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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: In yesterday's discussion of the 'unexpected' fractal, I commented on an unusual area of chaos connected with the south branch of Seahorse Valley and lying some distance from the main figure. Since then, I have examined this chaotic area and found it more interesting than expected. In fact, the area holds intact midgets, one of which appears as today's image. I am now wondering what this area will change into when I tweak the parameters. Perhaps by the time tomorrow's image appears, we shall know. Instead of the well-defined bands of equal-iteration count, in today's image we see symmetrically-arranged bits and pieces of decorative reddish-green elements floating before a chaotic purplish background. An unexpected quadratic Mandelbrot set midget lies, as usual, at the center of the frame, serving as a unifying theme. I named today's image "Super Unexpected", since the chaotic area appears to be the beginning of something entirely new, unlike anything that exists in the classic M-set. Because of its colors, on which I put a bit of extra effort, the image rates a 7. A 6-1/2 might be more accurate, but I wanted to give myself a little pat on the back. The render time of 16 minutes is appropriate for such an unexpected scene. And even this short time may be eliminated by downloading the finished GIF image from the FOTD web site at: A slightly hot 88F 31C but otherwise absolutely perfect day here at Fractal Central on Sunday gave the fractal cats abundant reason to pass the afternoon sleeping in the holly thicket. Their repose was uninterrupted by wandering tomcats. Today is starting sunny and a bit warmer. It might be too warm for the duo to spend another afternoon outside. For me it's work first, fractals second, the next of which will appear in 24 hours. Until then, take care, and take it easy when pondering the imponderable. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Super-Unexpected { ; time=0:16:07.72--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=ident passes=1
center-mag=-15.52168938650432000/+0.77168018950929\
570/738.5992/1/132.5/4.69839209205069608e-009
params=-1/1.01/1/-1/0/3600 float=y maxiter=3000
inside=0 logmap=187 periodicity=10
colors=000FbcFaaF`_F_YGZXGYVGWTGVRGTPGSOGRMGQKGOIG\
OGGMFIOEKODMPCOPCRQBSRAVR9WS9ZS8_T7bT6aU7`W7_X7ZY7\
YZ7X`8Wa8Vb8Uc8Ud8Te8Sg9Rh9Qi9Pj9Ok9NmAMnAMoALpAKq\
AJrAItBbuBOvBTwBYxBbyBgxDlxEqxGvxHvxIvxKvxLvxMvxOl\
xPbyPTxQJwRKwRMvSOuSPuTRtUTtUUsVWrVYrWZqW`pXbpYcoY\
eoZgnZhm_jm`ll`mkaokaqjbtkarjbqicpidohenhfmgglghjf\
iiejhekgdlfdmecndcobbpaaq`ar_`sZ`tY_uYXwX_vWavVcvU\
euThuSjuRltQntQsuPptPntPlsOjsOhrOfrNdqNbqN`pMZpMXo\
MVoMTnLRnLPmLNmKLlKJlKHkJFkJDjJBjGAkI9jJ9jL9jM9jN9\
iP9iQ9iR9iT9iU9hW9hX9hY9h_9h`9ga9gc9gd9gc9gb9fb9fb\
9fb9fb6bb8db9fbAhdBi`CkXDmTEoPFpLGrHHtEIuGJrIKpJLn\
LMlMMjONhPOfRPcSQaUQ_VRYXSWYTU_USWUQaRScOUeMWfLYgK\
_fJ`eIbdHdcGebFgaEi`Dj_ClZBnYAoX9qW8sV7tU6vT5xS5yU\
4zW4zY4z_4za3zc3ze3zg3zi2zk2zm2zo2zq1zs1zu1zu0zu0z\
u1zu2zu3zu4zt5zt6zt7zt7zs8zs9zsAzrBzrCzrDzrDzqEzqF\
zqGzpHzpIzpJzqKzqKzqKzqKz }
frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l }
END PARAMETER FILE=========================================
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times.
