Fractal visionaries and enthusiasts:  

Today's image is a simple scene deep in the northern branch of Scepter Valley of the Mandelbrot set.  But this parent Mandelbrot set is not your everyday Mandelbrot set.  It is a slice down the middle of a four-dimensional HyperMandelbrot set.  As long as the real(p3) parameter in the generating formula remains at zero, the parent fractal is the M-set.  But when the value is changed, strange things begin to happen.  Tomorrow's image will show the beginning of the strangeness.

The name of the image, "The Eighth Dimension", indicates that the scene is a slice through an 8-dimensional Julibrot, which will become apparent in the images to follow.

The artistic rating of a 6 is what the image itself is worth, since despite the hype, it is simply a scene in the Mandelbrot set.  The math rating of an 8 shows that some quite unusual mathematical things are to come.

The calculation time of 6-1/2 minutes is rather slow.  Luckily, the web sites can speed up things significantly.

The day began with a snow flurry here at Fractal Central, which dropped a full 1/2cm 1/4-inch of snow.  By late morning the clouds blew away, leading to a sunny but blustery afternoon with a high temperature of only freezing.  The fractal cats enjoyed the afternoon sun on their shelf, while the fractal humans wondered when the spring greenery would appear.

The next FOTD will be posted in 24 hours.  Until then, take care, and become one with the numbers.

Jim Muth
jimmuth@earthlink.net


START PARAMETER FILE=======================================

TheEighthDimension { ; time=0:06:30.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=HyperMandelbrot2 passes=1
  center-mag=-1.250229217708301/+0.01137634927677889\
  /6.174502e+010/1/-155/0 params=0/0/0/0/0/0/1e-100/0
  float=y maxiter=12000 inside=0 periodicity=0
  colors=000l6cl7_n8Wn9ToBPoCMoBJrAGo8Ck59j2Ii2Lg2Pg\
  2Kh6HjCGlKDoTAs_8o`NndeoevjaogZldWgaUbYQZWOWUKSRIO\
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  fNrlRvpTztXzyZzzazzczkWvSPeCHS8DE6B54A03800S13nG4r\
  L7sNIvSUwXfzaalOZ`DZS5YT8YUCWUGWWKVYPWYTYZYzXmwOnw\
  IovCpv7rN3l2Ic3Mh7QmCUrMZvUcz`ezcizgmzkqzotzqzzpyo\
  nzgizEds4Yo3Wj2Vd2UZ1UU0SR3SN6SJASGESDHRAKR6OR3SS1\
  YS1`Q2eO5lN8rMBwMEzMGwOIvOKsPMrQNnRQlSRjSUgUVdVXbV\
  X`WZZWZZ_`__`W``VdcSgcRldOoeN```ScoIezDWn9MU6ED370\
  120000000000000000000000002004006OBPzlqzhqvdpn_oiX\
  rcUsYRsSOvMLwHIzCFz8Dz5Az4Bw4Ar3Bl2Be1C`0CW0DR0EM0\
  EH0FDAO7PW1ec2dU2bL2`D1Z61Y11P60IC0CK09W06e44r7Kw4\
  ez5az5Xw4Uw4Sv4Os5Ls7L3oN4rQ4sS4sT4sU4sW4sX4sY4r_4\
  ra3oa3oc3ne3nf3lg3jj4hl5f }

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=========================================