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Fractal of the Day
by Jim Muth
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Fractal visionaries: A cloudy day with a temperature of 41F 5C, and the slushy melting snow, made conditions perfect for hunting for fractals. I went hunting once again in the MandelbrotMix7 formula. But before getting to the fractal I found, I must tell of a tiny mystery here in fractal country. There is a small woods about three blocks from fractal central, and in that woods about two months ago I discovered something I have never before seen. While walking through the woods along a narrow path at the bottom of a shallow valley, I noticed something glittering in the late afternoon sunlight a short distance up the hillside. Investigating, I found a shrine that had been set up there in memory of a young man who had died two years previously. A rough, wooden cross stood stiff in the autumn air, its base embedded deeply and firmly in the earth. Attached to the cross were a number of carefully written memorial poems. Some were still fresh, others had nearly disintegrated from exposure to the elements. A bouquet of roses not more than two days old lay at the left side of the cross, while a collection of angel statues lay at the right side and family photos lay all around. An inexpensive set of headphones was nailed to the top of the cross, with an attached note which read, "I love you; I know you can hear me with these." Since discovering the spot, I have visited it about once a week. I have found that it is still being maintained by some unknown person. Once a week, fresh roses appear, and on the evening before Christmas I found a tiny tree adorned with a string of battery-powered lights standing poignantly in the snow beside the cross. A woman's footprints led from the spot out of the woods, only to be lost in the mass of footprints on the sidewalk. The next evening I returned and found the lights still burning, but by the following evening they had gone dark. The identity of those involved is a mystery, and perhaps it should remain that way, but I shall continue to visit the spot once a week until the memorials there are forgotten and crumble to dust. What does this have to do with fractals? When I saw today's fractal, I was reminded of those tiny lights burning in the snowy dusk. I promptly named the picture "Celestial Midget". It was created with the MandelbrotMix7 formula and is a scene in the fractal that results when Z^(-1.005) is subtracted from Z^-0.99. Once again, the parameter file runs quite slow -- over two hours on a 486-100mhz. But the GIF file is posted to:alt.binaries.pictures.fractalsand to: I'll be here again tomorrow with another fractal and another few words about the fractal. Until then, take care, and I wonder if a clue to the answer to the riddle of life can be found if we look deeply enough into the world of fractals. 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=========================================
Celestial_Midget { ; 2-1/2hr on 486-100, 640x480
reset=1960 type=formula formulafile=critical.frm
formulaname=MandelbrotMix7 passes=1
center-mag=+0.09165816355988156/-0.14337973096377420\
/340319.4/1/112.499 params=1/-0.99/-1/-1.005/100/0
float=y maxiter=12000 bailout=25 inside=0 logmap=375
symmetry=xaxis periodicity=10
colors=66666666666966E66I66I66OLBN66X66X<2>66j66e66p\
66t<2>66t0Qz66t<49>66t96t96t96tE6tE6tE6tI6tI6tI6tO6t\
O6tO6tS6tS6tS6tX6tX6tX6t`6t`6t`6te6te6te6tj6tj6tj6tp\
6tp6tp6tt6t<26>t6tz6tt6tt6tt6tzd0p_2e6tX6tS6tI6t96t6\
6t<6>66t66p66p6Qz66t66`66`66X66S66O66I66N66I<3>66I66\
N<2>66N66Q66Q<4>66W66X66X66`<6>66`69`69`6Ee6Ee6Ie6Ie\
6Oe6Oe6Se6Se6Xe6Xe6`j6`j6ej6ej6jj6jj6pj6pj6tj6tp<4>6\
tp6tj<4>6tj6te<4>6te6t`<4>6t`6tX<2>6tX9tX9tXEtSEtSIt\
SItSItSOtOOtOStOStOStOXtOXtI`tI`tI`tIetIetIjtEjtE
}
END PARAMETER FILE===========================================
START 19.6 PARAMETER-FORMULA FILE============================
Celestial_Midget { ; 2-1/2hr on 486-100, 640x480
reset=1960 type=formula formulafile=critical.frm
formulaname=MandelbrotMix7 passes=1
center-mag=+0.09165816355988156/-0.14337973096377420\
/340319.4/1/112.499 params=1/-0.99/-1/-1.005/100/0
float=y maxiter=12000 bailout=25 inside=0 logmap=375
symmetry=xaxis periodicity=10
colors=66666666666966E66I66I66OLBN66X66X<2>66j66e66p\
66t<2>66t0Qz66t<49>66t96t96t96tE6tE6tE6tI6tI6tI6tO6t\
O6tO6tS6tS6tS6tX6tX6tX6t`6t`6t`6te6te6te6tj6tj6tj6tp\
6tp6tp6tt6t<26>t6tz6tt6tt6tt6tzd0p_2e6tX6tS6tI6t96t6\
6t<6>66t66p66p6Qz66t66`66`66X66S66O66I66N66I<3>66I66\
N<2>66N66Q66Q<4>66W66X66X66`<6>66`69`69`6Ee6Ee6Ie6Ie\
6Oe6Oe6Se6Se6Xe6Xe6`j6`j6ej6ej6jj6jj6pj6pj6tj6tp<4>6\
tp6tj<4>6tj6te<4>6te6t`<4>6t`6tX<2>6tX9tX9tXEtSEtSIt\
SItSItSOtOOtOStOStOStOXtOXtI`tI`tI`tIetIetIjtEjtE
}
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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times.
