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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: In today's fractal formula we combine 1 part of Z^(1.5) with 1/2 part of Z3 and add straight C. This formula produces a parent fractal that consists of two symmetrical and partially merged Mandelbrot sets facing north and south. Today's image is located on the western shoreline near the X-axis, where the two sets merge, and a small but curious kind of bud is located. The parent of today's image is symmetrical around the X-axis, but it is a very critical type of symmetry. If the exponents of Z are changed from 1.5 and 3, the symmetry vanishes at once. If Z3 is changed to Z2.5, and all else kept the same, the resulting parent fractal is one of the most unusual I have yet encountered. I named today's image "Uncut Jewels". The four faceted elements remind me of diamonds in the rough. I rated it at a 7, which might be a bit high, but it's really a rather pleasing fractal. The included parameter file runs in 31 seconds on my fast fractal computer. The old P200 would take about 3 minutes to finish the job. As always, the best way to see the finished image is to go online to the FOTD web site at: With a temperature of 86F 30C, Monday was a bit too warm to be considered perfect. But I doubt that anyone noticed the deficiency. The cats kept themselves occupied chasing each other, hiding, and suddenly pouncing. My day was suitably busy. If all goes well, tomorrow will be the same. The next FOTD will appear in 24 hours. Until then, take care, and if a farmer has seven daughters and each daughter has a brother, how many children does the farmer have? Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Uncut_Jewels { ; time=0:00:31.04-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandAutoCritInZ function=ident inside=0
center-mag=-0.26485847107386810/-0.037316662862560\
15/1.227384e+009/1/97.5/-7.40612221022743378e-005
params=1/1.5/0.5/3/0/0/0/0 logmap=64 periodicity=10
float=y maxiter=750
colors=000666999DDDGGGJJJNNNQQQZZZiiilllnnn0rp0tr0\
uz0uz3lwBelGZlJblNglQllUrlOpXOlIOiGOjGOlENlEUj9Zi5\
eg2j`0pQ0j90b00m89nTSp_VrdVtlhuruzzzzzzNG6B8600600\
6808S08N08E08809O0BeBJwNUzZbzjlzwuzz0zz0zzzzz0zz0z\
rSzUOz6LzcU0z`0zX0zW0zU0zQ0zO0zN0zJ0zG5zD9z9Gz6Lz3\
Qz2Sz0Uz0Wz0Xz0Xz0Zz0`z2`zDbzQbzbcznczzXyjSyXNwJGw\
5Bu06u0WzwZyu`rtbircbrgWpiNnjGll9lbQuSezIwz8zzIzzS\
zz`ztjzjtzcuziuzlwznwppycryUtzItz8uz0wz0yz0yu0zp0z\
j0zc0zZ3zU9zNEzIJzDOz6Uz2`z0ez0jz0pz0uzNG0OL0QQ0QU\
0SZ0Ub0Ug0Wj0Xp0Xt0Zy0Zz0Sz0Lz0Ez08z02z00z20z50z65\
n0OS0i60z00z00z00z03z0Bz0Lz0Uz3bz5jz6tz3jz0cz0Xz0Q\
z0Jz0Dz06z00z00z60zD0zJ0zQ0zX0zc0zj0zr0zy0zz0zz0zz\
2zz3zz3zzDzzLzzUzzbzzlzzuzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzbzzDzz0zz0zz0zz0zz0zz0zz2zz5zz8zzBzzEzzIzzL\
zzOzzSzzWzzQzzNzzJzzEzzBzz8zz5zz0zz0zz0zz0zz0zz0zz\
0zz0zz0zz0zz0zz0zz0zz0zz0 }
frm:MandAutoCritInZ {; 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)+(p4)),
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l }
END PARAMETER FILE=========================================
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times.
