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Fractal of the Day
by Jim Muth
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Fractal visionaries: It was cloudy today here in fractal land, with a few light showers in the evening. The high temperature of 68F 20C was perfect for exploring a hyperfractal, which I did with my Mandel_4-D formula. Every fractal explorer knows that when the starting point of Z is perturbed, the features of the resulting image are distorted. But when the fractal is a four-dimensional Mandelbrot set, the distortion can be downright grotesque, as today's image shows. The mis-shapen object in today's picture is the prominent midget on the negative tail of the 4-D hyper-M-set, viewed in a remote perturbed plane. I have named the picture "Mandelbrot Maestro" because that phrase popped into my head as I studied the image. I can't begin to explain why it looks the way it does. Nor can I explain exactly what the formula does. At times, the fractals drawn by this formula don't make sense, leading me to suspect that some of the images are artifacts. I'll need to do quite a bit of testing before I can add comment lines -- something that I have resolved to start doing with all my formulas. (Nothing is more annoying than having a formula and not knowing how to make it work.) The GIF file of today's quick image has been posted to ABPF and to: Tomorrow . . . who knows? I'll be here again with another fractal -- that's for sure, but as to what type of fractal it will be -- I won't know until I actually see it. Even then I may not know. So until then, take care, and didn't someone once claim that the fractals of Autumn are the best of the entire year? Jim Muth jamth@mindspring.com |
START FORMULA================================================
Mandel_4-D {; 4-D Mandelbrot, 8-D Julibrot
a=(p1), b=(0,0), d=p2+2:
f=sqr(a)-sqr(b)+pixel
b=d*a*b+p3
a=f
|a|+|b| <16
}
END FORMULA==================================================
START PARAMETER FILE=========================================
Mandelbrot_Maestro { ; 1-1/2min on a 486-100mhz, 640x480
reset=1960 type=formula formulafile=jim.frm
formulaname=Mandel_4-D
center-mag=-1.75909/0.00219158/69.70197
params=0/0/0/1.137/0.001/0
float=y maxiter=1200 bailout=25 inside=0
logmap=yes symmetry=none periodicity=0
colors=000KYN<8>1u43n7029<3>06H47H<4>TEOYAPbGQg7RlISmCT\
nPUoIVpVWpOXq`YrPZsc_oNzsb_lHgkaekJckZakL_kWYkNXkYVkPTk\
VRkRP<3>kVIkWGlYH<12>hD0<7>4p0<13>l7y<3>DRq0_r<7>VA_Z7Y\
b1X<13>R_MRaMPcO<6>EpWHxa<2>BhZ4f`<12>u9N<2>lTCi_9dd3\
<12>sg_<15>a38<10>SgUNoMJwF<14>ZaV_`W`ZZ<9>bPx<3>lxe<6>\
ZrmYrnWpl<9>L``<2>GlZKcQNVIfJHy7HdALKDOVLY<3>NWQ
}
END PARAMETER FILE===========================================
START 19.6 PARAMETER-FORMULA FILE============================
Mandelbrot_Maestro { ; 1-1/2min on a 486-100mhz, 640x480
reset=1960 type=formula formulafile=jim.frm
formulaname=Mandel_4-D
center-mag=-1.75909/0.00219158/69.70197
params=0/0/0/1.137/0.001/0
float=y maxiter=1200 bailout=25 inside=0
logmap=yes symmetry=none periodicity=0
colors=000KYN<8>1u43n7029<3>06H47H<4>TEOYAPbGQg7RlISmCT\
nPUoIVpVWpOXq`YrPZsc_oNzsb_lHgkaekJckZakL_kWYkNXkYVkPTk\
VRkRP<3>kVIkWGlYH<12>hD0<7>4p0<13>l7y<3>DRq0_r<7>VA_Z7Y\
b1X<13>R_MRaMPcO<6>EpWHxa<2>BhZ4f`<12>u9N<2>lTCi_9dd3\
<12>sg_<15>a38<10>SgUNoMJwF<14>ZaV_`W`ZZ<9>bPx<3>lxe<6>\
ZrmYrnWpl<9>L``<2>GlZKcQNVIfJHy7HdALKDOVLY<3>NWQ
}
frm:Mandel_4-D {; 4-D Mandelbrot, 8-D Julibrot
a=(p1), b=(0,0), d=p2+2:
f=sqr(a)-sqr(b)+pixel
b=d*a*b+p3
a=f
|a|+|b| <16
}
END 19.6 PARAMETER-FORMULA FILE==============================
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times.
