Fractal of the Day
by Jim Muth
FOTD -- December 15, 1998
Fractal visionaries:
A perfectly average late autumn day has just ended. The temperature of 44F 6.5C was average and the expected low tonight of 25F -4C is also just about average. In honor of the average day, I found an average fractal -- well actually I found it yesterday -- and here it is in all its one-day-later glory.
I found this confused but interesting scene in a perturbed plane of the (-Z)^1.09+C Mandeloid. On the left, fractured spirals whirl like a dervish, while on the right, a perfect isoceles triangle rises from a flat plateau.
I have named the picture "Euclidean Geometry" after the discipline that we so loved in High School. (At least I loved it.) And yes, I did give the colors a little boost in another program.
Unfortunately, the parameter file of today's image runs slow, requiring 1/2 hour on even the fastest Pentium, but salvation is at hand, for I have posted the finished GIF file to Usenet at:alt.binaries.pictures.fractalsand to the Web at:http://home.att.net/~Paul.N.Lee/FotD/FotD.html
Tomorrow will bring another fractal and a few words to go with it. Until then, take care, and remember that two objects equal to a third object are equal to each other. (I guess that's how the axiom was worded.)
Jim Muth
jamth@mindspring.com
START FORMULA================================================
MandelbrotMiN {; Jim Muth
b=p1, z=p2, c=p3+pixel:
z=(-z)^(b)+c,
|z| <= 16
}
END FORMULA==================================================
START PARAMETER FILE=========================================
Euclidean_Geometry {; 3 long hours -- pick-up from net
reset=1960 type=formula formulafile=slices.frm
formulaname=MandelbrotMiN passes=t
center-mag=2.83347/0.170723/2.400168/1/90
params=1.09/0/1.64/0/0/0 float=y maxiter=32000
bailout=25 inside=0 logmap=29 symmetry=none
periodicity=10 colors=0000nz0pz0lw0it0fs0bq0_n0Yl0Vk0\
Ri0Of<2>0Ga0D_09X06V02T01R00O<2>00J00E00I00J00L20O60Q\
90RE0TI0XL0YQ1_T2aX4da6fd8gi6kg8ig8gg9fg9dgBbgBagD_gD\
YgEXgEVgGTgGRgIQgIOgJNgJLgLJgLIgNGgNEgODgOBgQ9gQ8gR6g\
R4gT2gT1iX2iY2i_2ia2kd4kf4kg4ki4ll6<2>lq6lsBlsBls6bs1\
Os04s08t09t0Bw1Dw4Ex6Gx9IzDLzG<2>QzORzRTzVVzXXz__zbaz\
f<2>fzngzmizUlzUkzUkzUkzQkw9st0ns0ks0gq0bq0_q0Xp0Tp0O\
p0Ln0In0En0Ik0Ji0Lf0Nd0Qa2R_6TX8<2>_QIaOLbLOdJRgGTiEX\
kB_l9bn8fq4is2lt0nw0qz0tz0xz0z<5>z0zz0zz2zz6z<6>zOzzQ\
zzTxzVxzYxzaxzbwzfwzgwzkwzltzptzstzttzxszzszzszzizznz\
zsqzxizzazzJzz2zs0zn4zLJz0<3>Qz1Rz4Tz9VzDVzGXzJYzN_zQ\
azVbzYdzafzdfzggzkizp<2>nzzpzztzzqzzpzzlzzkzzgzzfzzbz\
zazzYzzXzzTzzRzzOzzNzzJzzIzzEzzDzzDzzBzz<11>Bzz4zz<3>\
Izz0zz0zz0zz
}
END PARAMETER FILE===========================================
START 19.6 PARAMETER-FORMULA FILE============================
Euclidean_Geometry {; 3 long hours -- pick-up from net
reset=1960 type=formula formulafile=slices.frm
formulaname=MandelbrotMiN passes=t
center-mag=2.83347/0.170723/2.400168/1/90
params=1.09/0/1.64/0/0/0 float=y maxiter=32000
bailout=25 inside=0 logmap=29 symmetry=none
periodicity=10 colors=0000nz0pz0lw0it0fs0bq0_n0Yl0Vk0\
Ri0Of<2>0Ga0D_09X06V02T01R00O<2>00J00E00I00J00L20O60Q\
90RE0TI0XL0YQ1_T2aX4da6fd8gi6kg8ig8gg9fg9dgBbgBagD_gD\
YgEXgEVgGTgGRgIQgIOgJNgJLgLJgLIgNGgNEgODgOBgQ9gQ8gR6g\
R4gT2gT1iX2iY2i_2ia2kd4kf4kg4ki4ll6<2>lq6lsBlsBls6bs1\
Os04s08t09t0Bw1Dw4Ex6Gx9IzDLzG<2>QzORzRTzVVzXXz__zbaz\
f<2>fzngzmizUlzUkzUkzUkzQkw9st0ns0ks0gq0bq0_q0Xp0Tp0O\
p0Ln0In0En0Ik0Ji0Lf0Nd0Qa2R_6TX8<2>_QIaOLbLOdJRgGTiEX\
kB_l9bn8fq4is2lt0nw0qz0tz0xz0z<5>z0zz0zz2zz6z<6>zOzzQ\
zzTxzVxzYxzaxzbwzfwzgwzkwzltzptzstzttzxszzszzszzizznz\
zsqzxizzazzJzz2zs0zn4zLJz0<3>Qz1Rz4Tz9VzDVzGXzJYzN_zQ\
azVbzYdzafzdfzggzkizp<2>nzzpzztzzqzzpzzlzzkzzgzzfzzbz\
zazzYzzXzzTzzRzzOzzNzzJzzIzzEzzDzzDzzBzz<11>Bzz4zz<3>\
Izz0zz0zz0zz
}
frm:MandelbrotMiN {; Jim Muth
b=p1, z=p2, c=p3+pixel:
z=(-z)^(b)+c,
|z| <= 16
}
END 19.6 PARAMETER-FORMULA FILE==============================
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