;     Date: Tue, 14 Jan 2003 11:51:54 -0500
;     From: Jim Muth <jamth@mindspring.com>
;  Subject: [Fractint] FOTD 14-01-03 (Polytope Paradise [6])
;       Id: <1.5.4.16.20030114115441.29ef9b7a@pop.mindspring.com>
; ---------
; FOTD -- January 14, 2003 (Rating 6)
; 
; Fractal visionaries and enthusiasts:
; 
; While at least one member of the Fractint list appears to 
; perhaps be losing a bit of enthusiasm for fractals, there is no 
; danger of a similar fate befalling myself.  The only thing I 
; regret is that I lack the time to explore more of the infinitely 
; infinite world of fractals.
; 
; Perhaps the first sign of impending boredom with fractals is the 
; desire to add multiple layers, as if a single-layer fractal 
; needed something to give it more interest.  Then again, perhaps 
; my devotion to single-layer fractals is an individual quirk of 
; mine, caused perhaps by my typical male tendency to concentrate 
; on one task at a time.  After all, multiple layers works very 
; well in the case of music, which is candy for the ears; why not 
; in the case of fractals, which are candy for the eyes?
; 
; I named today's image "Polytope Paradise".  I can give no 
; logical reason why I chose such a name, since a polytope is a 
; geometrical figure, existing in n-dimensional space and enclosed 
; by a finite number of planes or hyperplanes.  The strings of 
; bubbles in today's image are enclosed by curved 2-D surfaces 
; rather than planes, and therefore cannot truthfully be consid-
; ered polytopes.
; 
; As a matter of interest, the word 'polytope' was invented by 
; Alicia Boole, the daughter of logician George Boole.  In 1-space 
; and 2-space, an infinity of regular polytopes are possible.  In 
; our everyday 3-space, only 5 regular polytopes are possible.  In 
; 4-space, 6 are possible, but in 5-space and all higher spaces, 
; only 3 regular polytopes can exist.
; 
; Today's image is another ghostly one, consisting entirely of 
; trapped points whose orbits have been made visible by the bof60 
; inside fill.  The generating formula combines 1/Z and Z^(-2), 
; then adds 1/C.  The image itself rates a 6.
; 
; The render time of 41 minutes for today's image is admittedly 
; slow.  The wait can be avoided by downloading the completed GIF 
; image from:
; 
;           <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
; 
; or from:
; 
;           <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>
; 
; The fractal weather was actually not too bad on Monday, with 
; warm sun, little wind, and a temperature of 43F 6C.  The fractal 
; cats found the outdoors reasonably comfortable.  Tippy, the lean 
; lanky tabby, spent nearly two hours in the yard.  Thomas, the 
; overweight yellow, returned indoors after one hour.  No treats 
; were needed.
; 
; Today however is much colder, and the dynamic pair will not find 
; it so pleasant out of doors.  I will not find it pleasant until 
; the work is finished.  The next FOTD will appear in 24 hours, so 
; take care, and see you then.
; 
; 
; Jim Muth
; jamth@mindspring.com
; jimmuth@aol.com
; 
; 
; START PARAMETER FILE================================

Polytope_Paradise { ; time=0:41:12.86--SF5 on a p200
  reset=2002 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+0.84049791931695570/+0.257654873112327\
  50/235620.6/1/-65/5.48976843151027794e-010
  params=1/-1/1/-2/-32/1e+100 float=y maxiter=900
  inside=bof60 logmap=yes periodicity=10
  colors=000zzzzwyzuxzswyqvyouymtxlsxksxjrwirwhqwgqv\
  fpqepldjgbcb`YYZRTXLNWGOVFPUFPTEQSEQRERQDRPDSODTNC\
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  O_TN`TMbTLcTKeTJfTIhTHiTIqNGjTEcZCXdAQj8Jp5Dx7Cv9C\
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  i72j62k50m22k44j66i88g99fBBeDDcEFbGGaII`JKZLMYNOXO\
  PVQRUSTTTVSVWQXYPY_O_aMacLbdKdfJfhHgjGikFkmDloCnqB\
  prAqVNIXPLYQN_RP`SRaTTcUV }

frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l }

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