8&&y>0.03995&&y<0.06605) test24 = chr630&&y>0.023&&y<0.083 test=test1||test3||test5||test7||test9||test11||test13||test15||tes\ t17||test19||test21||test23 test0=test2||test4||test6||test8||test10||test12||test14||test16||t\ est18||test20||test22||test24 z=c=pixel: z=z*z+c |z|<=4&&test0==0 } have fun, Guy

3 7

FOTD 21-05-02 (Cutoff Disconnected [6])
by Jim Muth 21 May '02

21 May '02

FOTD -- May 21, 2002 (Rating 6) Fractal visionaries and enthusiasts: Do not give up hope. The FOTD CD is past the halfway point, and sometime this summer the 1,700 or so fractal images and discussions will be available for distribution. Even better news is that, when the CD is completed, the ongoing FOTD will return to the daily schedule, while hopefully increasing in quality. The midget at the center of today's image, which exists in the fractal created by the formula (Z^3)+0.4(Z^5)+C, is located in the suburbs of a larger midget in a cut-off feature deep in an un-named valley of its bloated parent fractal. Since the feature in which today's midget lies is cut off from the main body of the fractal, the midget itself is cut off from its surroundings. I needed to include the <mathtolerance=/1> entry in the parameter file because of the magnitude of the image, which, at close to 9*10^12, is in the borderline range where strange things begin to happen. In fact, strange things are already happening. The pattern surrounding the midget is infinitely disconnected. Regardless of how close to the actual shore-line of the midget a particular feature lies, that feature will be disconnected from the main body of the midget. The situation is somewhat similar to that of the Newton's images, where the areas leading to different roots lie adjacent to each other with no space between them, yet at no point do they actually touch. The boundaries between the basins are fractal in nature. I have named today's image "Cutoff Disconnected", a redundant name that emphasizes the nature of the midget at the center. I rated it a 6, a rating I have been using quite a lot since cutting the frequency of the FOTD's by 2/3. The image is nice, it is interesting, it is curious, but such words really mean nothing. IMO, today's image is worth no more than the present rating. With a render time in the vicinity of 20 minutes, the parameter file of today's image is a bit of a drag to run. Wise fractalists, (that is everyone), will let Paul and Scott do the rendering, and download the completed GIF image from one of their web sites. Paul's site is at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Scott's is at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Monday here at Fractal Central was mostly sunny, but with occasional cloudy periods. The chilly temperature of 59F 15C combined with the breaks in the periods of sun kept the dynamic duo of fractal cats dashing in and out all afternoon. As for myself, I've got to dash off to finish some important work so that I can get back to the fun work on that FOTD CD, which despite fears is progressing just a bit behind schedule. I shall return on the 24th with another fractal to amaze and delight even the mathematically challenged. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ CutoffDisconnected { ; time=0:22:23.97--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=ident passes=1 center-mag=+0.09846970716854085/-0.977478678397672\ 90/8.71082e+012/1/-144.990106256018947/-0.00765988\ 837549030216 params=1/3/0.4/5/0/0/0/0 float=y maxiter=2000 inside=0 logmap=446 periodicity=10 mathtolerance=/1 colors=000ONTRQWTTZWVaZYd``gccjee\ lggmhinjkpkmqmnrnntpouqpvspxtpzuozrowpornomlphjqdh\ rafs_dsYbtV`uTZvQXwOVxMTyJRzHPzF_ze`wdardcmbehagc`\ ic_kcZmdYoeXqgWshVujUwkTxlSneOdZKVSGAADAAERNETOEWP\ EYQF`RFbSFeTFhUGjVGmWGoXGrYHtZHw_Hy`HHWJJXMLXOMXQO\ XSQXURXWTXYVX_WXaYXc_Xe`XgTVaMUWFTR8SL1RG4OJ7MLAKO\ CIQFGTIDVKBYN9_Q7bS5hQ6cP6cO6bM6bL6aK6aI6`H6`G6_E6\ _D6ZC6ZBBbBFfBJiBNmBRpBVtBZwD`uEbtFdsGeqHgpJioKkmL\ llMnkNpiPrhQsgRueSwdTxcRq`PkYNeVL_TJUQHONFILGKMGMM\ GNMGPMGQMGSMGTMGVMGWMGYMGZMG`MGaMGcMGdMI`LJXLLTLMQ\ LOMLPIKRFKSBKU7KV4KT4IS4HR4FQ4EO4CN4BM4AL48K47I45H\ 44G42F41E40MgXHbPCZI7UB2Q4AUDHYLOaUVdaSb`Qa_O`ZM_Y\ KZXIYWFXVDWUBVT9US7TR5SQANNEILJDIN9GO7BR8CU9DXAE_A\ FbBGeCHhCHkDInEJqEKtFLwGMzIMwKLuMKrOKpQJnSJkUIiWHf\ YHd_GbaG_cFYeEVgETiDRkDTmHUmKWmNXmQYmT_mX`m_bmbcme\ dmhbmgamf`me_mdZmcYmbWmaVm`Um_TmZSmYRmYMmQ } frm:MandelbrotMix2 {; 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 20.0 PAR-FORMULA FILE==================================

1 0

Re: [Fractint] At it again...
by Franktal Gallery 20 May '02

20 May '02

>From: "Morgan L. Owens" <packrat(a)nznet.gen.nz> > >I think it's probably more likely due to the difficulty of manufacturing >optics, mirrored spheres, and CCDs/film emulsions to the required >precision/resolution. No, what I meant was, if you build a physical mirror ball stack, with a physical camera mounted inside (no matter how precise/small), the resultant picture would be modified by the infinite reflections of the camera itself. So, you'd need a virtual camera to make sure there's no perturbation introduced. Regards, Miguel > >At 02:29 20/05/2002, Franktal Gallery wrote: > >>Andrew, you might like to check out my ray-traced fractals >>made from infinite reflections inside a stack of mirrored >>spheres. I think these pictures show something impossible >>to reproduce in the real world, because of the perturbation >>introduced by a real camera. This seems related to the >>uncertainty principle, I guess.... The virtual camera >>overcomes this obstacle. _________________________________________________________________ MSN Photos is the easiest way to share and print your photos: http://photos.msn.com/support/worldwide.aspx

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Fwd: Re: [Fractint] At it again... (threecircles1 fix)
by Morgan L. Owens 20 May '02

20 May '02

>I've just started on another where each pixel is coloured according to how >many reflections a ray starting from that point goes through before >escaping the system, but at the moment it's still a bit buggy: Oh, of course. That's what happens when I'm not reading what I'm typing. In threecircles1 the line direction=cos(theta)+i*sin(theta) ; We'll use a vector representaion ; of the direction should of course be direction=cos(theta)+(0,1)*sin(theta) ; We'll use a vector representaion ; of the direction Morgan L. Owens "I'm so sorry, I was miles away."

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Second test
by JimMuth＠aol.com 19 May '02

19 May '02

this is the second test

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test (par included)
by Franktal Gallery 19 May '02

19 May '02

This is a test message. A par is included to comply with netiquette ISO standards. I need to see if my messages are reaching the list (I'm not receiving the usual copy). Regards, Miguel --- A_Love_Supreme { ; by Miguel Fliguer - 1999 ; uses A0 ; Palette: MIGMULTI.MAP ; Title from John Coltrane's masterwork reset=1960 type=formula formulafile=miguel.frm formulaname=a0 function=sqrt/recip/sqr/cotanh center-mag=-0.56828087873239030/-0.16055600848866020/1278.823/1/119.978/\ 0.035 float=y logmode=fly decomp=256 colors=eVM021010000220<24>wwu<9>fYNeVKeVK<3>ZL6XI2VF0<10>wU0<22>QD0OC0OC\ 0OC0<7>w00<22>OO0<22>ww0<27>II0HK2<12>2tq0wu0ut<16>0FT<18>0Uu<36>033 } frm:a0 {; (c) by Miguel Fliguer z=c=pixel: z=fn1(z/fn2(z/fn3(z/fn4(z))))+c |z|<4 } _________________________________________________________________ Chat with friends online, try MSN Messenger: http://messenger.msn.com

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Test
by JimMuth＠aol.com 19 May '02

19 May '02

Is the list working?

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Re: [Fractint] At it again...
by Franktal Gallery 18 May '02

18 May '02

Andrew, you might like to check out my ray-traced fractals made from infinite reflections inside a stack of mirrored spheres. I think these pictures show something impossible to reproduce in the real world, because of the perturbation introduced by a real camera. This seems related to the uncertainty principle, I guess.... The virtual camera overcomes this obstacle. Best regards, Miguel Fliguer . Buenos Aires, Argentina Franktal Gallery - http://www.geocities.com/franktal2002 >From: "Andrew Coppin" <orphi69(a)hotmail.com> ><snip> >I've come up with the "hall of mirrors" analogy. Have you ever been to a >department store where they have mirrors on the columns supporting the >roof? >If you stand between two columns (assuming both have mirrors), you can see >an infinite number of reflections of yourself! But, of course, the mirrors >are always slightly greenish (never any other colou... mmm....) and never >completely flat. > >The Julia sets are the same. It seems that the infinite progression of >spirals/forks/dust are mirror images of one single such feature. _________________________________________________________________ Chat with friends online, try MSN Messenger: http://messenger.msn.com

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