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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image is titled "Nobody's Perfect". The body I am referring to is myself. I recently wrote that the strange rectangle appears only in the Julia sets of the Z^(2.003)+C Julibrot. But today, just to be double sure, I carefully checked the Mandelbrot aspect of the area. Nobody could have been more surprised than me when I found the near-perfect rectangles scattered everywhere. To make things even worse, there are Mandelbrot midgets in the area, surrounded by empty rectangles. All this goes to show that, just because I have been writing the FOTD for over 9 years, makes me no expert in the field of fractals, which remain unpredictable. I doubt that anyone including Mandelbrot himself could claim to know any more than a tiny part of all there is to know about fractals. Today's image shows a most curious feature, which almost looks like a living figure. It has round holes and rectangles everywhere. The quadratic midgets within it are not that difficult to find, but I will show none until the month ends. After all, this is supposed to be a month without a midget. The render time of 7-1/2 minutes may be ignored by visiting the FOTD web site at: Sometimes it was cloudy here at New Fractal Central on Sunday, and sometimes it was almost clear. There were even a few drops of rain in the morning. But the temperature reached a pleasant 75F 24C, and the fractal cats totally ignored it. A friendly cat tussle got a bit out of control at one point, but the duo quickly made up. My day was good enough. With any luck, tomorrow will be the same. But I think that a rather sizable job might come in by afternoon. If all goes well, the FOTD will appear before the job arrives. Until next time, take care, and be of good cheer even if your team lost the big game. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Nobody's_Perfect { ; time=0:07:32.86--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=SliceJulibrot4
center-mag=-0.00000032538104575/-0.000000103263196\
45/2.43078e+008/1/-52.5/-1.14117049143658278e-013
params=0/0/0/0/-1.7435/0/0/0/2.003/0 float=y
maxiter=4500 inside=0 periodicity=10
colors=000OZkLYmJXoGWqEVsBUu9Tw7Tx9SwBRvCQvEQuFPtH\
OtIOsKNrLMrNLqOLpQKpRJoTJnUInWHmXHmWFkWEiWDgWCeWBc\
WAaW9_V8YV7WV6UV5SV4QV3OV2NW1MX1MX1MY1LY1LZ1LZ1L_0\
K`0K`0Ka0Ja0Jb0Jb0J`4M_7PYBSXEVWIYUL`TPbSSeQWhPZkO\
bnMeqLitKlvJjtJhrIfqIdoIbmH`lHZjGXhGWgGUeFScFQbEO`\
EMZEKYDIWDGUDFTFJVHMXIPZKS`LVaNYcO`eQdgRgiTjjUmlWp\
nXspZvr_ys`xtawtbwtbvucuuduudtuesvfsvfrvgqvhqwipwi\
owjowknxkmxlmxmlxmkynkyojyojyjdwf_vaUuYPtTKrPEqK9p\
G4oJ5lL6jN7gP8eS9bUA`WAYYBW`CTbDRdEOfFMiGJkGHmHEoI\
CrJ9tK7vL4xM2zM0tN1oO2iO3dP4ZP5UQ6PQ7RO9TNBVMDXLEZ\
KG`JIbIKdHLfFNhEPjDRlCSnBUpAWr9Yt8ZoDXkIWgNVcSUZXS\
VaRRfQNkPJpOLlKNhGPeDRa9SZ6U_6Wa7Yb7_c7ae7cf7eh7gi\
7ij7_d8QZ8GT86N89SCCWFF_JHdMKhQNlTPpWNoULnTJmSIlRG\
kQEkPCjNBiM9hL7gK5fJ4fI7eHAdHCcHFcHIbHKaHN`HQ`HS_H\
VZHXZHU_FS_DP_CN`AK`9I`7Fa5Da4Aa28a19c4Ad6Be8CfADh\
DEiFFjHGkJHmMYacV`eT_gQZi }
frm:SliceJulibrot4 {; draws most slices of Julibrot
pix=pixel, u=real(pix), v=imag(pix),
a=pi*real(p1*0.0055555555555556),
b=pi*imag(p1*0.0055555555555556),
g=pi*real(p2*0.0055555555555556),
d=pi*imag(p2*0.0055555555555556),
ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g),
sg=sin(g), cd=cos(d), sd=sin(d),
p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd),
q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd),
r=u*sg+v*ca*sb*cg, s=v*sin(a),
c=p+flip(q)+p3, z=r+flip(s)+p4:
z=z^(p5)+c
|z| <= 9 }
END PARAMETER FILE=========================================
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times.
