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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: When I found the first version of today's image with the HyperMandelbrot2 formula, I shifted to the type=hypercomplex formula, thinking it would be faster. I was totally surprised when the type=hypercomplex formula took almost five times as long to draw exactly the same image. Since then, I have made a few minor changes to the parameters, so the final version that appears as today's FOTD cannot be drawn by the type=hypercomplex. But it is only fair to comment that the periodicity need not be turned off with the type=hypercomplex, which means that images with a significant amount of 'inside' area, may run in about the same time under both formulas. Today's image shows a minibrot in East Valley. The little guy is in a bit of trouble, for it appears he is starting to close up. Actually, the HyperMandelbrot set consists of two classic M-sets that can be made to overlap in various ways, and this is what has happened to the minibrot in today's image. The surrounding elements have split apart, which is why I named the image "Seeing Double". I rated it at a 6 because I can see nothing out of the ordinary with it, nor did I put any significant effort into the coloring. Perhaps the best thing about the image is its fireball calculation time of under 2 minutes. And even this speed might be exceeded by going to the FOTD web site at: Heavy clouds and occasional rain spoiled the mild temperature of 48F 9C here at Fractal Central on Tuesday, while the fractal cats spent the day watching the world pass by. I spent the day working and trying not to work. The work won. The next FOTD will be posted in 24 hours. Until then, take care, and did reality really exist before someone dreamed up the concept? Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Seeing_Double { ; time=0:01:55.40-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=HyperMandelbrot2 passes=1 periodicity=0
center-mag=+0.301038546627/+0.023570365936/1.7e+007\
/1/115/0 params=0/0/0/0/-0.0025/0/1e-008/0 inside=0
float=y maxiter=3600 logmap=247
colors=000N0UO0UP0UQ0UQ0UQ0UQ0UQ0VR0WR0XR0YR0ZR0_S\
3`S3aS4`S4_S4ZS4YP7aM9eJChGElDHpAJsCMqEOpGQoISnKUm\
MWlOZjQ`iSbhUdgWffYieYlgZidZfa_bZ_ZW`VT`RQaNNaJKbF\
Ha7KbBEcF8cI3nPJyVYuTVrSToRRlQPhPNeOLbMI_LGWKETJCQ\
IANH8NC3RG6VJ8`NBeQDlUFtXIw`KzdJy`MxVOwMQzDUwEStFQ\
qGOnHMkIKhJIeKGbLE_MCXMAXNBXNBXOCXOCXOCXPDXPDXPDXQ\
EXQEXRFXRFXRFXSGXSGXSGZTH`VIbWJdYKfZLh`NjbOlcPneQp\
fRrhStiTvkUxlVufWraXoXYlSYiUWfWUcXS`ZQY_OVaMSbLPdJ\
MeHJgFGhDDjBAkAAjBBiCChDDgEEfFFeGFdHGcIHaKI`LJ_MJZ\
NKYOLXPMWQNUSOTTOSUPRVQQWRPXSOYFyNGvOHsPIpQJmRKjSL\
gTMdUNaVOZWPWXQTYRQZ3Tc8RcDQfIPdNObujZmdZfZZZTZpzF\
nvGmsHloIkkJiiKhgLgfMfdNdcOcaPb_QaZR_XSZWTYUUXTVVR\
WUQXTOY5jP6iQ7mQ8qR9wRAwRBmSBhSChSDiTEjTFkUGlUHmUH\
nVLoVPpVUqWZsWcuXhwXmzXrzYvzYzzYzzZzzZzzuzzqzznzzk\
zzgzzdzzazzKzzLzzLzzMzzMzzNzzNzzOzzOzzPzzPzzQzzQzz\
RzzRzzSzzSzzTzzTzzUzzUzzV }
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=========================================
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times.
