Fractal visionaries and enthusiasts:  

Today's image is the last in the series of hyperminibrot images.  It takes us as far as we can go into the HyperMandelbrot set with the DOS Fractint program, which after 20 years or so of supreme service is now far from state of the art.

A minibrot was once at this spot, but now it's gone.  It leaves only its memory to carry on.  (To see the minibrot, change the real(p3) parameter to zero, raise the maxiter to 8000, shut off the logmap, shrink the view-window, and wait a few minutes.)

The name "Patterns in Nothing" indicates that a good part of the image lies inside an originally empty area of the now-vanished minibrot.

The outer edge of the fractal ring retains the eight elements of the original minibrot, but the next ring inward has 30 elements, which is followed by a ring of 14 elements and then at the very center, a near-invisible ring of 6 elements.  The series seems to cut each level in half and subtract the number one as it progresses inward.  If this series continues, it would lead to a ring of only 2 elements at the next inward level, and zero elements at the level beyond that.  Unfortunately the next level inward beyond the 6 is beyond resolution.

One of these days, some fractal math expert, which I am not, might determine exactly what such an unlikely series means.  As I see it, all the stuff in today's image might be nothing more than artifacts of math imprecision.  If so, it still makes no difference, since what we have on the screen is still a fractal.

The worth of the art aspect, at least in my opinion, is a very high 8.  The math aspect rates an even higher 9.

The calculation time of 6-3/4 minutes is slow indeed, but relief is available on the FOTD web sites.

The day began with clouds and occasional sprinkles of rain here at Fractal Central.  This situation continued through the morning.  The rain grew heavier and steadier by noon, and continued through much of the afternoon, with snowflakes mixing in as the day progressed, while the temperature hung around 37F +3C.  The fractal cats busied themselves watching the world go by and complaining about the lack of sun.  We humans, also of a fractal nature, had no need to take extraordinary steps to keep ourselves busy.

The next FOTD will be posted when it is.  For a more specific schedule, check back here often.  Until next time, take care, and keeping busy is an integral part of the hectic modern day lifestyle, which is based on the scientific assumption that we exist on earth only one brief moment, and therefore must grab all the action we can before we go 'poof' like a wandering soap bubble drifting in the night.

Jim Muth
jimmuth@earthlink.net


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

PatternsInNothing  { ; time=0:06:45.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=HyperMandelbrot2 passes=1 float=y
  center-mag=-1.250229217708186/+0.01137634927674942\
  /1.4e+011/1/-142.5/0 params=0/0/0/0/0.23/0/1e-100/0
  maxiter=2100 inside=0 logmap=-1762 periodicity=0
  colors=000DUcDUcDUcDUcDUcDUcDUcDUcDUaDU`DUZDUYDUWD\
  UVDUWDUXCUYBUZAU_9U`8Ua6Ub5Uc4Ud3Ue2Uf1Ug0Ug2Th4Si\
  6Rj8Qj9NkBLlDJlFHmFFnFDnECmCAl98k66i44f67b7A_8DX9G\
  VAISCKUDMUEOU7QU7SU9UUAUUBUUCUUDUUEUSFTQGROHNMIJKN\
  HARFAUDAUBAU9CU8EUA7UC0UE4UG7UIBUKEUMFUPFUUFVZFWaF\
  X_FYXF_UG`SGaPGbMGcKGdHGeFGdGEcHDcHCbIBFVLGYJI`HJc\
  FKfDLiBMl9JgCHbFFZIDULBQOILLPGJVBGa6Eg2Ch3Dh3Ei4Ei\
  4Fi5Fj5Gj5Gj6Hk6Ik7Ik7Jl8Jl8Kl8KhCMdGOaKQwUswXrwVq\
  wUpwUowUnwUmwUkwUiwUgwUewUcwUawU_wUYwUWwKUwIUwQUwP\
  UwOUwNSwMQwLOvKMuJLtIKsHIrGGqFEpECoDAnC6mB5lA5i94f\
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  glDdoBfrAjt8nv6rx5vz3zz1zz0zz6zzCJjIHlOFmUDn_Bpe9q\
  k7rq5sv8prAnoCllFjhHheJfbLdZObWQ`TSZPUXMXVJZTF`RCb\
  P9gTPkXdo_sr`jt`bqZ_oXYmVWkTUiRSgQQdOObMM`KKZIIXGG\
  VFEUJCTMBSPASS9RVAQYKP`UPccUemZgvcizqkzwmzwozwqzws\
  zzuzzwzzxzzyzzzzzzzzzzzzz }

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