Fractal visionaries and enthusiasts:

Today's rather harmless image is named "Empire of Numbers".  The name refers to the entire world of fractals, whose building blocks are the abstractions we call numbers.  And for all I know, the name might refer to the 'real' world as well.  The building blocks of the 'real' world are atomic 'particles', and any serious book on quantum theory soon leaves the impression that these 'particles' resemble numbers rather than the tiny electrically-charged billiard balls that usually come to mind.  Unfortunately, the 6.5 quality of the image fails to live up to the magnificence of the idea that the universe is made of numbers.

The image lies in the Z^(2.02)+C Mandeloid as it appears one level down the complex logarithmic hyperladder (hyperspiral) with the 'recip' function applied.  This parent fractal is a fairly normal Mandelbrot set rotated about 30 degrees CCW so that the main spike shoots out toward the WSW.  Today's image lies in a clump of debris piled along the negative X-axis, just north of the large period-2 bud of the rotated parent.

The rating of a 6.5 is all I could manage for the image.  There is nothing really wrong with it, but neither is there anything outstanding.  Additional color work might have raised the rating to a 7; I failed to see enough potential to try however.  Curiously, in keeping with the season, the parameter file coding for color registers 1, 2 and 3 is BOO.

The calculation time of 2-1/2 minutes is an estimate.  The image actually took 8-1/2 minutes to finish on the 200mhz machine.

Sunny skies and a mild temperature of 61F 16C made today a pleasant one here at Fractal Central.  The fractal cats took to their shelf to enjoy the warm sun, which once again streams quite strongly through the southwest window on sunny days.  My day was spent trying to decide whether to try to resurrect the out-of-action 2000mhz fractal computer.  I finally decided to put it off until tomorrow.  The machine has so many problems that it would likely be a losing battle.  For a while, I'll probably use the old warhorse 200mhz machine, (It's slow but it runs perfectly).  If the out-of-action unit is truly down for the count, I'll see if one of the spare business machines can be converted to Fractint duty.  The next FOTD will be posted in 24 hours.  Until then, take care, and the world is not quite the way it appears.

Jim Muth
jamth@mindspring.com
jimmuth@aol.com


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

Empire_of_Numbers  { ; time=0:02:30.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandelbrotBC3 function=recip passes=1
  center-mag=-0.961447228066923/-0.00000005309672964\
  /5.98e+11/1/90/0 params=2.02/0/-1/0 float=y
  logmap=233 maxiter=2000 inside=0
  periodicity=6 mathtolerance=0.05/1
  colors=000B00B00B00B01B02B03C04C15C26C37D48D59D6AE\
  7BE8CD8BF9DIBFMDGRFIVGJYILaKNeLOhNQmORrQSzURvRStON\
  rMNpJNnGNoBNlENjGNhINfKNdMNbOO`QPZS_WVbUXfS_hQbjOe\
  oMhrKkzImwHipHejH`bGXSGTHGOGGLAFIBFEBFBCE98F8CF7GG\
  6JG5NH4QH3UH2XL7RPBMTGHXKCVQD`O7lP0iO0fN2dM6aLAZKE\
  XJIUJNSIRPHVMGZKFbHEf99nFEjKIfPMbUQZ_UVdcRimNmwOnr\
  MnwKnrInwHxdDrYDoWBoUAoS8oQ6oO4vK0rM2oN3lP4iQ5fS6c\
  T7_V9XWAUYBRZCO`DJg7KdBLaEMZHNWKOTNPQQQNURKXSH_TEb\
  UBeV8hV3jW5kX7lY9lZBm_Dn`FnaHobJocLpdNqePqfRrgTreW\
  pdYoc_nbamacl`ej_giZihYkgXmfUqiWoeXmbZk__iXagTbeQd\
  cNeaKhbIf`HeZGdXGcVFbTF`RE_PEcTQYMDXKCVICUGBTEBSCA\
  UA3RBAOBHLBOIBVFBaACiCBgDCeEEdFGbGIaHK_IMZJOXKQVLS\
  UMUSNWROYPP_OQaMRcLPePOgSMiWLkZKmbIoeHqiEsnGtlIukK\
  viMwhOxfQyeSzdUzbWzaYz__zZazXczWhzWfzVdzVmzVmzVmzU\
  mzUmzUzzUzzTzzTzzTzzVzzUzzTzzSzzRzzQzzPzzOzzNzzMzz\
  LzzKzzJzzIzz8zz9zzBzzCzzD }

frm:MandelbrotBC3   { ; by several Fractint users
  e=p1, a=imag(p2)+100
  p=real(p2)+PI
  q=2*PI*fn1(p/(2*PI))
  r=real(p2)+PI-q
  Z=C=Pixel:
    Z=log(Z)
    IF(imag(Z)>r)
      Z=Z+flip(2*PI)
    ENDIF
    Z=exp(e*(Z+flip(q)))+C
  |Z|<a }

END PARAMETER FILE=========================================