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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: For the second day of the second year of the third millennium we have a fractal image that rates a much-above-average 8. It is one of my 'evaporated' scenes, where I take an image that contains a negative power of Z, find something interesting, and then raise the bailout radius to one-googol, which causes the screen to go blank. Next, I apply one of the non-flat inside fills to the image, which now consists totally of 'inside' points. Sometimes, nothing much happens, but usually, the inside fill reveals the 'ghost' of the scene that originally was there. Thus, today's image is a ghost, a thing which in the world of fractals certainly does exist. I was a bit puzzled when the time came to give a name to the image. It reminded me of something...but what? Then, after pondering for several minutes, I thought of a jellyfish. This was it. The image, with its appearance of transparency, reminds me of a jellyfish drifting gently in a warm ocean current. Of course, no real jellyfish is so symmetrical. It is the effect of transparent elements before an infinite blue background that earns the name. The warhorse MandelbrotMix4 formula calculated a critical plane of the expression 45Z^(-0.8)-36Z^(-0.9)+(1/C) to create the parent fractal of today's image. When calculated with the default bailout radius, this parent is little more than a circle filled with great blobs of fractal glop. But a small bud of Mandel-material lies on the X-axis, and today's image is located at the tip of a filament stretching from a sub-bud of this bud into an open area, where it finally dies out. The 37-minute render time of the attached parameter file is slow. Those with other things to do as the normal work routine resumes will want to download the completed GIF image from Paul's web site at: With the temperature hanging in the middle 40'sF (around 6C), it rained steadily all day Wednesday here at Fractal Central, sometimes quite heavily with occasional claps of thunder. Some minor flooding was reported around the area, but F.C. remained dry. The dynamic cats were very depressed however as they sat at their window, watching the rain and wishing they could go out. An evening treat of tuna helped ease their depression, but they still ended the day in a sullen mood. Though today is starting cloudy, at least the rain has ended, which is a good sign. Now, if the mud in the yard would dry, the dynamic ones might have a pleasant day. It will take more than a dry yard to make my day pleasant however. This will not happen until the design work is finished, and it will not be finished until I begin. So until tomorrow, take care, and be kind to your fractals. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
Jellyfish { ; time=0:30:23.25--SF5 on a P200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip passes=t
center-mag=-0.4004091333751482/+0.0215282924423132\
/3.080974e+007/1/80/-1.5530640837951859e-007
params=45/-0.8/-36/-0.9/0/1e+100 float=y logmap=yes
maxiter=1200 inside=fmod proximity=1 periodicity=10
colors=000UPqUQpURnUSlUTjUUhUVfUXeUYdWZcY_b_a`ab_c\
cZedYfeWgeVfeUfeTeeSefQdfPdeOceNcfLbfKbfJafIafHZeK\
XdMVcNTbPQaQO`RM_TK_UHZVFYXDXYBWY8V_6U`4Ta2Tb1S`1S\
_1SZ1SX1SW1SW1SV1RV1RV1RU1RU1RV1RV1RW1QX1QX1QY1QZ1\
QZ1Q_1Q`2R_2RZ3SY3SX4TX4TW4UV5UU5VU6VT6WS7WR7XQ7XQ\
8YP8YO9ZN9ZNA_MA_LA`KBaJBbJCcICdHDdGDfGDfFEgEEgDFh\
CFiCGjBGjAGk9Hl9Hm8In7Io6Io6Hn8HmAGmBGlDFlEFlGEkHE\
jJDjKDiMCiNCiPBhQBgSAgUAgV9eX9eY8e_8d`7cb7cc6be6bf\
5ah5ai6`g6_e6Zd6Yb7Xa7W_7VZ7UX7TV8SU8RS8QR8PP8OO9N\
M9MK9LJ9KHAJGAIEAHDAGBAF9BE8BD6BC5BB3BB2BB2BC2BC2B\
D2BD2HQ5Mb8RoAQnCQmEQlFPkHPjIPiKPhMOgNOfPOeQOdSNcT\
NbVNaXN`YM__MZ`PYbUYcZagcejhimmmqrrtwwwzzzwxtrtnmp\
hhmbcfVZ`NaUSbEWcA_gBShBLfCEbC7ZC0YE1XG2WH3VJ4UK5T\
M6SN7RP8RQ9PP9NO9KNAIMAGLAEKAFJFGJKGJOHJTIJYIJaJJf\
KJkKJoLHpLGpLFpLEpLDpLCqLBqLAqL9qL8qL7rL6rL5rL4rL3\
rP7pTAoXDn`GmdJlhMklPjpSi }
frm:MandelbrotMix4 {; 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,
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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