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FOTD 24-05-02 (Hexagons and Circles [7])
by Jim Muth 24 May '02

24 May '02

FOTD -- May 24, 2002 (Rating 7) Fractal visionaries and enthusiasts: To begin, I will answer a few questions about the FOTD CD that must be causing unlimited concern to the members of the list. :-) Q -- When will the CD be ready? A -- Before the end of (northern hemisphere) summer if all goes well. Q -- Will there be a charge for the disk? A -- Yes -- blank disks are not free. Q -- How much will the charge be? A -- I haven't decided. Q -- Will the disk have a graphic-user-interface? A -- At this point, no. Q -- What kind of indexing will the disk have? A -- That depends on how much time I have to work on it. Q -- Will the Fractint program be included on the disk? A -- Probably not. The notice that the program may not be sold is still at the bottom of the Fractint opening credits screen. And those who would want the disk will probably have a more recent version of the program by the time they receive the disk. Finally, those who have recently discovered fractals have probably done so with one of the Windows programs, and would have little interest in a DOS program. The disk is intended to be a convenience rather than a commercial success. Q -- Are the above answers fixed in stone? A -- No! As for today's image, I must confess a bit of thievery. I found today's fractal image while noodling with a formula named Klein_tri_lattice that was posted recently to the Fractint list. I have no time to check through my old mail to see who wrote the original formula, but I give thanks regardless. Since the formula has no changeable parameters, what I have done basically amounts to tweaking someone else's fractal. Normally I never tweak the images of other fractalists, but today's tweak makes such a striking image that I could not keep it to myself. I named the image "Hexagons and Circles". I gave it this name because the densest packing of circles in a plane is in the shape of a hexagonal grid. The rating of 7 seems appropriate. With a run-time of under five seconds on most machines, today's parameter file is one of the all-time fastest. The completed GIF image will still be available for quick download on Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and on Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> With total sun and a temperature of 77F 25C, the fractal weather Thursday was ideal for man and cats alike. The man spent the day working; the cats spent the day resting and having fun. Today promises to be a repeat, so I'd best get busy with the work. Until Monday the 27th, take care, and see you then. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ HexagonsAndCircles { ; time=0:00:05.55--SF5 on a P200 reset=2002 type=formula formulafile=kleintri.frm formulaname=Klein_tri_lattice passes=1 center-mag=-0.00254816/0.00115498/0.5537159 float=y maxiter=1023 inside=255 proximity=40 outside=fmod symmetry=xyaxis periodicity=0 colors=000Ld`GTTC`Ozzzzzzxvxrpp`X_mliggaaaVXYO903D\ 0UIPZUDCPMFviirfdmdajaYf`Va_Q_XOVVJC0xLDaz9ApJDDSA\ LTDX40V90VC0TF3TI6TL9SOCSQF06V0AS3DQ7GODLMIOJOQI7J\ vFOgMQTLpaMjYOfTPaPQYLrzzmvzjrsgmmdif`d_Y`TVXMCYdF\ X`GXYJVVLVSMVPPTMQTJ0Jv0Mm3OdCQXLSOc0IaM3YP7VSCDQ0\ TxJSoISgIS`GQjzSfxSaiSYVg00c60_D3VMAmzQizOfvMaoL_g\ JV`I0`l0_f1Ya7XYCXTIVPOTLJr7MiAP`DSSvSToSTiSTcSTYS\ TSSTMVVOTTLTTJSTIudMoaLj`Jf_J`XIXVGz7zuFmfMXzz`zzY\ vxVrsSlmQfgOacLXYIju0fo0cj0`f4Ya9VYDg00A9rDClGFfJI\ `LLXOOQQQLX0SV0PV6OTCMTIJSOIOrxPmpPiiQdaQ`VSXO0sc0\ o_1jV7fSFaOMYJY0IV9GyD0dPx0dC0aD9_FJXG0z01u36p6Al7\ FfAJaCOYFzmuoffc_T0uO7jLIaIzzimoV9vzCrzFoyGjrJgjMc\ aO`VQXOJz0Oo96aTA`QD_PGYOJXLMVJPTILxTMsQOoPOlOPgMQ\ cLQ`JSXI0uI1pG6mG9iGDfGIcGL_GPXGJCLLFJMIJOLIPOIQQG\ zCxzFpxIioLagOV_QOzYGzXGzXGuVGoVGiVGcTGYTGPGzQLpQO\ dSQSI9Xmvzgszcpz_msVjmPgf } frm:Klein_tri_lattice(XYAXIS){ ang=pi/3 r=1/2 rr=r*r z=pixel t1=sin(ang) t2=tan(ang) t3=exp(flip(ang)) : inside=0 m = round(imag(z)/t1) n = round(real(z)-imag(z)/t2) c0=n+m*t3 c1=n+(m-1)*t3 c2=n+(m+1)*t3 c3=(n-1)+m*t3 c4=(n+1)+m*t3 if(|z-c0|<rr) z=r*conj(r/(z-c0))+c0 inside=1 elseif(|z-c1|<rr) z=r*conj(r/(z-c1))+c1 inside=1 elseif(|z-c2|<rr) z=r*conj(r/(z-c2))+c2 inside=1 elseif(|z-c3|<rr) z=r*conj(r/(z-c3))+c3 inside=1 elseif(|z-c4|<rr) z=r*conj(r/(z-c4))+c4 inside=1 endif inside} END 20.0 PAR-FORMULA FILE==================================

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FractInt under Windows XP Pro
by Paul N. Lee 24 May '02

24 May '02

I recently was in a conversation with someone about running FractInt under Microsoft's Windows XP Pro edition. And was told that they experienced a few problems at first, but now seems to be functioning quite fine. Here are two different emails (posted with permission) that state some of the specifics about the Property settings for FractInt under Win-XP: _______________________________________________________________________ From: "Steven A. Hessler" <shessler1(a)attbi.com> Date: Thu, 23 May 2002 15:23:42 -0500 Fractint (V 20.0) works on my computer under WinXP Pro, using a Diamond Viper 550 video card, which uses the Nvidia compatible Riva TNT chipset. It Has 16mb video memory installed. (WinXP drivers used are NV4.sys and NV4.INI.) No Diamond-released XP drivers exist, although some Riva TNT generic XP drivers Released by third parties DO appear to work properly if installed, although They are NOT digitally signed by MS. (I never noticed any difference in performance of XP when using the generic drivers, which I found by searching the internet.) Fractint is started using a desktop icon. The memory options are conventional-- The Initial Environment is set to AUTO. No EMS is used. No XMS is used. Uses HMA is checked. MS-DOS protected-mode (DPMI) memory is set to AUTO. Under SCREEN settings, Fast ROM emulation and Dynamic memory allocation are Both checked. It's set to start up in Full Screen mode. Compatibility mode is NOT active. The Fractint video drivers that work are the SVGA/VESA AUTODETECT drivers (SF2-SF7). VESA STANDARD INTERFACE (SF8-SF9) also appear to work. Saving a fractal to GIF file works, saving the fractal normally. ALL OF THESE DRIVERS FUNCTION USING 256 COLOR MODE. Although some of the VESA True-Color drivers appear to work, they in fact appear to create fractals Using only one color-- blue. Experimenting with some of the EMS or XMS memory settings does not seem to Have any effect one way or the other on the program's performance or on the Performance of the video drivers. Before V. 20.0 came out, I also experimented with the last V19.x Release. It appeared to perform identically. Steve H. _______________________________________________________________________ _______________________________________________________________________ From: "Steven A. Hessler" <shessler1(a)attbi.com> Date: Thu, 23 May 2002 18:08:28 -0500 I just downloaded the developer's version of Fractint, and much to my Amazement, all the VESA True-Color video drivers suddenly work properly Under XP Pro. ......(snipped other stuff)..... Regards, Steve H. _______________________________________________________________________ Sincerely, P.N.L. -------------------------------------------------------------- http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go

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New Gallery by "O"
by Paul N. Lee 23 May '02

23 May '02

Greetings, For those unfamiliar with "O", then this will be something unique. For everyone else, this will be a location to see around twelve hundred of O's creations. The new Domain and web site have been available for a couple of months now. Not everything is quite complete, a few of the images are missing and hopefully will be made available as soon as possible. But there are at least 1,160 graphics which should keep most anybody busy for a few hours of browsing: http://www.o3-designs.com/ Hope you can visit and enjoy the view!! :-) Sincerely, P.N.L. -------------------------------------------------------------- http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go

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fractint on mac
by Alex Dukay 23 May '02

23 May '02

I've purchased a MAC and I want to know whether anyone has had success running fractint with the program VPC (virtual PC) on a MAC? Can it be done? I would like some advice before installing VPC. Thanks, Alex

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Sorry for the double posting...
by Gerald K. Dobiasovsky 22 May '02

22 May '02

...somehow I managed to leave a copy of the already sent mail in the queue. Gerald

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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

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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

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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==================================

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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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