|
Fractal of the Day
by Jim Muth
|
|
Fractal visionaries and enthusiasts: Today is the last day of January, and the last day of the theme of January -- scenes in Seahorse Valley. The tour has taken us far afield, even into spaces of 8 dimensions to explore HyperSeahorse Valley. Today's image focuses on a point very near the point where the classic valley's two branches would reach the X-axis if they were calculated to infinity. I named the image "Seahorse Asymptote", a name that makes it look like I know what I'm talking about when I discuss fractal mathematics. Then I gave it a rating of a 7, a rather generic rating which means that, even though I can find nothing exceptional in the image, I am not disappointed by it either. It is immediately apparent that HyperSeahorse Valley is a far more complex thing than classic Seahorse Valley. The hyper version of the valley has networks of arms spanning the empty spaces between major elements that are far more intricate than those in the more familiar valley. Today's image is but a small example of the intricacy lurking in the HyperSeahorse Valley. It is also apparent that the image is actually a perturbed one. Since the HyperMandelbrot set is 4-dimensional, the hyper-minibrots within it must be 4-dimensional also. And I assume they are oriented in any possible direction within the 4-D Mandelbrot set, just as the classic minibrots are oriented in all possible directions in the classic 2-D M-set. But who knows what variety of perturbed slices this means are possible. The theme for February will be HyperEast Valley of the Hyper M-set. I will not refer to it as HyperElephant Valley, since elephants are already hyper enough without expletives added. I expect quite a few strange and perhaps entirely new things to show up on the eastern fringes of the main hyperbay. The calculation time of today's image is 6-1/2 minutes. This time may be cut by 1/3 by using one of the faster calculating algorithms, but when this is done, there is always a chance that some of the finer detail will be missed. Considering all of the above, the best way to see the complete scene intact is to visit the FOTD web site at: Overnight rain ended at daybreak Wednesday here at Fractal Central, and the sky cleared by 9:00am, but the high winds of 50mph (80kph) that prevailed for the rest of the day made the temperature of 34F 1C feel far too chilly for comfort. The fractal cats agreed and rolled over on their shelf on top of the radiator. My day was fairly busy; tomorrow will likely be the same. The next FOTD will appear in 24 hours. Until then, take care, and be at one with the secular universe. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Seahorse_Asymptote { ; time=0:06:38.48-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=HyperMandelbrot2 passes=1 periodicity=0
params=0/0/0/0/0.1/0/1.091e-005/0 float=y inside=0
center-mag=-0.74371926345344550/0/3475050/1/-90/0
maxiter=1800
colors=000q`MqZMrXMrWMrUMrTMrRMrPMrOMrMMrKMrJMrHMq\
ELrGMrHNrIOrKOrLPrMQrORrPRrQSrSTrTTsUUsWVsXWsYWs_X\
s`YsaZscZsd_se`veZsf`qfaogbmgcjgdhhffhgdhhaii_ijYi\
kWjmTjnRjoPkpNkqLkrKiqKgqJfqJdpJbpIapI_pIYoHXoHVoG\
UoGSnGQnFPnFNnFMmENmENmENmENmENmENmENmEOmEPmEQmERm\
ESmESmESmESmESmESmESmESmERmEShETcDUdDUaDTaDVcDZd9c\
n9bn9an9`n9_n9Zn9Yn9Xn9WnEVnIUnLTnOSnQRnTRnWWmYVm`\
TmcSmeQmhPmkOmmOmlRlkTkkUjjWiiXhiYhhZgh_fg`efadfbc\
eccedbdeacf`cg_bhZbiZajY`kX`lW_mVCvh_nVYlTWjSUiQSg\
PQeNOdMNbLL`JJ_IHYGFWFDVDBTCASBDUAGVAJW9LX9OY9RZ8U\
`8Wa7Zb7ac7dd6fe6if5lh5oi5qj4tk4wl3zm3zn3xl6uk9qjB\
nhEkgGgfJdeLacOYbRVaTS_WOZYLY`IXbP_ZWbVbeSihOplFoj\
LniQmhVli`mg_mf_md_nc_na_n`_nZ_oY_oW_oV_oT_pSZpQZp\
PZqNZqMZqKZqJZrHZrGZrEZqB`rDZsEYtFWtHVuITvJSvLQwMP\
xNNxPMyQKzRJzTHzUGzVEzXDzYBzZAz_9zaAzbBzcCydCxeDvf\
EugEthFsiGrjGqkHolIqcMqaM }
frm:HyperMandelbrot2 {; periodicity must be turned off
a=(p1),b=(p2):
q=sqr(a)-sqr(b)+pixel,
b=(p3+2)*a*b+p4,
a=q,
|a|+|b| <= 100 }
END PARAMETER FILE=========================================
|
times.
