Fractal visionaries and enthusiasts:  

Believe it or not, today's image has the same 'C' coordinates in the Mandelbrot set as yesterday's.  But the appearance has totally changed.  The central minibrot as well as everything around it has vanished and been replaced by a series of 14 converging arms.

The reason for the change is the real(p3) parameter, which has been raised from zero to 0.248 and thereby offset the slice ever so slightly in one of the other six directions that are perpendicular to the plane of the image in the 8-D Julibrot.

The name "Mystery Epicycles" refers to the 14 converging arms that have replaced the minibrot.  The number 14 is strange enough, but the next deeper series of converging arms, barely visible at the center, numbers only six.  I have no idea what determines these series, so they are still a big mystery.  BTW, epicycles are what the strange retrograde motions of the planets were called before we knew the nature of the solar system and the laws of gravity.

The art aspect, which in my opinion is a little better than yesterday's, rates a 7.  The math aspect reveals its full mystery in today's image, and honestly earns its superior rating of a 9.

The calculation time of 11 minutes is definitely slow, making the web sites a far better way of viewing the scene.

Clouds moved in just after noon here at Fractal Central today.  Things were not as bad as they might have been however, as the temperature reached 46F +8C.  The fractal cats grumbled when the sun was obscured just as it reached their window shelf.  The fractal humans simply did their usual grumbling.

The next FOTD will be posted in a moderate number of hours.  Until we find out what moderate means, take care, and the perfect SAT test would be one in which every student scores the same mark.  But if we ever achieved this ideal goal, why would we need the test?

Jim Muth
jimmuth@earthlink.net


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

Mystery_Epicycles  { ; time=0:11:00.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=HyperMandelbrot2 passes=1 periodicity=0
  center-mag=-1.250229217708301/+0.01137634927677889\
  /6.17e+010/1/-155/0 params=0/0/0/0/0.248/0/1e-100/0
  float=y maxiter=12000 inside=0 mathtolerance=0.05/1
  colors=000l6cl7_n8Wn9ToBPoCMoBJpAGl8Cf54`2DV2BM08F\
  27867jCGlKDoTAs_8o`NndeoevjaogZldWgaUbYQZWOWUKSRIO\
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  L7sNIvSUwXfzaalOZ`DZS5YT8YUCWUGWWKVYPWYTYZYzXmwOnw\
  IovCpv7rN3l22g32e77eCLeHVdO_dTedZkbbpbisgqsisrwosj\
  jtNgrE`p4Ym3Wj2Vd2UZ1UU0SR3SN6SJASGESDHRAKR6OR3SS1\
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  120000000000000000000000002004006OBPzlqzhqvdpn_oiX\
  rcUsYRsSOvMLwHIzCFz8Dz5Az4Bw4Ar3Bl2Be1C`0CW0DR0EM0\
  EH0FDAO7PW1ec2dU2bL2`D1Z61Y11P60IC0CK09W06e44r7Kw4\
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  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=========================================