Fractal of the Day
by Jim Muth
FOTD -- December 03, 1998
Fractal visionaries:
It was a real beauty today here at Fractal Central, with crystal blue skies, brilliant sun, and a temperature of 65F 18C making it ideal for a fractal search.
Today I searched in the Z^4+C Julibrot, and found the FOTD. It is a scene rotated only 1-1/2 degrees from the Julia direction toward the Rectangular direction. To see the pure Julia slice, change real p1 to 90, and watch the diagonal bridge widen until it fills the entire interior of the outer figure. At the same time a circular hole will appear in the bridge. This hole is the midget at the intersection of the J-set with the M-set.
I named the picture "Do Not Enter Here" because with its diagonal stripe, it reminds me of a "do not enter" traffic sign. I have colored the scene in a somber but peaceful blue palette to emphasize the stripe, and also because I have been in a somewhat somber mood all day.
The image is fast, taking but 4 minutes on a 486 and one minute or less on a Pentium. The GIF file has been posted to:alt.binaries.pictures.fractalsand to:http://home.att.net/~Paul.N.Lee/FotD/FotD.html
Tomorrow, I'll have another fractal. But be forewarned, I feel another spate of amateur philosophy coming on. Until then, take care, and be at peace.
Jim Muth
jamth@mindspring.com
START FORMULA================================================
multirot04-XY-ZW {; draws 6 planes and many rotations
;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J
;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J
a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994,
z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p2,
c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p3:
z=sqr(sqr(z))+c,
|z| <= 36 }
END FORMULA==================================================
START PARAMETER FILE=========================================
Do_Not_Enter_Here { ; 4min on a 486-100, 640x480
reset=1960 type=formula formulafile=jim.frm
formulaname=multirot04-XY-ZW function=flip/ident
passes=1
center-mag=-7.77156e-016/4.996e-016/0.9861933/1/-45
params=88.5/90/0/0/-1.05953834/0.06839796 float=y
maxiter=6000 bailout=25 inside=255 logmap=yes
symmetry=none periodicity=10
colors=00007H17J27K<5>77Z86a96cA5fA5h<4>DOaD0rCHjCHj\
<2>C3yK6mR9b<6>Ga6<12>3Kc<9>FZwG_xI_s<9>Y_D<9>6QZOLg\
eHphKojOn<2>ArL<6>DyEEzDEzCEzB<2>Fz8<9>KzoKzsJzq<7>H\
zbHzaIzb<9>KzeKzeIzf<2>EziDziEzj<28>JzpJzpLzo<24>izg\
<8>GzQ<8>nzU<9>7z4<5>5zW<15>lzMwzt<9>KzeFAU
}
END PARAMETER FILE===========================================
START 19.6 PARAMETER-FORMULA FILE============================
Do_Not_Enter_Here { ; 4min on a 486-100, 640x480
reset=1960 type=formula formulafile=jim.frm
formulaname=multirot04-XY-ZW function=flip/ident
passes=1
center-mag=-7.77156e-016/4.996e-016/0.9861933/1/-45
params=88.5/90/0/0/-1.05953834/0.06839796 float=y
maxiter=6000 bailout=25 inside=255 logmap=yes
symmetry=none periodicity=10
colors=00007H17J27K<5>77Z86a96cA5fA5h<4>DOaD0rCHjCHj\
<2>C3yK6mR9b<6>Ga6<12>3Kc<9>FZwG_xI_s<9>Y_D<9>6QZOLg\
eHphKojOn<2>ArL<6>DyEEzDEzCEzB<2>Fz8<9>KzoKzsJzq<7>H\
zbHzaIzb<9>KzeKzeIzf<2>EziDziEzj<28>JzpJzpLzo<24>izg\
<8>GzQ<8>nzU<9>7z4<5>5zW<15>lzMwzt<9>KzeFAU
}
frm:multirot04-XY-ZW {; draws 6 planes and many rotations
;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J
;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J
a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994,
z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p2,
c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p3:
z=sqr(sqr(z))+c,
|z| <= 36 }
END 19.6 PARAMETER-FORMULA FILE==============================
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