|
Fractal of the Day
by Jim Muth
|
|
Fractal visionaries and enthusiasts: Recovery is in progress. With today's image, we raise the FOTD standard to a rating of 5. This is only an average rating, but it is still better than yesterday's rating of an abysmal 3. The scene that earns the rating is that of a cubic midget in the Z^3+C Mandeloid, deep in the valley that splits the top bud. This valley corresponds to nothing in the classic Mandelbrot set, and therefore holds some rather unique features. To begin, it is not infested with those over-rated spirals that for some reason have become so trendy among certain fractal groups. More importantly, at least in today's image, the orientation of the illustrated slice is not in the Mandelbrot direction; it is double rotated half-way toward the Julia direction. (Double rotation is one of those non-visualizable things that can exist only in spaces of more than three dimensions.) From this angle, all resemblance to the original cubic Mandel-midget is gone. Instead, we find a narrow diagonal slit. The powers-of-three sequence of features surrounding the midget is also gone, replaced by a stretched and disconnected mish-mash of bits and pieces of the original pattern. As we approach the central hole, there seems to be little if any order remaining. This inspired the name Chao-Brot. The render time of over 1/2 hour on my slow machine is admittedly too much for such a mediocre image. The better way of seeing the chaotic scene is to download the finished image from one of the FOTD web sites at: Monday was fair enough for cats here at Fractal Central, though it was a bit too warm for people. The hot sun and temperature of 88F 31C made outdoor activity seem unpleasantly strenuous unless something like ice-cold lemonade was handy. The cats had an average day in the yard, which for 13-year old ex-tomcats means sleeping. Today is starting cloudy however, and showers are threatening. It remains to be seen how the day will go. The only thing near certain is that the next FOTD will appear in 24 hours. Until then, take care, and be ready for actual up-to-date photographs of the dynamic duo of cats. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
Chao-Brot { ; time=0:31:06.70--SF5 on a P200
reset=2002 type=formula formulafile=allinone.frm
formulaname=multirot-XZ-YW-new passes=1
center-mag=+0.00000002434646647/-0.000000000003558\
43/3.165493e+010/1.089e-005/-179.995344305281634/-\
89.9990143502176352 params=45/45/3/0/1.63489133e-0\
06/1.08873023204355/1.63489133e-006/1.088730232043\
55 float=y maxiter=16000 inside=0 periodicity=10
colors=000UgqVfrWdsYbtZau__vaZwbXxcWybTwaQv`Ou_Lt_\
JrZGqYEpXBoX9n`M_cZLln4fj6af7Wc8R_ALXBGTCAQE5MF0JG\
GFKWBOi0Vk7SmDQnJOpPMqVJs`HtfFvlDwrBunGtkKrhPqeTob\
Xn_alXekUijagiiehqchybeu`cr_`oZZlYWiXUfWRcUP`TMYSK\
VRHSQFPPENSEMUDKXDJZCHaCGcFEaHD`KBZMAYP8XR7VU5UW4T\
T9XRD_PHbMLfKPiITl9ah1ie8faFcYM`VTYRZWOaUPcTPfSQhR\
QkQRmPRoQOqSLrTJqSKpSKpRKoRLoQLnQLnQLkSMiUNgWOeXOc\
ZPa`Q_bRYcRWeSUgTSiUQjUOlVMnWKoWLlULiSLfRLcPL`OLYM\
LVLLSJLPILMGLJFKLIKNLJOOJQRJRTITWIUZHWaHXdHZfG_iGa\
lFboFdrFetHbsJ_sLXrMUrORrQOqRLqTIpVFpWCpY9o_6o`3oO\
B_BJLDQUFXaGbiGbhGbhGbhGbgGbgGbgGbfGbfGbfGbeGbeGbe\
F`cE_bDZ`CY_B`ZA_X9ZW8XV7UT6SS5QQ4OP3LO2JM1KL0JK3N\
O6RR9UUCYXF`_HdcKgfNkiQnlTroVurUvsTvsTvtSvtRwuQwuQ\
wuPwvPwvOwwNwwNwwLsrKpnJljHifGebFbZE_VUfNimFjiDjeC\
jaBkY9kV8kR7lN5lJ4lF3lC2h8Hd5Wa2jZ5hW8gTAeQDdNGbKI\
aHL_EOZBQYNolOmmQlnRjoSip }
frm:multirot-XZ-YW-new {; Jim Muth
; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect
e=exp(flip(real(p1*.01745329251994))),
f=exp(flip(imag(p1*.01745329251994))),
z=f*real(pixel)+p3, c=e*imag(pixel)+p4:
z=z^(p2)+c,
|z| <= 36 }
END 20.0 PAR-FORMULA FILE==================================
|
times.
