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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image slices the Julibrot in the area of Seahorse Valley in an orientation 5/6 of the way from the Rectangular toward the Julia. The image bears little resemblance to either the Mandelbrot or Julia aspects of the area, which is not surprising, as Seahorse Valley is a four-dimensional thing with more ways to be sliced than a cat has of finding trouble. The Seahorse Valley Julia set is not far off however. To see it appear almost magically, change the real(p1) parameter to 90. This is most interesting if the change is done incrementally. To see the valley itself, change both parts of (p1) to zero and rotate the image minus-90 degrees. I named the image "Seahorse Swirls" because of the prominent bluish swirls on both sides of the blue center stripe, which is actually the coming together of the two branches of Seahorse Valley as seen from the side. I rated the image an average 6. I could give it nothing higher because this kind of image has been done so many times that it has become hackneyed. The image boasts one good feature however -- it is very fast, making its variations very easy to do. And as almost always, the finished image is available for download and judging on the FOTD web site at: I intended to take it easy on Saturday and that is what I did. I took it so easy that the day seemed only half as long as most days, and at the end of the day I was left thinking. It is amazing how fast time passes when one is not watching it pass. But what is time? Since we can partly control its apparent rate of passage, it must to some degree be a psychological creation, but if this is so, then space must also to some degree be a psychological creation. At this point, my team took the lead with a three-pointer and my thoughts turned to more immediate and important things. The fractal weather was quite pleasant on Saturday, with ample sun, gentle breezes, and a high temperature of 57.4F 14.1C as measured by the fractal digital thermometer. The cats, not worrying themselves with tenths of degrees, found the day pleasant enough to pass the entire afternoon in the yard, keeping away the mean tomcat from up the hill. They were quite successful, for the other cat never showed up. Today is starting chilly and foggy, with rain in the area. I fear the good day will not be repeated. For me it looks like another slow day on the way. Maybe I'll solve the puzzle of time and space, more likely not. But in any case, the next FOTD will appear in all its glory in 24 hours. Check back to see the great event. Until then, take care, and don't waste spacetime. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Seahorse_Swirls { ; time=0:00:41.20--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=multirot-xy-zw-new function=flip/ident
center-mag=0/0/1.131455/1/90/3.885780586188048e-016
params=75/90/2/0/0/0/-0.75/0 float=y maxiter=7500
inside=0 logmap=3 symmetry=xaxis periodicity=10
colors=000OHVPIUQJTRKSSLRUMQWNPYOO_PNaQMcRLeSKgTJi\
UIjVHkWGlXFmYEnZDo_Co`BpaApb9qc8rd7se6tf5ug7uh8vi8\
wj9xj9yj7zj4zj2yl3ym4xn5xp5wq6wr7vs8vu8uv9uwAuxAby\
ELzIOxHQvGStGUrFXpFZnE`lEbkDeiCggCieBkcBnaAp_ArY9t\
X9sQLrJWqCfp5qiBlbGfXFaVEXTDSRCTPBUNAULAUKAUMAUOAU\
QAURAVTAWVAXWAYYAZ_A_`A`b9ad8be7cg6ci5cj4ceAcaGmYM\
mURmQXmMbmIgmGfmEfmCemAem8dm6dm4cm3cm8YmDTmINzNIzS\
DzQFzPHzOJzNLzMNzLPzKRzJTzHVzGXzFZzE`zDbzCdzBfzAgz\
jezhbzf`zeZzcWzbUz`Sz_QzWPzTOzPOzMNzINzFMzCMzELzFL\
zHKzIKzKJzLJzMIzOIzPHzRHzSGzTGzFyzGtzGpzGlzHhzHdzH\
`zHXzIXzIWzJWzTJzXMzaPzeSzfUzgVzhXziYzj_zk`zlbzmcz\
nezofzphzqizrkzslziiz_fzQdz`TzaQzaOzaLzaJzaHzaEzaC\
zaAzuVztWztWzsXzsXzrYzrYzrYzqXzqXzqXzqWzqWzqWzqVzq\
VzqVzqUzqUzqUzcbzRjzErz1zz6uzBpzFkzKfzPazTXzYSzbNz\
fJzaLzYNzTPzPRzLTzRUzXVzbWzhXznXzoWzoWzL`zKZzKXzJU\
zJSzIQzHOzHLzGJzGHzFFzECz }
frm:multirot-XY-ZW-new {; draws 6 planes and 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))+p3,
c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4:
z=z^(p2)+c,
|z| <= 36 }
END PARAMETER FILE=========================================
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times.
