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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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FOTD 18-05-02 (The Blue Light [6])
by JimMuth＠aol.com 18 May '02

18 May '02

FOTD -- May 18, 2002 (Rating 6) Fractal visionaries and enthusiasts: The FOTD CD progresses, the rain falls, it's Preakness festival Saturday here in Fractal Land, and all else is well. (A Preakness is a horse race that tries to be another Kentucky Derby!) But the FOTD is about fractals, not horses. Today's image is a flowery affair which I found in the fractal that results when the formula Z^(-6)+6Z^(-1.6)+(1/C) is iterated. This parent fractal is an indescribable affair, with bays of all shapes and sizes, and lots of places that might harbor interesting scenes. (I leave it to the math experts to figure what all those bays represent.) Today's minibrot is located near the southern edge of the largest bay, actually in an area that at first glance appears to hold little promise. The area appears so hopeless in fact that I almost passed it by. Only an area of vague symmetry drew me to investigate further. And when I did investigate, I was glad that I had not passed by. I named the picture "The Blue Light". There is no obvious reason why I chose this name; I simply like its sound. I rated the image at a 6 because there is really nothing exceptional about it. Perhaps the best feature of today's image is its speed, rendering from the parameter file as it does in well under one minute. As always, those who would rather download than render may pick up the pre-rendered GIF image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Friday here at Fractal Central was near perfect, especially for the cats who wanted to be comfortable outdoors. Generous sun and a temperature of 81F 27C kept them happy in the yard all afternoon. Thinking he was once again a kitten, Tippy scampered up a holly tree, but the bird he was chasing flew away long before he reached the branch where the bird had perched. A heavy rain shower passed over in the evening, but by that time the dynamic duo had settled for the night in their favorite indoor spots. This morning the rain is continuing, and there's much work to do and only limited time in which to do it. So until Tuesday the 21st of May, take care, and search for truth. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ The_Blue_Light { ; time=0:00:20.43--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=b center-mag=-0.28394429430300750/-1.090882416624821\ 00/2939.972/1/57.4999999999925038/2.42871001088218\ 463e-011 params=1/-6/6/-1.6/0/525/0/0 float=y maxiter=265 inside=255 logmap=8 periodicity=10 colors=00000000000002606H0AT0Ad08o08sUQzGTzRbzdkzq\ vzzzzzzzzzzzzzzszzdzzPxzAuz0qz0mb0z80zEku4zu0zs0zs\ 8sdVLPdPPmRPuVPzXPzZPvgTioVXvXJz`6zb0zd0zV0zL0zC2z\ 24z0Az6GqHLZTPHd`EXkAPv6Hz4CuNHidNXvTLzXRzLXzAbz0g\ z0kz0gz0ds6`iJX`XTTiH`L8e00k0Es0Rx2dzGqzTszbuqivgs\ xXzzNzzEzz4zzNzzdzzuzzzzzzzzzzzzzzzzzqzzkzzmzzozzq\ zzszzvzozzbzzPzzCzz0zzAzzJzqTzbbzNkz8Azd0zz2zxVzov\ zggzkVzoHzs2zv0zz0zz0zm0z`0zN0z82z06z0Ez0Jz4PzGXzP\ bz`gzkmzuxz0sz0oz0zzzzzzzzuszkizbbzTizEqz0xz0Nz40z\ P0zT0zV6zZCz`JzbPzeXzgbzigzdmz`szVxzRzzNzzHzzEzzAz\ z6zz2zz0zz0zz0zz0zz0zz0zz0zz00zP0zZ6zeGzmPzuXzzZzv\ Zzq`zm`zgbzdbzZbzV0z00z40zH0zV0zg0zu0zk0zb0zT0zJ0z\ A0zL0zX0zg0zs0zz0zz0zzzzzzzzzzzzzzzzzzzzzzzzzzzzxz\ zzxzzqzzizzbzzVzzNzzJzgGz8Cz0Jz0Rz0Zz0ez0mz0uz0zz0\ xzCxzTxzixzxgzbTzHEz00z00z00z00z00z00z00z00z00z00z\ o0z00zooz0ozooz0ozoCzC000 } 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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FOTD 18-05-02 (The Blue Light [6])
by Jim Muth 18 May '02

18 May '02

FOTD -- May 18, 2002 (Rating 6) Fractal visionaries and enthusiasts: The FOTD CD progresses, the rain falls, it's Preakness festival Saturday here in Fractal Land, and all else is well. (A Preakness is a horse race that tries to be another Kentucky Derby!) But the FOTD is about fractals, not horses. Today's image is a flowery affair which I found in the fractal that results when the formula Z^(-6)+6Z^(-1.6)+(1/C) is iterated. This parent fractal is an indescribable affair, with bays of all shapes and sizes, and lots of places that might harbor interesting scenes. (I leave it to the math experts to figure what all those bays represent.) Today's minibrot is located near the southern edge of the largest bay, actually in an area that at first glance appears to hold little promise. The area appears so hopeless in fact that I almost passed it by. Only an area of vague symmetry drew me to investigate further. And when I did investigate, I was glad that I had not passed by. I named the picture "The Blue Light". There is no obvious reason why I chose this name; I simply like its sound. I rated the image at a 6 because there is really nothing exceptional about it. Perhaps the best feature of today's image is its speed, rendering from the parameter file as it does in well under one minute. As always, those who would rather download than render may pick up the pre-rendered GIF image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Friday here at Fractal Central was near perfect, especially for the cats who wanted to be comfortable outdoors. Generous sun and a temperature of 81F 27C kept them happy in the yard all afternoon. Thinking he was once again a kitten, Tippy scampered up a holly tree, but the bird he was chasing flew away long before he reached the branch where the bird had perched. A heavy rain shower passed over in the evening, but by that time the dynamic duo had settled for the night in their favorite indoor spots. This morning the rain is continuing, and there's much work to do and only limited time in which to do it. So until Tuesday the 21st of May, take care, and search for truth. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ The_Blue_Light { ; time=0:00:20.43--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=b center-mag=-0.28394429430300750/-1.090882416624821\ 00/2939.972/1/57.4999999999925038/2.42871001088218\ 463e-011 params=1/-6/6/-1.6/0/525/0/0 float=y maxiter=265 inside=255 logmap=8 periodicity=10 colors=00000000000002606H0AT0Ad08o08sUQzGTzRbzdkzq\ vzzzzzzzzzzzzzzszzdzzPxzAuz0qz0mb0z80zEku4zu0zs0zs\ 8sdVLPdPPmRPuVPzXPzZPvgTioVXvXJz`6zb0zd0zV0zL0zC2z\ 24z0Az6GqHLZTPHd`EXkAPv6Hz4CuNHidNXvTLzXRzLXzAbz0g\ z0kz0gz0ds6`iJX`XTTiH`L8e00k0Es0Rx2dzGqzTszbuqivgs\ xXzzNzzEzz4zzNzzdzzuzzzzzzzzzzzzzzzzzqzzkzzmzzozzq\ zzszzvzozzbzzPzzCzz0zzAzzJzqTzbbzNkz8Azd0zz2zxVzov\ zggzkVzoHzs2zv0zz0zz0zm0z`0zN0z82z06z0Ez0Jz4PzGXzP\ bz`gzkmzuxz0sz0oz0zzzzzzzzuszkizbbzTizEqz0xz0Nz40z\ P0zT0zV6zZCz`JzbPzeXzgbzigzdmz`szVxzRzzNzzHzzEzzAz\ z6zz2zz0zz0zz0zz0zz0zz0zz0zz00zP0zZ6zeGzmPzuXzzZzv\ Zzq`zm`zgbzdbzZbzV0z00z40zH0zV0zg0zu0zk0zb0zT0zJ0z\ A0zL0zX0zg0zs0zz0zz0zzzzzzzzzzzzzzzzzzzzzzzzzzzzxz\ zzxzzqzzizzbzzVzzNzzJzgGz8Cz0Jz0Rz0Zz0ez0mz0uz0zz0\ xzCxzTxzixzxgzbTzHEz00z00z00z00z00z00z00z00z00z00z\ o0z00zooz0ozooz0ozoCzC000 } 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] FOTD 15-05-02 (Mandelia [6])
by Jim Muth 18 May '02

18 May '02

FOTD -- May 18, 2002 (Rating 6) Fractal visionaries and enthusiasts: The FOTD CD progresses, the rain falls, it's Preakness festival Saturday here in Fractal Land, and all else is well. (A Preakness is a horse race that tries to be another Kentucky Derby!) But the FOTD is about fractals, not horses. Today's image is a flowery affair which I found in the fractal that results when the formula Z^(-6)+6Z^(-1.6)+(1/C) is iterated. This parent fractal is an indescribable affair, with bays of all shapes and sizes, and lots of places that might harbor interesting scenes. (I leave it to the math experts to figure what all those bays represent.) Today's minibrot is located near the southern edge of the largest bay, actually in an area that at first glance appears to hold little promise. The area appears so hopeless in fact that I almost passed it by. Only an area of vague symmetry drew me to investigate further. And when I did investigate, I was glad that I had not passed by. I named the picture "The Blue Light". There is no obvious reason why I chose this name; I simply like its sound. I rated the image at a 6 because there is really nothing exceptional about it. Perhaps the best feature of today's image is its speed, rendering from the parameter file as it does in well under one minute. As always, those who would rather download than render may pick up the pre-rendered GIF image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Friday here at Fractal Central was near perfect, especially for the cats who wanted to be comfortable outdoors. Generous sun and a temperature of 81F 27C kept them happy in the yard all afternoon. Thinking he was once again a kitten, Tippy scampered up a holly tree, but the bird he was chasing flew away long before he reached the branch where the bird had perched. A heavy rain shower passed over in the evening, but by that time the dynamic duo had settled for the night in their favorite indoor spots. This morning the rain is continuing, and there's much work to do and only limited time in which to do it. So until Tuesday the 21st of May, take care, and search for truth. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ The_Blue_Light { ; time=0:00:20.43--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=b center-mag=-0.28394429430300750/-1.090882416624821\ 00/2939.972/1/57.4999999999925038/2.42871001088218\ 463e-011 params=1/-6/6/-1.6/0/525/0/0 float=y maxiter=265 inside=255 logmap=8 periodicity=10 colors=00000000000002606H0AT0Ad08o08sUQzGTzRbzdkzq\ vzzzzzzzzzzzzzzszzdzzPxzAuz0qz0mb0z80zEku4zu0zs0zs\ 8sdVLPdPPmRPuVPzXPzZPvgTioVXvXJz`6zb0zd0zV0zL0zC2z\ 24z0Az6GqHLZTPHd`EXkAPv6Hz4CuNHidNXvTLzXRzLXzAbz0g\ z0kz0gz0ds6`iJX`XTTiH`L8e00k0Es0Rx2dzGqzTszbuqivgs\ xXzzNzzEzz4zzNzzdzzuzzzzzzzzzzzzzzzzzqzzkzzmzzozzq\ zzszzvzozzbzzPzzCzz0zzAzzJzqTzbbzNkz8Azd0zz2zxVzov\ zggzkVzoHzs2zv0zz0zz0zm0z`0zN0z82z06z0Ez0Jz4PzGXzP\ bz`gzkmzuxz0sz0oz0zzzzzzzzuszkizbbzTizEqz0xz0Nz40z\ P0zT0zV6zZCz`JzbPzeXzgbzigzdmz`szVxzRzzNzzHzzEzzAz\ z6zz2zz0zz0zz0zz0zz0zz0zz0zz00zP0zZ6zeGzmPzuXzzZzv\ Zzq`zm`zgbzdbzZbzV0z00z40zH0zV0zg0zu0zk0zb0zT0zJ0z\ A0zL0zX0zg0zs0zz0zz0zzzzzzzzzzzzzzzzzzzzzzzzzzzzxz\ zzxzzqzzizzbzzVzzNzzJzgGz8Cz0Jz0Rz0Zz0ez0mz0uz0zz0\ xzCxzTxzixzxgzbTzHEz00z00z00z00z00z00z00z00z00z00z\ o0z00zooz0ozooz0ozoCzC000 } 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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At it again...
by Andrew Coppin 18 May '02

18 May '02

On 15/05/02, Morgan L. Owens wrote... over 9x2^10 octets of stuff! 8-0 Thanks for that mate - my head hurts so much! :S As regards the 4D generalisations of M and J sets... aren't they just simple surfaces of rotation of the ordinary complex versions? (Hmmm... some day I've GOT to download the POVRay source code and find out how the hell it renders 3D slices of the 4D Julias...) While I'm here, I thought I'd just report some of my recent fractal antics. I've been busily revising for my final year exams, but in between I've done some fractal work... Not content with Julia sets, after much experimentation I've persuaded WinAmp's AVS to draw (linear) IFS! (Figuring out the correct blit settings was highly non-trivial I can tell you!) As with the Julia sets, the trick is finding good patterns to apply the mapping to... I found that if I draw white graphics, and apply different colour filters to each transformation of the system, the results are really quite pretty! I also did some work with POVRay, drawing graphs for forwards and backwards iterations of the quadratic mapping (with Z-depth indicating iteration count), trying to work out where those complex patters derrive from. I mean, z => z^2 is a very simple function; it's just a big troff! (Oh dear... too much UNIX :S) The Julia set reflects this - it's a circle. Adding the c term only moves the center of the thing... and yet this creates amazingly complicated patterns. Why? Through my WinAmp experiments, it has become clear that ANY patters that has the quadratic mapping applied to it turns up these wonderful patterns. (Unsuprising really...) Also, my POVRay work has shown that the adjasent points on the graph which look so like they are images of each other, are in fact derrived from distant points. (Internally, the Julias seem to be a lot less symmetric than you might think!) 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. (To look at it the other way - the orbits of distant points are ending up in the same vicinity. That's the fun part - the forward transformation of the individual orbits can be seen as the reverse transformation of the bailout boundery...) Erm... am I making sense here? 8-| OK, well anyway, I've also been investigating the Julia sets embedded in M. (Apparently these are quite a well known feature - as I discovered when I first mentioned them on this list!) It seems many an explorer knows that if you tunnel into the center of just a mini Julia, you find 2, 4, 8, 16... groups of the pattern outlining the equipotential curves of a minibrot (how deep depending on how close to the parent minibrow you found this minijulia in the first place). Well... I've been exploring the minijulias of the largest minibrot (the lowest-period one on the negative stem on the M set). Here every minijulia is scuered with a beautiful curving line. And at every major junction of this line, a minijulia sits. The one in the center leads (eventually) to a minibrot, as described above. However If you zoom into other parts of the minijulia, the minijulias you find dotted around the various junctions (and it's a nightmare to try to index them!) don't follow the equipotential curves of a minibrot. The outer most ring isn't a ring. Typically that are S-shaped groups, or just chaotic (but beautiful) "clusters", who's underlying pattern is difficult to understand. I'm still a long way off finding the pattern in all this... To anyone who thinks that M has been completely explored and holds no mysteries any more, I say KNICKERS! B^P OK, now I *am* jibbering... I'm gonna stop typing now... might send a PAR of the mini Julia patterns in a while tho... Thanks. Andrew. _________________________________________________________________ Join the worlds largest e-mail service with MSN Hotmail. http://www.hotmail.com

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At it again... Pars!
by Andrew Coppin 18 May '02

18 May '02

Have a look at this lot... (I mean... if you're bored that is!) Mini-Julia { ; A typical mini Julia in M. reset=2002 type=mandel center-mag=-1.74710622469804600/+0.00137745649736071/44635.92 params=0/0 float=y maxiter=65536 inside=255 sound=off } Spiral-Cross { ; A non-typical mini Julia arrangement! reset=2002 type=mandel center-mag=-1.74711451785152400/+0.00138682610202126/1.089744e+007 params=0/0 float=y maxiter=65536 inside=255 sound=off } Spiral-Cross-Z { ; The minibrot as it's heart... reset=2002 type=mandel center-mag=-1.74711452819077400/+0.00138682821036616/2.391468e+008 params=0/0 float=y maxiter=65536 inside=255 sound=off } Spiral { ; Another unusual arrangement. reset=2002 type=mandel center-mag=-1.74709858222257700/+0.00138213246963899/7390053 params=0/0 float=y maxiter=65536 inside=255 sound=off } Spiral-Z { ; ...and it's minibrot reset=2002 type=mandel center-mag=-1.74709858052979200/+0.00138213299873782/1.154696e+008 params=0/0 float=y maxiter=65536 inside=255 sound=off } Twin-Spiral { ; It goes on... reset=2002 type=mandel center-mag=-1.74710019324498000/+0.00138058047460226/4.658619e+009 params=0/0 float=y maxiter=65536 inside=255 sound=off } Double-S { ; It gets stranger... reset=2002 type=mandel center-mag=-1.74711328280191700/+0.00138630427456312/1.417572e+009 params=0/0 float=y maxiter=65536 inside=255 sound=off colors=000<87>000000000<3>000w00<25>C00A00800<2>200000003<8>00b00f00j<3>\ 00z<9>`bOdfKhjG<3>wz0<9>xObyKfyGj<3>z0z<9>O0OK0KG0G<3>000<41>oooppprrr<3\ >www000<14>000 } Mini-Julia2 { ; Another mini Julia. reset=2002 type=mandel center-mag=-1.76904186275559900/+0.00315554134874867/64710.86 params=0/0 float=y maxiter=65536 inside=255 sound=off } Sausage { ; Curiouse... reset=2002 type=mandel center-mag=-1.76904179326671400/+0.00315920536912995/1.12082e+011 params=0/0 float=y maxiter=65536 inside=255 sound=off } Sausage2 { ; [Ditto!] reset=2002 type=mandel center-mag=-1.76904179326680700/+0.00315920536933926/1.12082e+012/0.9999 params=0/0 float=y maxiter=65536 inside=255 sound=off } Thanks. Andrew. _________________________________________________________________ Send and receive Hotmail on your mobile device: http://mobile.msn.com

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