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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image is a scene deep in the Z^(sqrt(2))+C Mandel fractal. I named it "Logarithmic Spiral" because of the vividly demonstrated spiral patterns surrounding the midget. These patterns can almost be seen trailing off the screen into remote imaginary dimensions. I enjoy exploring the Z^(sqrt(2))+C fractal because in it the midgets are quite challenging to find, yet often give away their presence by lying at the center of two symmetrical features -- just as midgets do in the classic M-set. Today's image can rate only a mediocre 5 however, for due to lack of time, I could give it only a cursory coloring effort. To add to the disappointment, the parameter file requires a one-hour wait before the image is finished. Some degree of salvation is at hand however in the form of the FOTD web sites, where the image will be available as soon as Paul and Scott can render and post it. Paul's site is at: The fractal weather Tuesday here at Fractal Central was cat-pleasing. Warm sunshine, gentle breezes and a temperature of 64F 18C made outdoor conditions near perfect for the aging but still dynamic duo, who spent several hours lounging in their porch chairs. But with design work to get done, a CD to work on, fractal philosophy to write, and fractal grass nearing the trimming stage, I have no time to lounge. So until next time, take good care, and cultivate patience. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Logarithmic_Spiral { ; time=1:00:01.10--SF5 on a p200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotBC1 function=floor passes=1
center-mag=+0.41397782356481880/+0.885364077781793\
80/6.328408e+010/1/130.000071851788562/-0.00018653\
2972593252133 params=1.4142/0/13/0 float=y
maxiter=16000 inside=0 logmap=-1750 periodicity=10
colors=0CCxCOwCOwCOvHOtPMtXMrhMpmMoeKoXKmPKkHKkCJj\
CJhCJfCJfCHeCHcCHcCHbCF`CFZCFZCFYCDWCDWCDUCDSCCRCC\
RCCPCCNCCNCCMCCKCCICCICCHCCFCCFCCDCCCCCACCACC9CC7C\
C5CC7CC9CCACCACCCCCDCCDCDFCDHCFHCHICJKCJKCKMCMNCMN\
COPCPRCRRCRSCSUCUWCWWCWYCXZCZZCZ`C`bCabCccCceCeeCf\
fChhChhCjjClkCmkCmmCooCqoCqpCrrCttCutCuvCwwCywCzxC\
zxCzxCzxCzxCzxCzxCzxCzxCzxCzxCzxCzxCzxCzxCzxCzxCzx\
CzxCzxCzxHzxKzxPzxSzxWzw`zvczthztlzrozptzowzmzzkzz\
kzzmzzmyzouzouzouypuupuqpumrujruetuatuXtuUvuPvuMvu\
JmuOeuRZuWRtZKrcCqf5ol0mo0la0jr0hz7fz5hz5jz5lz5lz5\
mz4oz4qz4qz4rz4tz4tz2uz2wz2yz2yz2zz2zz0zz0zz0zz0zz\
0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zy0zy0zw0zw0zu0zu0z\
t0zt0zt0zq0zo4zl5zj9zhAzeDzcFzaIzZKzXNzWPzSSzRUzOY\
zMZzKbzHczFfzDhzCkzCmzCfzCbzCZzCYzDWzDWzFUzFUzHSzH\
RzHRzJPzJPzKNzKNzMMzMKzMKzOIzOIzPHzPHzRFzRDzRDzSCz\
SCzUAzUAzW9zW7zW7zX5zX5zZ
}
frm:MandelbrotBC1 { ; by several Fractint users
e=p1, a=imag(p2)+100
p=real(p2)+PI
q=2*PI*fn1(p/(2*PI))
r=real(p2)-q
Z=C=Pixel:
Z=log(Z)
IF(imag(Z) > r)
Z=Z+flip(2*PI)
ENDIF
Z=exp(e*(Z+flip(q)))+C
|Z| < a }
END 20.0 PAR-FORMULA FILE==================================
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times.
