|
Fractal of the Day
by Jim Muth
|
|
Fractal visionaries and enthusiasts: I rarely choose an entire parent fractal to be the FOTD, but today I have done so. Today's image is the parent fractal of yesterday's 'purr-fect' image. True, I have increased the escape radius to 3700, but I did this only so that none of the fractal would be cut off. The image is named "The Unexpected". The name refers to the unexpected degree of distortion suffered by the Mandeloid that fills the screen. All the parts of the classic Mandelbrot set are there, a fact that can be demonstrated by examining the nature of the inner detail, but the parts are arranged in a manner that has little to do with the classic Mandelbrot set that we know so well. To start, the largest bay in the image is not the main bay, it is the period-2 bud. The smaller bay attached to the upper right edge of the largest bay is actually the 'main' bay of the Mandeloid, and the colorful valley separating the two bays is actually Seahorse Valley. East Valley of today's Mandeloid is barely visible, appearing as a tiny dimple on the northeast shore line of the main (but smaller) bay. In the lower left of the frame lies Scepter Valley, with the remaining buds and the main stem extending relatively undistorted beyond. As for the arrangement of the iteration bands, it makes no sense at all. Instead of being centered around the origin, as would be expected, they are centered around the apex of Seahorse Valley. And centered is hardly the proper word to use for their arrangement. In fact, the iteration bands actually open to form an entirely new fractal near the right edge of the frame. This area appears to hold nothing but total chaos, but it is worth a closer look, which I will give it later today. The rating of a 6 is really a bit overblown. The image is blatantly average. But I kind of enjoy doing things to Mandeloids, and what has happened to today's Mandeloid is worth the one-point increase. Another good feature is the high speed of the image, which renders in only 1-1/2 minutes on my old warhorse machine, and will render in less than one minute on almost any present-day unit that is not Fractint challenged. Those whose computers roll over and play dead when Fractint is booted may still see the image by downloading it from the FOTD web site at: The high temperature of 86F 30C, accompanied by warm sun and gentle breezes, kept the dynamic duo at peace all day Saturday here at Fractal Central, and when old-timer cats are at peace, they really are peaceful. The day was nearly as uneventful for me. This morning is starting about the same. I expect the same results. Regardless of what happens, the next FOTD will appear in 24 hours. Until that moment of glory arrives, take care, and did you ever wonder what potential energy is made of? Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
The_Unexpected { ; time=0:01:39.19--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=ident
center-mag=2.77947/19.1932/0.046875/1/147.5/-2.505\
63458870090e-014 params=-1/1.01/1/-1/0/3600 float=y
maxiter=1000 inside=0 periodicity=10
colors=000HusHysKvlNseQpZSmSVjLYgE_d7`b8`a9`_A`ZB`\
XC`WD`UE`TE`SF`QG`PH`NI`MJ`KK`JL`ILYJMWJMUJMSKMQKM\
NKMLKMJJMHLMFIMDLMFJPHMRJLTLNWNNYPO_RObTPdVOfXQiWP\
i_QmXQkURjRRiORgLSfISeFTcCSb9Ua7S`6WZ5YX5_W4bU4dT3\
gR2jP2lO1oM1qL5jN8dOBZPETQHNRKHSNBTQ5U_8YhAafCbeEb\
dGccIcaKc`Md_OdZQeXSeWUeVWfUYfTZfZdecjeipenvejpbgk\
_dfXaaUYXSVSPSNMPIJMDHLFGLGFKHEKIEKJDJKCJLBIMBINAI\
O9HP8HQ8GR7GS6GT6HV7HW8IX9IY9JZAJ`BKaBKbCLcDLdDMfE\
MgFNhFNZGOUHOOHOLDO39S77WA5_D3cG2bUNagfatziwrqykEa\
CF`PF_aFZnRKETHCUEAVB8W87PN8I`9JcPElbKecz3b1fO8gZE\
ghu5YJbfKdiKelKfonGwgu5_pMSkbzOHEiBC45GOU6rKOVzYF7\
YeVRfff5tZIsRVrnWFhfQWgdWM9SUPO`czlgkjkYhoVCoRNpNY\
qUapSVzQZxOavMdt4`ATh8IYKJaWKdggLFr`b1a_8cfEelelQ2\
sl_4eUIjPVnMNpNOpOOpRMnTLmVJlXIk_GiaFhcEgeCfhBdj9c\
l8bn7aoCdoHfpMipQkqVnq_pqcrpbkobenbZmbTlaNkaGjaAja\
4AJpBOqCTqDYqEbrEfrFkrGps }
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=========================================
|
times.
