Fractal of the Day
by Jim Muth
FOTD -- December 09, 1998
Fractal visionaries:
Today was perfect for fractals -- dull, dreary, overcast, occasional light rain, and a temperature of 53F 12C, which is still above average but far more reasonable than what we've had so far this month.
To start, let me confess that I have no earth-shaking philosophy today. My excuse is that I got involved in setting up the Christmas tree and pondering how to decorate it. (When I decorate a tree, the position of every ornament and every light must be calculated to an accuracy of seven decimal points.)
For my fractal, I turned to my MandelbrotMix7 formula and checked what happens when Z^(-0.4999) is subtracted from Z^(-0.5) and a critical plane is calculated. At first glance, what happens appears to be not much more than the traditional disappointing blank screen. But just off the right edge lies a curious fractal object -- a disconnected edge, a bunch of blobs, and a spidery outline of a Mandelbrot section.
When enlarged, this outline reveals unexpected detail. It has valleys and the valleys have thickness. Today's picture is a glimpse of the center of the most prominent valley. Most of my fractals are centered on a midget M-set; today's fractal has no sign of a midget. What it does have is a very unusual fractal herringbone pattern combined with a 3-spiral filament network.
I have named the picture "Herringbone Fractal" for an obvious reason -- because that's what it is. The parameter file runs in 20 minutes on a fast 486, and the GIF file has been posted to:alt.binaries.pictures.fractalsand to the WWW at:http://home.att.net/~Paul.N.Lee/FotD/FotD.html
Tomorrow, I'll try again for that profound philosophy. If that fails, I'll bring a fractal. Until then, take care, and when boredom strikes, consider livening things up with a never-before-seen fractal.
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=========================================
HerringboneFractal { ; 25min on a 486-100mhz, 640x480
reset=1960 type=formula formulafile=critical.frm
formulaname=MandelbrotMix7 passes=1 center-mag=+4.681\
16329017693600/+0.28683485136808030/87.17949
params=1/-0.5/-1/-0.499/5000/0 float=y maxiter=1200
bailout=25 inside=0 logmap=22 symmetry=none
periodicity=10 colors=000qXvqZvr`vtavtcvvev<5>vqvvrvvv\
v<21>vvvvvvvtvvrtvqrvorvmqvkoviovgmvekvckvaiv`gvZgvXev\
VcvTcvRavP`vN`vLZvJXvHXvFVvDTvCTvARv8Pv6Pv4Nv2Lt0Lt0Jt\
0Ht0Hr0Fr0Dr0Dq0Cq0Aq0Aq08o06o06o04o02m02m00m00m00k00k\
02i02i04g04g06e08e08c06c06a06a06`06`06Z06Z06X06X06V06V\
06V06T06T06R06R06P06P06N06N06L06L26J26J46H66H66F86F86D\
A6DC6DC6CD6CD6AF6AH68H68J66J66L64N64N62P62P60R60T60T60\
V60V60X60X60V60V60V60V60T60T60T62T62R62R62R64R64R64P66\
P66P66P66N68N68N68N68N66L66L66L66L66J6<2>6J66J66H64H64\
H64H64F6<2>4F64F64D64D64D62D6<3>2C62C62A6<2>2A62A60880\
86086086066<2>066066046040040040020<2>020020000<2>0000\
06<8>006606<4>q06v06<3>v06v06v26v46v86vA6rC6qF6iJ6kL6k\
N6mP6oR6oT6
}
END PARAMETER FILE===========================================
START 19.6 PARAMETER-FORMULA FILE============================
HerringboneFractal { ; 25min on a 486-100mhz, 640x480
reset=1960 type=formula formulafile=critical.frm
formulaname=MandelbrotMix7 passes=1 center-mag=+4.681\
16329017693600/+0.28683485136808030/87.17949
params=1/-0.5/-1/-0.499/5000/0 float=y maxiter=1200
bailout=25 inside=0 logmap=22 symmetry=none
periodicity=10 colors=000qXvqZvr`vtavtcvvev<5>vqvvrvvv\
v<21>vvvvvvvtvvrtvqrvorvmqvkoviovgmvekvckvaiv`gvZgvXev\
VcvTcvRavP`vN`vLZvJXvHXvFVvDTvCTvARv8Pv6Pv4Nv2Lt0Lt0Jt\
0Ht0Hr0Fr0Dr0Dq0Cq0Aq0Aq08o06o06o04o02m02m00m00m00k00k\
02i02i04g04g06e08e08c06c06a06a06`06`06Z06Z06X06X06V06V\
06V06T06T06R06R06P06P06N06N06L06L26J26J46H66H66F86F86D\
A6DC6DC6CD6CD6AF6AH68H68J66J66L64N64N62P62P60R60T60T60\
V60V60X60X60V60V60V60V60T60T60T62T62R62R62R64R64R64P66\
P66P66P66N68N68N68N68N66L66L66L66L66J6<2>6J66J66H64H64\
H64H64F6<2>4F64F64D64D64D62D6<3>2C62C62A6<2>2A62A60880\
86086086066<2>066066046040040040020<2>020020000<2>0000\
06<8>006606<4>q06v06<3>v06v06v26v46v86vA6rC6qF6iJ6kL6k\
N6mP6oR6oT6
}
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==============================
This URL has been accessed approximately 
times.
Go back to top, or to the main FotD index page.
Go to Paul's Fractal pages or Home Page.
Want to create, see or know more about fractals?
Go to my Fractal Links webpage.
Website brought to you by the AT&T Personal Web Pages from the AT&T WorldNet Service.
Copyright © 1994--2006 Nahee Enterprises. All rights reserved. Reproduction in whole or in part in any form or medium without express written permission of Nahee Enterprises is prohibited. Nahee Enterprises and the Nahee Enterprises logo are trademarks.
