FOTD 31-08-05 (Storm Clouds [6])

31 Aug 2005

      FOTD -- August 31, 2005 (Rating 6)

Fractal visionaries and enthusiasts:

With all the news about storms on the TV, it seemed only proper 
that we should have a stormy fractal.  Once again the Fractint 
program and the world of math obliged, and we got our stormy 
fractal.

There are two images in today's parameter file.  The first one 
is named "Graph", and it is exactly what its name implies.  The 
'Graph' image is a graph of the function entered into the 
formula.  The critical points are now obvious.  They are the 
imaginary values of the tips of the parabolic curves, the points 
where the tangents to the curve are vertical, the points where 
the derivative is zero.  The problem lies in determining the 
exact Y-values of these points, but this can be done by repeat-
edly compressing the imaginary direction and thereby sharpening 
the parabolic curves.

The graph shows three critical points -- 9.3944253327, 
6.0457442391 and -0.4401695778.  Today's image lies in the 
parent Mandeloid determined by the first critical point.

I named today's image "Storm Clouds".  With a little stretch of 
the imagination it could be a dark and stormy sky.  The image 
is half-inside and half-outside.  The inside parts have been 
rendered with the 'fmod' option, with the proximity set to 27.

The image appears to be at least slightly above average, though 
the coloring could certainly use more work.  I rated it at a 6.  
With its maxiter of 2, the "Graph" image renders instantly.  The 
"Storm Clouds" image requires 1/2 hour to complete on my tired 
old fractal machine.  The stormy image is posted on the FOTD web 
site at:

       <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

the graph image is so simple that it can be rendered in less 
than 1/4 second.  Surely everyone can spare that much time.

Philosophy fans take heart.  I expect to have an outburst ready 
in time to appear in the philofractal version of tomorrow's 
FOTD.

It remained warm and very humid here at Fractal Central on 
Tuesday.  The temperature reached 84F 29C, but no rain fell and 
the fractal cats enjoyed a full afternoon in the holly patch.  
Today is starting much the same.  If the rain holds off again, 
it will be another good day.  For me, it will be an average day. 
The next FOTD fractal will appear in 24 hours.  Until then, take 
care, and some mysteries are more easily answered than others.

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

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

Graph              { ; time=0:00:00.24--SF5 on a P200
  reset=2004 type=formula formulafile=allinone.frm
  formulaname=ParabolicMix3 function=ident
  center-mag=1.8579/4.2739/0.1162964 params=1/2/-0.2\
  /3/1/1/0.01/4/0/0 float=y maxiter=2 inside=0
  symmetry=none periodicity=10
  colors=00000e0e00eee00e0eeL0eeeLLLLLzLzLLzzzLLzLzz\
  zLzzz000555888BBBEEEHHHKKKOOOSSSWWW___ccchhhmmmsss\
  zzz00zG0zV0zj0zz0zz0jz0Vz0Gz00zG0zV0zj0zz0jz0Vz0Gz\
  00z00zG0zV0zj0zz0jz0Vz0GzVVzbVzjVzrVzzVzzVrzVjzVbz\
  VVzbVzjVzrVzzVrzVjzVbzVVzVVzbVzjVzrVzzVrzVjzVbzhhz\
  lhzqhzuhzzhzzhuzhqzhlzhhzlhzqhzuhzzhuzhqzhlzhhzhhz\
  lhzqhzuhzzhuzhqzhlz00S70SE0SL0SS0SS0LS0ES07S00S70S\
  E0SL0SS0LS0ES07S00S00S70SE0SL0SS0LS0ES07SEESHESLES\
  OESSESSEOSELSEHSEESHESLESOESSEOSELSEHSEESEESHESLES\
  OESSEOSELSEHSKKSMKSOKSQKSSKSSKQSKOSKMSKKSMKSOKSQKS\
  SKQSKOSKMSKKSKKSMKSOKSQKSSKQSKOSKMS00G40G80GC0GG0G\
  G0CG08G04G00G40G80GC0GG0CG08G04G00G00G40G80GC0GG0C\
  G08G04G88GA8GC8GE8GG8GG8EG8CG8AG88GA8GC8GE8GG8EG8C\
  G8AG88G88GA8GC8GE8GG8EG8CG8AGBBGCBGDBGFBGGBGGBFGBD\
  GBCGBBGCBGDBGFBGGBFGBDGBCGBBGBBGCBGDBGFBGGBFGBDGBC\
  G000000000000000000000000 }

Storm_Clouds       { ; time=0:30:30.30--SF5 on a P200
  reset=2004 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix3a function=ident passes=1
  center-mag=-5.09875460590885100/+0.991687004724402\
  60/2.341077e+009/1/-32.5/-7.09176330104810404e-007
  params=1/2/-0.2/3/1/1/0.01/4/9.3944253327/525
  float=y maxiter=1500 inside=fmod proximity=27
  symmetry=none periodicity=10
  colors=00085C5592560537C8EICKOGRUKY`PcfTjlXqr`wxdi\
  t`XpYJlU6iRIjPTkOdkMolLzlKxjLvhLufLsdLqbLpaMn_MmYM\
  kWMiUMhTNfRNdPNcNNaLN`KNYNLVQKSTJPVHMYGJ`FGbDDeCAh\
  B8jA8hCIPTGRTEUTCWT9ZS7`S5cS3eS1gS5dS8bSB`SEZSHWSK\
  USNSSQQSwq1tl6rhAodFm`JjXNhTSePWcL_`JaZHcXFeUEgSCi\
  QAkO9mPCiPFfQIcQL`QOYRRVRUSRXPS_LSbITeFThCTk9Un6Uq\
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  vpuwTww5tu8rtBpsDnqGlpJioLgmOelQckTaiWZhYXg`VecTde\
  RchPbjUchYdfaeeefcjgbnh`ri_vjYzjXui_qhbmhdiggdgi`f\
  lXfnTeqPesNgpLinJkkImiJlhJkhJkgJjgJifJifJhfJgeJgeJ\
  fdJedJedKdfLcgMbhNaiO`jP_kPZmQYnRXoSWpTVqUUrUTsVMg\
  VGXW9LW3AbLRUbfTevRiuQktOmsNkrLjqKhpIfoHdnFcmEalC_\
  kBYjAXi9SeN5SK5PH5ME5JB5F }

frm:ParabolicMix3 {; Jim Muth
z=imag(pixel)+flip(real(p5)),
c=fn1(real(pixel))+flip(imag(p5)),
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=real(p3), h=imag(p3), j=real(p4), k=imag(p4):
z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c,
|z| <= 100 }

frm:MandelbrotMix3a {; Jim Muth
z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1),
d=real(p2), f=imag(p2), g=real(p3), h=imag(p3),
j=real(p4), k=imag(p4), l=imag(p5)+100:
z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c,
|z| <=l }

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

Jim Muth

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