;     Date: Fri, 20 Jun 2003 09:09:31 -0400
;     From: Jim Muth <jamth@mindspring.com>
;  Subject: [Fractint] FOTD 20-06-03 (Pure Wholeness [6])
;       Id: <1.5.4.16.20030620090916.0d57400e@pop.mindspring.com>
; ---------
; 
; FOTD -- June 20, 2003 (Rating 6)
; 
; Fractal visionaries and enthusiasts:
; 
; When a discontinuous function is iterated, a discontinuous 
; fractal results.  Most of the FOTD fractals that are generated 
; by the MandelbrotMix4 (or 2) formula are discontinuous, and 
; indeed, the discontinuities often create the image.
; 
; Today's image however is continuous.  It combines 0.3 parts of 
; Z^(-2) with 0.3 negative parts of Z^4 before it adds (1/C).  The 
; resulting parent fractal is an oversized area of chaos, rotated 
; 45 degrees, which needs two outzooms before it totally fits on 
; the screen.  Near the center are two symmetrical and completely 
; outrageous mutant Mandeloids, with no relation at all to the 
; proper Mandel shape.  But these Mandeloids have no discontinui-
; ties, and that alone makes them interesting.
; 
; Today's scene is located rather deep in one of the less-likely 
; valleys of the eastern Mandeloid.  (In this Mandel-figure, all 
; valleys are unlikely.)  One of my taken-for-granted midgets is 
; located as usual at the center, though it is too small to occupy 
; more than a few pixels.  But the midget is not the center of 
; attention.  That honor goes to the elements that fill the image, 
; and delineate a kind of cogwheel.
; 
; These elements are almost totally disconnected, but they are 
; unbroken.  Not a single discontinuity mars the wholeness of the 
; image.  This is how the fractals with fractional negative 
; exponents would appear if a way could be found to eliminate the 
; discontinuities, a task that is impossible but still fun to 
; speculate about.
; 
; I named today's image "Pure Wholeness" because that's what it 
; is.  Too bad I could rate it no higher than a 6, but even a 6 is 
; at least slightly above average.
; 
; Running the parameter file, with its render time of almost 9 
; minutes, is one way of admiring the wholeness of today's image.  
; A second way is to download the completed GIF image from one of 
; the FOTD web sites at:
; 
;           <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
; 
; and at:
; 
;           <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>
; 
; Clouds were plentiful here at Fractal Central on Thursday, but 
; the temperature reached 81F 27C and the rain held off until 
; nightfall.  These pleasant conditions enabled the cats to enjoy 
; several hours in the yard and enabled me to save a can of tuna.
; 
; Today should be a wetter repeat.  If I get the routine work done 
; early enough, and if the rain does hold off, it might turn out 
; to be another good day for both cats and humans.  But to finish 
; I must start, so until the next FOTD in 24 hours, take care, and 
; study them as we might, we will never understand all there is to 
; know about fractals.
; 
; 
; Jim Muth
; jamth@mindspring.com
; jimmuth@aol.com
; 
; 
; START PARAMETER FILE================================

Pure_Wholeness { ; time=0:08:37.50--SF5 on a P200
  reset=2002 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix2 function=recip passes=1
  center-mag=+2.486158315330713/-0.00021229147922154\
  /3.847846e+009 params=-0.3/4/0.3/-2/0/525/0/0
  float=y maxiter=3600 inside=0 periodicity=10
  colors=000cyVbzPbzKVqHNfGGXE8MC0CBEJ9SP9cT8q_8ze6z\
  i6zcPz_eyVvx`pveiuicsp_quTpyNpzJupByc4zQ0zE0z10z40\
  x80sB0mC0fG0bJ0XM0SN1XK8_HEbEJeBPi8Vm4_p1es0im0kf0\
  n`0pV0sP0uGzuSzxcvzpnzzfzxcvsbmn`ci_VeYM`XCXV3ST0J\
  _qXfvhnzvvzzzz0QH0VM8_QGbVPf_XiccnhkqkcpfYnbSm_MkV\
  EiQ8hN1fJ0fG1cC8`9EY6KX3QT0XQ0bN0hM0s8Mz0p0zz8xzNk\
  zbYzqMzkJueGm_CeVB_xmYmqScuMVyGMz9Cz33z00z00z00z0C\
  z0Pz0bz0pz0zz0zk8yXExHMx1ScKKM`E3s60z00z93zJCzSMz`\
  VzicyskxzfssbnkYicTeXP`PKXHGT9JXCM_EPbGScHVfJYiK`k\
  MVQCQ44T18X09_0B`0Cc0Ef0Gh0He0Jc1Kb9M_HNYPPXXPQ0cT\
  4hV6p0Qy4GsB6mH0f`TnVNhPJcJE_C9V84QHG_PPhXYpcfykpz\
  syzmnzfczbTzXKzS9zM0zH0zf0`z440pu6qiHq_SsPbsEmu3xu\
  0ui0s_0pQ0nG0m60iE8hKEeQMcXSbc__ieYpmXvsPpkJicCcX4\
  YP0SH0M90H30Q40Y60e80m90uB0zC0vE0qG1kH3fJ6bK8XMBSN\
  CNPHHYMBeQ4nT0vN0uH1sB3q44p06p9cmG`TKY9PX00J0ihqme\
  snbup_vqXvuTxvQyxNzyKzev` }

frm:MandelbrotMix2 {; 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)+(p4)),
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==================================
;