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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's resurrected formula was never quite as dead as some of the other formulas in the jim.frm file, which is where I store the formulas that I have almost but not quite forgotten. I have already used it a number of times to create FOTD images. But like most of the other half-forgotten formulas, I have no idea what I was trying to accomplish when I wrote it. Actually, this particular formula holds quite a bit of potential. It could be the most under-appreciated in my vast collection of near-forgettable efforts, and certainly deserves a place in my active allinone.frm file. With the inside set to number zero, the formula draws nothing but empty circles, regardless of how the parameters and function are tweaked. But when the inside is set to an active fill, such as the 'bof61' of today's image, the empty circles are filled with strange and often totally unpredictable fractal patterns unlike anything seen in normal inside-outside images. The bof61 fill colors the pixels according to the number of the iteration that takes that point closest to the origin. Today's image, which consists entirely of 'inside' material, is named "Almost an M-set". While studying it, I noticed a shape in the center that looks like it is trying to be a midget Mandelbrot set, but is not quite making it. It comes close enough however to be the source of the name for the entire image. Trying to rate the image proved more difficult than expected. When I first saw it, I thought, wow this is great -- it rates an 8! Then I looked again and thought, now what's so unusual about it -- it's just another fractal like I've seen hundreds of times before, and it rates only a 3. I finally decided on a rating of an average 5. That way I could not be too far off. The render time of 4 minutes is acceptably fast for an average image. Simply copy this letter into your Fractint directory (folder) with a .par extension, and run it as you would any other parameter file. If something goes wrong, do not panic. Simply go to the FOTD web site at: The clouds hung heavy all day Thursday here at Fractal Central, with short light showers at frequent intervals and a high temperature of 77F 25C. Though only 0.04 inch (1mm) of rain fell all day, the grass stayed wet, making it just another rainy day from the cats point of view. They passed the day on their shelf by the window, wishing it were a better day. Today is starting with flood warnings in effect. This does not bode well for the cat duo. For me things look quite average. The next FOTD will appear in 24 hours. Until then, take care, and where was today's fractal hiding when the (theoretical) big bang happened? Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Almost_an_M-set { ; time=0:04:12.66--SF5 on a P200
reset=2004 type=formula function=cotan passes=1
formulafile=jim.frm formulaname=Mystic2
center-mag=0.0482742/5.55112e-016/11.46736
params=-1/3.2/-2.4/-1.6/4.5/0.0025 float=y
maxiter=95 inside=bof61 periodicity=0
colors=000ebLaTHOHmQIZ1kYOKdSNiVVUD4FK9EREEddQaXMz\
_IjcWl55h98dCA`GCj3Qe9MaEIe7ZaRB`PC_NDZLELOZRaLYVm\
YRaYNQs82_cmZXaYQQsiT3tpcVMaRJ_NG4N7dbgDZuzqWk_Ntj\
1aVl`Sc_PVZMMijBe3Rc7NaBK_FHzPfIYcMUXQQRUMKKc6PX9U\
QC9MwGLkMK`SJPSFBUHCWIDLknQaaUSQ7AmGDaPGQGA61T1IO8\
nmkeYV1vSR7cUBVWFMPJRSJMVJI_sJZfHYVF84eF8ZLCSSGL3k\
Hayi_jZZXOfdxcZlaU`_OP35qEAcOFRwZ9nTBeODRXjTTaVQUX\
MMm5JIm`MeVQYPUQJdfAb`B`VCZPDjh9TJPc7y`DaqwNjiKcWH\
puqZX6_26Z78ZBAYFCjeJcUGuuOmhKeWHerWbfQ_VKZSIYPGYM\
FMVQOrGSfFVVEQGHWy_BZcKkPTxBSpQRhdRareYVsV7fPBVJFJ\
DJQFRWHZaJe_JWcILZJNk`1dS8b9jOCwREkTG`WIPwdvpZjjU_\
cOPYL6tsL`Mx_LlZK`YJPLJUPJQSJMVJIJYwNUkRQ`VMP8PMQV\
wSSkUP`WMPm0Zi5TeAOaFJ9KA5CcKGR6GtKIZuoTofPiZLcRH3\
5ZGanMVaSPQz0ir5akAUdFMFyxPc`HMTKUbROQrf`l`VgVPbPJ\
ckfacZ`XSZQLjgAcVCQFMTHJWIGOfCSZDVREaQN`OK_MIZKGQ`\
ETVEWPEZeBPlISbGVTFmvSilO }
frm:Mystic2 {; Jim Muth
a=real(p1), b=imag(p1), c=real(p2),
d=imag(p2), k=real(p3), f=imag(p3),
g=pixel, z=(pixel)^a+(b*(pixel))^c:
z=(fn1(z)+(d*(g)))^k+(f*(cos(g)))
g=sqr(g),
LastSqr <= 100 }
END PARAMETER FILE=========================================
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