Fractal of the Day
by Jim Muth
FOTD -- December 12, 1998
Fractal visionaries:
Another perfect day has passed uneventfully here at fractal central. Actually, one event did occur -- the earliest sunset of the year. This evening at 4:43pm, the center of the sun's disk slipped below the horizon. I realize that the shortest day does not arrive until December 21, but at this latitude, (39N), the earliest sunset does not coincide with the shortest day. Curiously enough, the latest sunrise will not happen until January 6.
The weather on this short day was perfect. The slightly above average temperature of 48F 9C was ideal for searching for fractals. Always ready to take advantage of perfect conditions, I began the search. My search led me to a formula I have not used until now -- mult2-5-XZ-YW. This formula takes the Z^2.5+C Julibrot and rotates it through the odd planes. I chose a midget in East Valley for the center of rotation.
The Mandeloids of fractional power are necessarily filled with discontinuities, and in the odd planes the discontinuities become even more apparent. This is especially evident in today's fractal, which I have named "Broken up Galaxy". I gave it such a name not only after yesterday's FOTD, which was named "Breakdown" but because I see midgets in fractals somewhat like I see a black hole at the center of a galaxy, attracting the cosmic material ever tighter around itself.
In the Mandelbrot set orientation, the narrow open slit at the center of today's fractal appears as a lovely two-headed Mandelbrot midget, with the broken spiral arms converging in increasing powers of 2.5. The midget itself would have made a fine picture, but to make things even more interesting, I looked at the midget from a different direction and found today's disorganized, yet unified jumble.
The GIF file has been posted to:alt.binaries.pictures.fractalsand to Paul Lee's web site at:http://home.att.net/~Paul.N.Lee/FotD/FotD.html
I noticed an article in today's newspaper reporting that someone in Japan has actually cloned four cows. It is obvious that if we can clone cows, people clones cannot be far behind. The philosophical implications of such an event would be staggering, and just what I need to bring out my inner philosopher. I expect that by tomorrow I'll have more than a few words to say about this article. Check in then to see what happens.
For now, we've come to the end of today's FOTD, so until we meet again, take care, and don't get broken up over a failed fractal.
Jim Muth
jamth@mindspring.com
START FORMULA================================================
mult2-5-XZ-YW {; Jim Muth
; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect
e=exp(flip(real(p1*.01745329251994))),
f=exp(flip(imag(p1*.01745329251994))),
z=f*real(pixel)+p2, c=e*imag(pixel)+p3:
z=z^2.5+c,
|z| <= 36 }
END FORMULA==================================================
START PARAMETER FILE=========================================
Broken_up_Galaxy { ; 7min on a 486-100mhz, 640x480
reset=1960 type=formula formulafile=multirot.frm
formulaname=mult2-5-XZ-YW
center-mag=0/0/393354.6/0.7631/0/-84.966 params=-38\
/-17/0.37685493212/-0.01812809027/0.37685493212/-0.01\
812809027 float=y maxiter=1200 bailout=25 inside=0
logmap=73 symmetry=none periodicity=10
colors=00000V00X<4>00p50t64x<4>4Fe3Ia3K_2MX2OQ2OO8NMD\
LLMIKSFJVCIYAI<15>zb6<9>R3iO0mM2e<5>ED0<6>SWM<10>tHL\
<9>4JJ<9>hIi<7>j_3<2>GJm2Rh<3>Oaw<13>Z4x<11>jCEkCBlEE\
<13>lWhXZO<2>2V53YB4`H<12>St8<9>4Ab<2>I4p<10>vdl<7>Xo\
a<7>jZx<5>I`h<10>1HJ<4>sPA<11>BWdMZbgbumZwrWxLk5IgCGdJ
}
END PARAMETER FILE===========================================
START 19.6 PARAMETER-FORMULA FILE============================
Broken_up_Galaxy { ; 7min on a 486-100mhz, 640x480
reset=1960 type=formula formulafile=multirot.frm
formulaname=mult2-5-XZ-YW
center-mag=0/0/393354.6/0.7631/0/-84.966 params=-38\
/-17/0.37685493212/-0.01812809027/0.37685493212/-0.01\
812809027 float=y maxiter=1200 bailout=25 inside=0
logmap=73 symmetry=none periodicity=10
colors=00000V00X<4>00p50t64x<4>4Fe3Ia3K_2MX2OQ2OO8NMD\
LLMIKSFJVCIYAI<15>zb6<9>R3iO0mM2e<5>ED0<6>SWM<10>tHL\
<9>4JJ<9>hIi<7>j_3<2>GJm2Rh<3>Oaw<13>Z4x<11>jCEkCBlEE\
<13>lWhXZO<2>2V53YB4`H<12>St8<9>4Ab<2>I4p<10>vdl<7>Xo\
a<7>jZx<5>I`h<10>1HJ<4>sPA<11>BWdMZbgbumZwrWxLk5IgCGdJ
}
frm:mult2-5-XZ-YW {; Jim Muth
; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect
e=exp(flip(real(p1*.01745329251994))),
f=exp(flip(imag(p1*.01745329251994))),
z=f*real(pixel)+p2, c=e*imag(pixel)+p3:
z=z^2.5+c,
|z| <= 36 }
END 19.6 PARAMETER-FORMULA FILE==============================
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