|
Fractal of the Day
by Jim Muth
|
|
Fractal visionaries and enthusiasts: Today's curious image is another venture into the fractal that results when 0.2 parts of Z3 are subtracted from Z2 before C is added. This fractal appears as a Mandelbrot set rotated 180 degrees, with an extra spike extending from its East Valley, which of course is on its west side. But today we ignore this extra spike and check the more conventional spike extending eastward from the Mandeloid's nose. There is a very prominent minibrot on this spike, which appears to be two partially merged minibrots. Today's image is located rather deep in the northern branch of what at first appears to be a Seahorse-type valley, but actually is an entirely new type of valley. I named the image "Hyper-Dry Valley" because despite the promising appearance of the chaotic yet symmetrical 'object', I could find no minibrot at the center. The minibrot might be there, but the resolution failed before I reached it. Despite the disappointment, I rated the image at a 6. The fractal object, if indeed it *is* an object, has such a real appearance that I could do no less. I'll leave it to the philosophers to argue the actual reality of fractal objects such as the Mandelbrot set. But one thing that cannot to be argued is the calculation time of the image, which is a rather slow 10-3/4 minutes on the fractal fireball, and just over one hour on the fractal snowball. The finished image has been sent ahead to Paul at the FOTD web site, and by the time you read this, it should be already posted and ready for instant viewing. Very fine weather prevailed here at Fractal Central on Monday, with sunny skies and a temperature of 68F 20C. The fractal cats enjoyed the sun from their shelf in the window. My day was as average as the fractal. I expect another average day tomorrow, but hopefully the fractal will be better. The next FOTD will appear in 24 hours. Until then, take care, and everyone has some degree of faith in something. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Hyper-Dry_Valley { ; time=0:10:44.72-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandAutoCritInZ function=ident float=y
center-mag=+1.589436551517345/+0.0185571325367402/\
7.396629e+011 params=1/2/-0.2/3/0/0/0/0 inside=255
maxiter=10000 periodicity=10
colors=000nVbmUflUikTlDVOB_O9dO7iN6gb5er3cz3cz3cq4\
dh9ZgFTfLNeRHdXBbbHahN_oUYePSWKMLEGLHHLKILNJLQKLTL\
LXNNYPPZRR_TUaWWbYYc_`ebaf_bgXchUdjRekOflLgnIjaOmO\
UqA`hGW_MRRSMIZHOcLUhQ_mVer_kwdrzilyhftg`pfVkdPgcJ\
bbDZa6U_B_eGekLlrIjmEggBda7bX4_R0XL9TNJOPTJSaEUk9W\
u4Zp6Wk9SeCP`FLWIIQLEOW_LgunJElNGjRIgVKe_NccP`gRZk\
TWpWZ`YaL`cJYfHViFSlDPoBMr9Ju7Gx4DxJNxYXxlfxzqrznk\
zkdzhZzdSzaLzZEzVKx`RugYsmdptknzrkzjguabhTYWQSeNLo\
KFyH8zGEzFKyEQtCWnBaiAgc8mYAgcCaiEahHagJ`fM`eP_dR_\
cUZbXZ`ZZ_aYZcYYfXXiXWkWVnWUqVSqVSpWSpWToXToXUnYUm\
YUmZVlZVl_Wk_Wj`XhZWeXVcVU`STZQRWOQULPRJOPHNMELNEQ\
ODSPDUQCURCUSBUTAUUAUV9RX8DTIJOSOJaTEkY9ucCqeGmgJi\
iNdkQ`mUXnXSo`OpcKqgFtdFqaFnYFkVFhSFeOFbLFdHFaEFZB\
FW7FT4FQ0GNBKLNOJYSHiWFu`Du`Gt_JsZNrYQqYTpXXoW_H00\
K00N00Q00T00W00Z00a50eA0iF0mK0qP0tU0wZ0yc0vh0sm0oh\
0lc0hZ0eU0bW0`X0YY0WZ0T_0 }
frm:MandAutoCritInZ {; 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)+(p4)),
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.
