Fractal of the Day
by Jim Muth
FOTD -- December 28, 1998
Fractal visionaries:
A hazy Winter day with a temperature of 36F 2C is perfect for fractal hunting. Since today met those conditions, I went on a fractal hunt. The scene I found is located in the difference area around the Z^1.274+C figure.
I named the picture "Patches of Color". It really is little more than a standard Mandelbrot midget surrounded by broken patches of color. Curiously, each patch seems to be part of a different but mostly unseen larger fractal, yet they all fit together into an organized pattern -- the familiar pattern that surrounds so many midgets.
Unfortunately, the fractal is a very slow one, taking over four hours on the fastest 486 when calculated from the parameter file. But luckily I have been able to post the finished GIF file to Usenet at:alt.binaries.pictures.fractalsand it is also available at:http://home.att.net/~Paul.N.Lee/FotD/FotD.html
Oh oh, I'd better end this right now. I hear my two cats downstairs fighting over one of the tree ornaments, which I fear they've just turned into a fractal. So while I'm breaking up the fight and cleaning up the mess, take care, and isn't Christmas strange. You wish it wasn't coming, and then when it arrives you wish it would never leave.
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======================================
Patches_of_Color { ; 4-3/4hrs on 486-100mhz, 640x480
reset=1960 type=formula formulafile=critical.frm
formulaname=MandelbrotMix7 passes=1 center-mag=+3.1\
4648308901950900/+0.00959892079798546/7327538/1/-120
params=0.998/1.275/-1.002/1.273/500/500 float=y
maxiter=45000 bailout=25 inside=0 logmap=825
symmetry=xaxis periodicity=10
colors=000bSY<19>iJA<7>96O<13>C80<16>IKEIKEKLG<16>g\
VXiWYlWZ<4>xZcz_dz_ez`fz`g<4>va`ua_uaZuaY<22>ra5ra4\
o`6<10>R`POeRbiTefUZcVV`VLZWMWW<2>NPYNNYNMXOKVOITOH\
QPFPPDMPCN<4>NDdNDgNDiOEhOEh<27>nRZoRZpQ_<4>kLdjKei\
KfhKg<6>aKn`Ko_LpZMqYNrXOsWPtXQu<2>WTxWUyWUzWUz<17>\
VUzVPzVUz<12>VUzaUzaUzbUz
}
END PARAMETER FILE========================================
START 19.6 PARAMETER-FORMULA FILE=========================
Patches_of_Color { ; 4-3/4hrs on 486-100mhz, 640x480
reset=1960 type=formula formulafile=critical.frm
formulaname=MandelbrotMix7 passes=1 center-mag=+3.1\
4648308901950900/+0.00959892079798546/7327538/1/-120
params=0.998/1.275/-1.002/1.273/500/500 float=y
maxiter=45000 bailout=25 inside=0 logmap=825
symmetry=xaxis periodicity=10
colors=000bSY<19>iJA<7>96O<13>C80<16>IKEIKEKLG<16>g\
VXiWYlWZ<4>xZcz_dz_ez`fz`g<4>va`ua_uaZuaY<22>ra5ra4\
o`6<10>R`POeRbiTefUZcVV`VLZWMWW<2>NPYNNYNMXOKVOITOH\
QPFPPDMPCN<4>NDdNDgNDiOEhOEh<27>nRZoRZpQ_<4>kLdjKei\
KfhKg<6>aKn`Ko_LpZMqYNrXOsWPtXQu<2>WTxWUyWUzWUz<17>\
VUzVPzVUz<12>VUzaUzaUzbUz
}
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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