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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: I'm getting rather interested in the fractal created by the formula Z^1.414+C, which I call the square root fractal of the Mandelbrot set. Like the M-set, this fractal has buds and midgets, though the buds are distorted and the midgets far more difficult to find. But unlike the M-set, the Z^1.414+C Mandeloid is infinite in two ways. Not only is it infinitely complex in its depths, it is infinite in its surface extent. Due to the multi-valued nature of the complex log function, the Z^1.414 mandel-fractal is actually in the shape of an infinite spiral, giving an endless supply of new things to see and new places to explore. The p2 parameter of the MandelbrotBC formula determines which part of the spiral will be drawn. The parent fractal of today's image is a mandel figure that looks like it has been sliced in half, with a mis-shapen bud on one end. The scene of today's image lies in a nest of sinuous filaments near this bud. As is true in most of my FOTD's, a midget lies near the center of the image. This midget is so small that its actual shape is indistinct, though another magnitude of enlargement will reveal the midget to be shaped like an eastern half of the classic M-set that has been cut off from the west half. After studying today's image for a few minutes, I imagined a crown of thorns effect. I named the picture "Crown of Thorns" and rated it a 6. With a render time of only three minutes from the parameter file, today's FOTD is a welcome relief from the slow images of recent days. If three minutes is still too long to wait, the GIF image file will soon be posted to: The fractal weather was pleasant enough today here at the place where all things are fractal. The partly sunny skies and temperature of 50F (10C) were pleasant enough, though the fractal cats couldn't decide whether they wanted to be indoors or outdoors. They finally settled on indoors, lured by a treat of sliced turkey. I have some philosophy all thought up and waiting to be written, but I was too busy today to write it out. I'll likely still be busy on the same job tomorrow, so the philosophy will probably not appear until the 11th, when it will do its tiny part in the enlightenment or mis-enlightenment of humanity. Until tomorrow and the next FOTD, take care, and see you then. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Crown_of_Thorns { ; time=0:03:03.33 -- SF5 on a P200
reset=2001 type=formula formulafile=branchct.frm
formulaname=mandelbrotbc passes=1
center-mag=-0.0827557054067479/+1.545045515561042/18\
3767/1/107.498 params=1.414213562373/0/1.5/0 float=y
maxiter=1200 inside=0 logmap=75 periodicity=10
colors=0005GZ2G`q0nr0qr0rr0tr1wt4xt7ztAztDzvGz<2>vOz\
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0zz<3>0zz0zz0zz0zz0zw1zq5zkCze<2>PzPTzJZzDcz7gz1kz0o\
z0vz0zz7<2>zzT<3>zzSzzSxzSwzStzSrzSozSnzSkzSjzSgzY\
<2>azj`znYzrWzwTzzSzzQzz`zwhzjrzYzzMhz`Qzm7zz<2>Wz\
zczzjzzrzzzzzzzzzzzxzxtzxozwmzwhzvdzv`ztYztOzQLzSG\
zTDzW8zY
}
frm:MandelbrotBC = { ; Z = Z^E + C
e=p1
p=real(p2)+PI
q=2*PI*trunc(p/(2*PI))
r=real(p2)-q
Z=C=Pixel:
Z=log(Z)
IF(imag(Z)>r)
Z=Z+flip(2*PI)
ENDIF
Z=exp(e*(Z+flip(q)))+C
|Z| < 100
}
END 20.0 PAR-FORMULA FILE==================================
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times.
