FOTD 07-12-04 (Yin and Yang [8])
FOTD -- December 07, 2004 (Rating 8) Fractal visionaries and enthusiasts: Today we tackle the last formula of the Fractint list, the 'volterra-lotka' formula, which appears in the book "The Beauty of Fractals". This formula is one of those that fully comes to life only when its inside parts are rendered with an active fill, such as the 'atan' that I used for today's image. Setting the 'decomp' feature to 256 helped the image also. Today's fractal has brought out the mystic in me. The reason for the name of the image, "Yin and Yang", is obvious as soon as the image is seen. The resemblance to the yin-yang symbol is striking. Yin and yang are not two Chinese farmers, they are the names the Chinese have given to the two great polar oppo- sites of the universe, the energies which manifest themselves in many contrasting ways, such as positive-negative, objective- subjective, matter-energy, time-space, past-future, wave- particle, male-female, heaven-earth, body-soul, brain-mind, etc., (though materialists would deny that things such as heaven and the soul exist, and would insist that the mind is somehow generated by the brain). Having caught myself waxing philosophic, which I have a tendency to do, I will now admit that in the second half of my life I find myself slowly drifting from the scientific view of the world toward the mystical view. In contrast to the scientific view, which breaks things down into their constituent parts and studies the pieces, the mystical view joins things together into larger units, the ultimate single unit being God. (Become one with ***** they say.) I have not yet found God, but then we are all like deep-sea fish searching for water. Fractals must in some way be connected to the ultimate unit, but we have gone far enough in the philosophical direction for one day. Today's fractal rates an 8 and renders in a little over 2 minutes, a combination that gives it an overall worth of 360 -- not bad for a yin-yang symbol. It will take no miracle to see today's image by running the included parameter file or by downloading it from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Cold, damp, dreary weather with occasional light rain here at Fractal Central kept the dynamic cats indoors all day Monday. Needless to say, much tuna was needed to keep them happy. Today is starting warmer but it is raining again. It looks like I should stock up on more tuna. For me the work is moderate. I should be at the fractal machine before the sun sets, which it does at 4:43pm today. Until tomorrow, take care, and despite the skepticism, never abandon the search for the part of existence that lies beyond the limits of the senses. Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= Yin_and_Yang { ; time=0:02:19.95--SF5 on a P200 reset=2004 type=volterra-lotka passes=1 center-mag=1.08715/1.13888/3.934074/1/-90/-1.23373\ 5336114705e-014 params=0.5008/0.4827 float=y maxiter=256 bailout=9 inside=atan outside=atan logmap=yes decomp=256 periodicity=0 colors=000UekWdkYck_ajc`ih_imXjrVkwTlzRmzPnzNozLqz\ JszguzewzczzazzZzzXzzUzzPzzKzzFzzAzz5zz0z000000000\ 000A0AA0AA0AA0AA5LB8NDBOFEQHHRJKTKNUMQVOTXQWYSZ_Ua\ `RBrSBrSArTArTArU9sU9tV9uV8vW8wW8xW8wVAuUBtUCrTDqT\ EpSGoSHoRIoRJnQKnQMnPNmPOmOPmOQlNSlNTlMUkMVkLWkLYj\ KZjK_jJ`iIaiIchHdhHehGfgGggFigFkfEmgEohDqiDsjCukCv\ mBwoBwqAwsAwu9ww9wy8wz8wzAwzBwzDwzEwzFwzHwzImzKjzL\ hzMfz3azQgzllzUSNB05A8H99T8Ad8BpSZqjuqPRX000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 0000000000000000000000000 } END PARAMETER FILE=========================================
The Lyapunov fractal type is one of my favourites. I attribute this to being an avid fan of science fiction, and of the "space opera" feeling that Lyapunovs tend to give me. I was thrilled a few years ago to discover a version of Lyapunov code posted to Fractint, because it meant that I could do with it what I like to do with my favourite fractal types: modify it, usually by adding functions here and there. After much tweaking through a number of versions, I arrived at several which produced Lyapunov variations to my liking. (The choice of a maxiter of 103 is critical to some of these variations; try 102 for disappoinment, 104 or 105 for some changes, and higher or lower maxiters for much less interest, especially with the passes=o mode, see below.) It took some puzzling through these variations until I reached number 7 before I was rewarded with a version and some parameters for it which also produced something more than a straight line or two in passes=o mode. And now for the main question, related to the latter several of the pars below: With this Lyapunov type in passes=o, why can I not zoom in further than about 1 and still see something being rendered on the screen? A further question - sorry, but I've just discovered digital printing of fractals as actual photographs here in the Republic of Georgia, maximum size 290 x 465 mm and 300 dpi. Passes=o, t and possibly other unusual rendering modes don't work in Disk/Ram Video sizes. Any chance of getting this changed? A large Buddahbrot would look STUNNING, for example. Thanks... Tony Hanmer Lyapunov2037k { ; 12 minutes on a 1300Mhz PIII reset=2001 type=formula formulafile=generalt.frm formulaname=Lyapunov02 function=tan/atan passes=1 center-mag=3.19117/3.61002/13.73246/1/90/-3.052882\ 51479236461 params=0.25/0.5625/0.25/0.5625/0.25/0.5625/10/1.4/\ 1000000/0 float=y maxiter=100 inside=bof60 outside=mult logmap=yes periodicity=0 sound=off colors=000`00c00e80<2>jE0kF0mI0oK0pM0qP0sS0tU0uW0v\ Z0wa0xe0<2>zm0zp0zt0zv0zy0zv0zt0zp0<2>xg0xe0wa0vZ0\ uW0tU0sS0qP0pM0oK0mI0kF0<3>e80c00`00Z00Y00<3>P00N0\ 0L00I00I00<3>R00T00W00Y00Z00`00c00e80<2>jE0kF0mI0o\ K0pM0qP0sS0tU0uW0vZ0wa0xe0<2>zm0zp0zt0zv0zy0zv0zt0\ zp0<2>xg0xe0wa0vZ0uW0000sS0qP0pM0oK0mI0kF0<3>e80c0\ 0`00Z00Y00<3>P00N00L00I00I00<3>R00T00W00Y00Z00`00c\ 00e80<2>jE0kF0mI0oK0pM0qP0sS0tU0uW0vZ0wa0xe0<2>zm0\ zp0zt0zv0zy0zv0zt0zp0<2>xg0xe0wa0vZ0uW0tU0sS0qP0pM\ 0oK0mI0kF0<3>e80c00`00Z00Y00<3>P00N00L00I00I00<3>R\ 00T00W00Y00Z00`00c00e80<2>jE0kF0mI0oK0pM0qP0sS0tU0\ uW0vZ0wa0xe0<2>zm0zp0zt0zv0zy0zv0zt0zp0<2>xg0xe0wa\ 0vZ0uW0tU0sS0qP0pM0oK0mI0kF0<3>e80c00`00Z00Y00<2>R\ 00L00<4>W00Y00Z00 } Lyapunov2039e { ; 18 minutes on a 1300Mhz PIII reset=2001 type=formula formulafile=generalt.frm formulaname=Lyapunov02 function=log/sin passes=1 center-mag=2.63575/1.93804/0.4813439 params=0.5/0.5625/0.5/0.5625/0.5/0.5625/10/1.4/100\ 0000/0 float=y maxiter=200 inside=bof60 outside=mult logmap=yes periodicity=0 sound=off colors=000L00<3>T00W00Y00Z00`00c00e80<2>jE0kF0mI0o\ K0pM0qP0sS0tU0uW0vZ0wa0xe0<2>zm0zp0zt0zv0zy0zv0zt0\ zp0<2>xg0xe0wa0vZ0uW0tU0sS0qP0pM0oK0mI0kF0<3>e80c0\ 0`00Z00Y00<3>P00N00L00I00I00<3>R00T00W00Y00Z00`00c\ 00e80<2>jE0kF0mI0oK0pM0qP0sS0tU0uW0vZ0wa0xe0<2>zm0\ zp0zt0zv0zy0zv0zt0zp0<2>xg0000wa0vZ0uW0tU0sS0qP0pM\ 0oK0mI0kF0<3>e80c00`00Z00Y00<3>P00N00L00I00I00<3>R\ 00T00W00Y00Z00`00c00e80<2>jE0kF0mI0oK0pM0qP0sS0tU0\ uW0vZ0wa0xe0<2>zm0zp0zt0zv0zy0zv0zt0zp0<2>xg0xe0wa\ 0vZ0uW0tU0sS0qP0pM0oK0mI0kF0<3>e80c00`00Z00Y00<3>P\ 00N00L00I00I00<3>R00T00W00Y00Z00`00c00e80<2>jE0kF0\ mI0oK0pM0qP0sS0tU0uW0vZ0wa0xe0<2>zm0zp0zt0zv0zy0zv\ 0zt0zp0<2>xg0xe0wa0vZ0uW0tU0sS0qP0pM0oK0mI0kF0<3>e\ 80c00`00Z00Y00<2>R00 } Lyapunov2039h { ; 10 minutes on a 1300Mhz PIII reset=2001 type=formula formulafile=generalt.frm formulaname=Lyapunov02 function=log/sin passes=1 center-mag=-1.37365/-1.43806/1.373246/1/180 params=0.5/0.5625/0.5/0.5625/0.5/0.5625/10/1.4/100\ 0000/0 float=y maxiter=100 inside=bof60 outside=mult logmap=yes periodicity=0 sound=off colors=000L00N00P00000T00W00Y00Z00`00c00e80<2>jE0k\ F0mI0oK0pM0qP0sS0tU0uW0vZ0wa0xe0<2>zm0zp0zt0zv0zy0\ zv0zt0zp0<2>xg0xe0wa0vZ0uW0tU0sS0qP0pM0oK0mI0kF0<3\
e80c00`00Z00Y00<3>P00N00L00I00I00<3>R00T00W00Y00Z\ 00`00c00e80<2>jE0kF0mI0oK0pM0qP0sS0tU0uW0vZ0wa0xe0\ <2>zm0zp0zt0zv0zy0zv0zt0000zm0yj0xg0xe0wa0vZ0uW0tU\ 0sS0qP0pM0oK0mI0kF0<3>e80c00`00Z00Y00<3>P00N00L00I\ 00I00<3>R00T00W00Y00Z00`00c00e80<2>jE0kF0mI0oK0pM0\ qP0sS0tU0uW0vZ0wa0xe0<2>zm0zp0zt0zv0zy0zv0zt0zp0<2\ xg0xe0wa0vZ0uW0tU0sS0qP0pM0oK0mI0kF0<3>e80c00`00Z\ 00Y00<3>P00N00L00I00I00<3>R00T00W00Y00Z00`00c00e80\ <2>jE0kF0mI0oK0pM0qP0sS0tU0uW0vZ0wa0xe0<2>zm0zp0zt\ 0zv0zy0zv0zt0zp0<2>xg0xe0wa0vZ0uW0tU0sS0qP0pM0oK0m\ I0kF0<3>e80c00`00Z00Y00<2>R00 }
Lyapunov2041 { ; 20 minutes on a 1300Mhz PIII ; Subtle differences from normal Lyapunovs. reset=2001 type=formula formulafile=generalt.frm formulaname=Lyapunov02 function=log/sin passes=1 center-mag=-1.56796/-1.4745/5.628057/1/180 params=0.5/0.5625/0.5/0.5625/0.5/0.5625/10/1.4/100\ 0000/0 float=y maxiter=200 inside=bof60 outside=mult logmap=yes periodicity=0 cyclerange=104/104 sound=off colors=000L00<3>T00W00Y00Z00`00c00e80<2>jE0kF0mI0o\ K0pM0qP0sS0tU0uW0vZ0wa0xe0<2>zm0zp0zt0zv0zy0zv0zt0\ zp0<2>xg0xe0wa0vZ0uW0tU0sS0qP0pM0oK0mI0kF0<3>e80c0\ 0`00Z00Y00<3>P00N00L00I00I00<3>R00T00W00Y00Z00`00c\ 00e80<2>jE0kF0mI0oK0pM0qP0sS0tU0uW0vZ0wa0xe0<2>zm0\ zp0zt0zv0zy0zv0zt0zp0<2>xg0000wa0vZ0uW0tU0sS0qP0pM\ 0oK0mI0kF0<3>e80c00`00Z00Y00<3>P00N00L00I00I00<3>R\ 00T00W00Y00Z00`00c00e80<2>jE0kF0mI0oK0pM0qP0sS0tU0\ uW0vZ0wa0xe0<2>zm0zp0zt0zv0zy0zv0zt0zp0<2>xg0xe0wa\ 0vZ0uW0tU0sS0qP0pM0oK0mI0kF0<3>e80c00`00Z00Y00<3>P\ 00N00L00I00I00<3>R00T00W00Y00Z00`00c00e80<2>jE0kF0\ mI0oK0pM0qP0sS0tU0uW0vZ0wa0xe0<2>zm0zp0zt0zv0zy0zv\ 0zt0zp0<2>xg0xe0wa0vZ0uW0tU0sS0qP0pM0oK0mI0kF0<3>e\ 80c00`00Z00Y00<2>R00 } Lyapunov7007 { ; 13 minutes on a 1300Mhz PIII ; Boring, but the start of passes=o play. reset=2001 type=formula formulafile=generalt.frm formulaname=Lyapunov07 function=asin/exp passes=1 center-mag=0/0/0.06666667 params=0.66/3/1/0.5/0.35/100/10/1.4/1000000/0 float=y maxiter=105 inside=zmag outside=255 logmap=yes sound=off colors=000L00<3>T00W00Y00Z00`00c00e80<2>jE0kF0mI0o\ K0pM0qP0sS0tU0uW0vZ0wa0xe0<2>zm0zp0zt0zv0zy0zv0zt0\ zp0<2>xg0xe0wa0vZ0uW0tU0sS0qP0pM0oK0mI0kF0<3>e80c0\ 0`00Z00Y00<3>P00N00L00I00I00<3>R00T00W00Y00Z00`00c\ 00e80<2>jE0kF0mI0oK0pM0qP0sS0tU0uW0vZ0wa0xe0<2>zm0\ zp0zt0zv0zy0zv0zt0zp0<2>xg0xe0wa0vZ0uW0tU0sS0qP0pM\ 0oK0mI0kF0<3>e80c00`00Z00Y00<3>P00N00L00I00I00<3>R\ 00T00W00Y00Z00`00c00e80<2>jE0kF0mI0oK0pM0qP0sS0tU0\ uW0vZ0wa0xe0<2>zm0zp0zt0zv0zy0zv0zt0zp0<2>xg0xe0wa\ 0vZ0uW0tU0sS0qP0pM0oK0mI0kF0<3>e80c00`00Z00Y00<3>P\ 00N00L00I00I00<3>R00T00W00Y00Z00`00c00e80<2>jE0kF0\ mI0oK0pM0qP0sS0tU0uW0vZ0wa0xe0<2>zm0zp0zt0zv0zy0zv\ 0zt0zp0<2>xg0xe0wa0vZ0uW0tU0sS0qP0pM0oK0mI0kF0<3>e\ 80c00`00Z00Y00<2>R00 } Lyapunov_o7001 { ; 12 minutes on a 1300Mhz PIII ; Passes=o; can't zoom past 1... reset=2001 type=formula formulafile=generalt.frm formulaname=Lyapunov07 function=acos/cos passes=o center-mag=-1.77636e-015/1.77636e-015/0.719912 params=0.66/3/1/0.5/0.35/100/10/1.4/1000000/0 float=y maxiter=103 inside=zmag outside=summ logmap=yes sound=off colors=000L00<3>T00W00Y00Z00`00c00e80<2>jE0kF0mI0o\ K0pM0qP0sS0tU0uW0vZ0wa0xe0<2>zm0zp0zt0zv0zy0zv0zt0\ zp0<2>xg0xe0wa0vZ0uW0tU0sS0qP0pM0oK0mI0kF0<3>e80c0\ 0`00Z00Y00<3>P00N00L00I00I00<3>R00T00W00Y00Z00`00c\ 00e80<2>jE0kF0mI0oK0pM0qP0sS0tU0uW0vZ0wa0xe0<2>zm0\ zp0zt0zv0zy0zv0zt0zp0<2>xg0xe0wa0vZ0uW0tU0sS0qP0pM\ 0oK0mI0kF0<3>e80c00`00Z00Y00<3>P00N00L00I00I00<3>R\ 00T00W00Y00Z00`00c00e80<2>jE0kF0mI0oK0pM0qP0sS0tU0\ uW0vZ0wa0xe0<2>zm0zp0zt0zv0zy0zv0zt0zp0<2>xg0xe0wa\ 0vZ0uW0tU0sS0qP0pM0oK0mI0kF0<3>e80c00`00Z00Y00<3>P\ 00N00L00I00I00<3>R00T00W00Y00Z00`00c00e80<2>jE0kF0\ mI0oK0pM0qP0sS0tU0uW0vZ0wa0xe0<2>zm0zp0zt0zv0zy0zv\ 0zt0zp0<2>xg0xe0wa0vZ0uW0tU0sS0qP0pM0oK0mI0kF0<3>e\ 80c00`00Z00Y00<2>R00 } Lyapunov_o7002 { ; 12 minutes on a 1300Mhz PIII ; Passes=o; can't zoom past 1... reset=2001 type=formula formulafile=generalt.frm formulaname=Lyapunov07 function=acosh/cos passes=o center-mag=1.67602/0/0.819912 params=0.66/3/1/0.5/0.35/100/10/1.4/1000000/0 float=y maxiter=103 inside=zmag outside=summ logmap=yes sound=off colors=000L00<3>T00W00Y00Z00`00c00e80<2>jE0kF0mI0o\ K0pM0qP0sS0tU0uW0vZ0wa0xe0<2>zm0zp0zt0zv0zy0zv0zt0\ zp0<2>xg0xe0wa0vZ0uW0tU0sS0qP0pM0oK0mI0kF0<3>e80c0\ 0`00Z00Y00<3>P00N00L00I00I00<3>R00T00W00Y00Z00`00c\ 00e80<2>jE0kF0mI0oK0pM0qP0sS0tU0uW0vZ0wa0xe0<2>zm0\ zp0zt0zv0zy0zv0zt0zp0<2>xg0xe0wa0vZ0uW0tU0sS0qP0pM\ 0oK0mI0kF0<3>e80c00`00Z00Y00<3>P00N00L00I00I00<3>R\ 00T00W00Y00Z00`00c00e80<2>jE0kF0mI0oK0pM0qP0sS0tU0\ uW0vZ0wa0xe0<2>zm0zp0zt0zv0zy0zv0zt0zp0<2>xg0xe0wa\ 0vZ0uW0tU0sS0qP0pM0oK0mI0kF0<3>e80c00`00Z00Y00<3>P\ 00N00L00I00I00<3>R00T00W00Y00Z00`00c00e80<2>jE0kF0\ mI0oK0pM0qP0sS0tU0uW0vZ0wa0xe0<2>zm0zp0zt0zv0zy0zv\ 0zt0zp0<2>xg0xe0wa0vZ0uW0tU0sS0qP0pM0oK0mI0kF0<3>e\ 80c00`00Z00Y00<2>R00 } Lyapunov_o7003 { ; 12 minutes on a 1300Mhz PIII ; Passes=o; can't zoom past 1... reset=2001 type=formula formulafile=generalt.frm formulaname=Lyapunov07 function=acosh/cos passes=o center-mag=1.67602/0/0.819912 params=0.66/3/1/0.5/0.35/100/10/1.4/1000000/0 float=y maxiter=104 inside=zmag outside=summ logmap=yes sound=off colors=000L00<3>T00W00Y00Z00`00c00e80<2>jE0kF0mI0o\ K0pM0qP0sS0tU0uW0vZ0wa0xe0<2>zm0zp0zt0zv0zy0zv0zt0\ zp0<2>xg0xe0wa0vZ0uW0tU0sS0qP0pM0oK0mI0kF0<3>e80c0\ 0`00Z00Y00<3>P00N00L00I00I00<3>R00T00W00Y00Z00`00c\ 00e80<2>jE0kF0mI0oK0pM0qP0sS0tU0uW0vZ0wa0xe0<2>zm0\ zp0zt0zv0zy0zv0zt0zp0<2>xg0xe0wa0vZ0uW0tU0sS0qP0pM\ 0oK0mI0kF0<3>e80c00`00Z00Y00<3>P00N00L00I00I00<3>R\ 00T00W00Y00Z00`00c00e80<2>jE0kF0mI0oK0pM0qP0sS0tU0\ uW0vZ0wa0xe0<2>zm0zp0zt0zv0zy0zv0zt0zp0<2>xg0xe0wa\ 0vZ0uW0tU0sS0qP0pM0oK0mI0kF0<3>e80c00`00Z00Y00<3>P\ 00N00L00I00I00<3>R00T00W00Y00Z00`00c00e80<2>jE0kF0\ mI0oK0pM0qP0sS0tU0uW0vZ0wa0xe0<2>zm0zp0zt0zv0zy0zv\ 0zt0zp0<2>xg0xe0wa0vZ0uW0tU0sS0qP0pM0oK0mI0kF0<3>e\ 80c00`00Z00Y00<2>R00 } Lyapunov_o7006 { ; 12 minutes on a 1300Mhz PIII ; Passes=o; can't zoom past 1... reset=2001 type=formula formulafile=generalt.frm formulaname=Lyapunov07 function=flip/log passes=o center-mag=-1.77636e-015/1.77636e-015/0.719912 params=0.66/3/1/0.5/0.35/100/10/1.4/1000000/0 float=y maxiter=103 inside=zmag outside=summ logmap=yes sound=off colors=000L00<3>T00W00Y00Z00`00c00e80<2>jE0kF0mI0o\ K0pM0qP0sS0tU0uW0vZ0wa0xe0<2>zm0zp0zt0zv0zy0zv0zt0\ zp0<2>xg0xe0wa0vZ0uW0tU0sS0qP0pM0oK0mI0kF0<3>e80c0\ 0`00Z00Y00<3>P00N00L00I00I00<3>R00T00W00Y00Z00`00c\ 00e80<2>jE0kF0mI0oK0pM0qP0sS0tU0uW0vZ0wa0xe0<2>zm0\ zp0zt0zv0zy0zv0zt0zp0<2>xg0xe0wa0vZ0uW0tU0sS0qP0pM\ 0oK0mI0kF0<3>e80c00`00Z00Y00<3>P00N00L00I00I00<3>R\ 00T00W00Y00Z00`00c00e80<2>jE0kF0mI0oK0pM0qP0sS0tU0\ uW0vZ0wa0xe0<2>zm0zp0zt0zv0zy0zv0zt0zp0<2>xg0xe0wa\ 0vZ0uW0tU0sS0qP0pM0oK0mI0kF0<3>e80c00`00Z00Y00<3>P\ 00N00L00I00I00<3>R00T00W00Y00Z00`00c00e80<2>jE0kF0\ mI0oK0pM0qP0sS0tU0uW0vZ0wa0xe0<2>zm0zp0zt0zv0zy0zv\ 0zt0zp0<2>xg0xe0wa0vZ0uW0tU0sS0qP0pM0oK0mI0kF0<3>e\ 80c00`00Z00Y00<2>R00 } frm:Lyapunov02 {;"standard" Lambda-Formula, ; altered by Anthony Hanmer 2001 ;abMax = Length of ab-string in the form of: 2^LENGTH - 1 ;periodicity=no, inside=zmag, outside=ColorNumber ; ;p1 ... Starting Value / abMax ;p2 ... ab-String / Scaling Exponent ;p3 ... Scaling Factor / Filter Cycles ;p4 ... Zero Level / Divergence Result ;p5 ... Bailout ; x = real(p1), max = imag(p1), ab = real(p2) se = imag(p2), sk = real(p3) n = imag(p3), z = imag(p4) mxi = n + 1 - maxit sum = 0: n = n - 1 ab = 2*ab IF (ab > max) ab = ab - max c = imag(pixel) ELSE c = real(pixel) ENDIF IF (n < 0) sum = sum + fn1(abs(c*(1-2*x))) IF (n <= mxi && sum < p4) z = fn2(sum/n)^se*sk ENDIF ENDIF x = c*x*(1-x) p5 >= abs(x) } frm:Lyapunov07 {;"standard" Lambda-Formula, ; altered by Anthony Hanmer 2001 ;abMax = Length of ab-string in the form of: 2^LENGTH - 1 ;periodicity=no, inside=zmag, outside=ColorNumber ; ;p1 ... Starting Value / abMax ;p2 ... ab-String / Scaling Exponent ;p3 ... Scaling Factor / Filter Cycles ;p4 ... Zero Level / Divergence Result ;p5 ... Bailout ; x = real(p1), max = imag(p1), ab = real(p2) se = imag(p2), sk = real(p3) n = imag(p3), z = imag(p4) mxi = n + 1 - maxit sum = 0: n = n - 1 ab = 2*ab IF (ab > max) ab = ab - max c = imag(pixel) ELSE c = real(pixel) ENDIF IF (n < 0) sum = fn2(sum) + (abs(c*(1-2*x))) IF (n <= mxi && sum < p4) z = fn1(sum/n)^se*sk ENDIF IF (n > 0) sum = fn1(sum) ENDIF ENDIF x = fn1(c*x*(1-x)) p5 >= abs(x) }
On Wed, 2004-12-08 at 00:04, Tony Hanmer wrote:
And now for the main question, related to the latter several of the pars below: With this Lyapunov type in passes=o, why can I not zoom in further than about 1 and still see something being rendered on the screen?
It helps to use periodicity=0. Also, both the displayed area and the calculation area are zooming together. This will be fixed, with the appropriate switch setting, in the next patch. Remember that you can't actually zoom into the passes=o image. You are zooming into the passes=1 image and displaying the orbits as passes=o.
A further question - sorry, but I've just discovered digital printing of fractals as actual photographs here in the Republic of Georgia, maximum size 290 x 465 mm and 300 dpi. Passes=o, t and possibly other unusual rendering modes don't work in Disk/Ram Video sizes. Any chance of getting this changed? A large Buddahbrot would look STUNNING, for example.
The passes=g, b, & t, use a buffer with a size limit of 2048 bytes. This is not easy to fix, otherwise it would already have been done. I'll have to look at passes=o to see if there would be any problem, other than thrashing your hard disk, that would prevent going above the current limit of 2048x2048. Jonathan
participants (3)
-
Jim Muth -
Jonathan Osuch -
Tony Hanmer