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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: The day started normally enough on Thursday here at F.C. When I checked my e-mail, I found that I had won three lotteries that I did not buy tickets for, and I also needed to verify my identity for three internet banking accounts that I do not have. One would doubt that anyone would actually fall for these scams, but from the way they keep proliferating, it is hard to believe that they totally fail to catch a few suckers. Maybe I should start selling certified authentic Mandelbrot sets. Today's striking image consists almost entirely of 'inside' stuff made visible by the 'bof61' fill. It is another variation of the strange rectangle in one of the Julia sets of the Z^(2.003)+C Mandeloid. The orientation is rotated only one degree toward the Elliptic plane, but the result is a very unusual variation. The rectangle is not really there. When the inside is set to the normal flat black, there is no sign of the rectangle. It has become a virtual rectangle. But the rectangle was virtual from the start, so now it has become virtually virtual, which is what I named it. The 'bof61' inside fill is not the only one that works with today's image. The 'fmod' fill also works quite well, and the 'zmag' fill works reasonably well also. The other inside fills simply color the inside areas a flat color. I did not rate the image, but if I had, it would probably have earned a rating of 8 or 9. The passes=b option not only works fastest with the image, it is by far the most interesting one to watch in action. The render time of 9-1/2 minutes will be irrelevant if the image is viewed on the FOTD web site at: Partly cloudy skies and a brisk high temperature of 68F 20C made things reasonably pleasant for the fractal cats, who spent the day indoors, unconcerned with the outside conditions. The light work load made my day pleasant also. The next FOTD will appear in 24 hours. Until then, take care, and if someone offends a fractal, expect no violent protest. Fractals are very peaceful. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Virtually_Virtual { ; time=0:09:24.40--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=SliceJulibrot4 passes=b
center-mag=-0.00368788/0/42.12754 params=90/0/89/0\
/-1.7435/0/0.00019/0.07388/2.0031/0 float=y
maxiter=1500 inside=bof61 periodicity=0
colors=000wwwzzzzzzzzzpvxfnsjdrP_kHTf8Lc1FZ09X08V4\
7U88S00CE7PH5PL4OP4NV4N00Bf4Mk5Nf5Nc6N`6O60BU7NR7N\
M7MK7OJ9O3A`FBPDCPBBR7BR5CR1C`0CS0CS0BV0BX0BY0Ae0A\
b0Ac0Af09h09i08m09n18p18x17u28w26r37z38x27r27u27s1\
7n27p28p18k17m18k17i17h18h07b07e08cM8b07`07`77R55S\
74OU2V91GB0DD0AG08J05`0MP01R02M12S23U54g5GV85V95SA\
5XC5YE5hM5ZH7`J7YK6bN7bO7hS8cS8eV9bW8fY9fZ9kXAhbAi\
cAidCkfCkgCmaDiiDikDimFinFipFpeFisHiuHhwIhxIizJvbH\
frKemLeiNdfNcbOicQcZRcXTcWUcWWbXYg__ZXYYYYYYYZYZ`_\
bkZc`_e`ah_`i_`mZanY`rWasVbwUbxUbzGae7hP0iB0n00c44\
VAAMFo`ILDPT6Ya0ej0mf2heccbG_`OYYXXXXWZeUZnRYxOYzN\
YzOZsQYmRYeTWZTUUUVUVVOUXJWXDXY8ZY3`xpzunzrlxpkumi\
rjgnigkedhccebbbZZZXXXUUURRROOOOOOMMMJLJGLHFJGCIDA\
IA8H85G54G33H42I51J61L71M80M90OA0PB0RC0SD0UE0UG0VG\
0XI0YJ0ZK0ZL3nZDzm4rZ0eL0`N0YO0VQ0SQ0PU1NV2KY3JZ3G\
b5Ec7Df7BhBGkFJmJNnOSrQVs }
frm:SliceJulibrot4 {; draws most slices of Julibrot
pix=pixel, u=real(pix), v=imag(pix),
a=pi*real(p1*0.0055555555555556),
b=pi*imag(p1*0.0055555555555556),
g=pi*real(p2*0.0055555555555556),
d=pi*imag(p2*0.0055555555555556),
ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g),
sg=sin(g), cd=cos(d), sd=sin(d),
p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd),
q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd),
r=u*sg+v*ca*sb*cg, s=v*sin(a),
c=p+flip(q)+p3, z=r+flip(s)+p4:
z=z^(p5)+c
|z| <= 9 }
END PARAMETER FILE=========================================
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times.
