Fractal of the Day
by Jim Muth
FOTD -- December 11, 1998
Fractal visionaries:
A lovely late Autumn day with a temperature of 50F 10C gave a surprise in the afternoon when a pair of sun dogs appeared in the SW sky. The dogs led to an evening of Fractalling and tree decorating. The tree is about half finished, while the fractal is completely finished.
But somewhere along the way, the fractal had a breakdown. I guess it was inevitable, given the sensory overload I carried over from too much time spent enduring the shopping madness of the local supermall. But all was not lost. I had pity on the poor confused fractal that I found, and declared it my FOTD for today.
This fractal is indeed unlike any I have posted before. Fractals are known for having sharp edges. This is why they are tricky to convert to JPEG. But today's fractal has no sharp edges -- in fact it is total blur. No, I did not run it through a blur filter. (Though I did crank up the colors a bit.) If I had blurred it, the blurring would not have translated into a parameter file. The blur is in the image.
To begin, I must say that the higher the resolution, the better this image will appear. I have posted it at a res of 640x480, but that is to keep the file to a manageable size. I recommend a minimum of 1024x768. Now about that blur.
The image is not a true fractal. It is an artifact of mathematical imprecision. What has happened is apparent once the "Z" screen is examined. The extreme value of real(p3) had already magnified the imprecision to the point where only a moderate bit of enlargement was needed for the breakdown to occur.
I named the broken-down fractal "Fractal Breakdown". But the overwrought GIF file has been tranquilly posted to:alt.binaries.pictures.fractalsand to:http://home.att.net/~Paul.N.Lee/FotD/FotD.html
Tomorrow, I'll have another fractal to wonder about. And don't give up on that ersatz philosophy I keep threatening to write. It actually might appear tomorrow. The only way to be sure is to check back here at about this same time 24 hours from now. Until then, take care, and always remember -- a fractal is a fractal and a mystery at the same time.
Jim Muth
jamth@mindspring.com
START FORMULA================================================
MandelbrotMix7 {; 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=pixel:
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| <= l
}
END FORMULA==================================================
START PARAMETER FILE=========================================
Fractal_Breakdown {; *1hr--draw at highest resolution
reset=1960 type=formula formulafile=jim.frm
formulaname=MandelbrotMix7 passes=1
center-mag=+1.08434279873081000/-0.01077824922803778\
/3035401 params=1/3.14159265359/-1/3.141592653589\
/5e011/0 float=y maxiter=1300 bailout=25
inside=255 logmap=64 symmetry=xaxis periodicity=10
colors=0004Ab2AeTJQzSCzW9zZ6z`3ze0zh0zk0si0ih0`f3Tf5L\
e8EcB8bE2bH0S80J00B00H04L0AR0HY2<2>bn9SQ3Z6nW1nV0oT0q\
S0qY0n`0lf0ik0hq0fv0cz0bz0`z3czAezJhzSizblzlntkoiio`h\
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zSczO_wVWt_SofOllLisJYcILRHCG<3>8AVSSS
}
END PARAMETER FILE===========================================
START 19.6 PARAMETER-FORMULA FILE============================
Fractal_Breakdown {; *1hr--draw at highest resolution
reset=1960 type=formula formulafile=jim.frm
formulaname=MandelbrotMix7 passes=1
center-mag=+1.08434279873081000/-0.01077824922803778\
/3035401 params=1/3.14159265359/-1/3.141592653589\
/5e011/0 float=y maxiter=1300 bailout=25
inside=255 logmap=64 symmetry=xaxis periodicity=10
colors=0004Ab2AeTJQzSCzW9zZ6z`3ze0zh0zk0si0ih0`f3Tf5L\
e8EcB8bE2bH0S80J00B00H04L0AR0HY2<2>bn9SQ3Z6nW1nV0oT0q\
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0RS0NR0JR0GR0CR19R27R3CV9HYEL`KRcRWhY`kcfnk_hlTcnO_oI\
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KEeJBZH9TG6ND3HC1C99G6HICIKIJLOKN<3>qQS0QbBNE_K0`J0bI\
1cH3eH6fG9hEBiDEiDH_GISIJKJK<2>1QO0RO0Ic2VOEhASv0Oq6K\
lDHhLEeVGfTHfTIhS<2>LiRNiRNiRQ`KRTGSLBVE6W82Y20Z00T10\
Q60LB0IH0EN0<2>5f0VB6<2>JD8GE9CGA<2>4HB7OIAVQ6_O3eN0i\
L0oK0vJ0zI2ncCczHfvKhnQkhTl`ZnVbqQhsJltE0zh6zcDz_LzWV\
zSczO_wVWt_SofOllLisJYcILRHCG<3>8AVSSS
}
frm:MandelbrotMix7 {; 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=pixel:
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| <= l
}
END 19.6 PARAMETER-FORMULA FILE==============================
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