[Fractint] FOTD 10-09-13 (Points Revealed [A-7,M-8])

11 Sep 2013

      FOTD -- September 10, 2013 (Rating A-7,M-8)

Fractal visionaries and enthusiasts:

While yesterday's fractal was a non-critical loser, today's 
fractal, which is critical, is a notable improvement.  It is a 
scene in the fractal that is generated when yesterday's fractal 
is re-calculated with Z initialized to the first of the three 
critical values of the iterated expression.  This value appears 
as the real(p5) parameter of today's image.

At first glance, today's parent fractal, which is critical, 
appears little changed from yesterday's image.  In its depths 
however it is totally different, with intact minibrots lurking 
where least expected.  Today's image, which I named "Spiraling 
Onward", lies on the west side of the north branch of what could 
be called a kind of Seahorse Valley.

The math value remains a superb 8, while the artistic value has 
risen from an abysmal 3 to a very respectable 7.

The three critical values of initial Z in yesterday's loser 
image were found by entering the same parameters into the 
CriticalPoints formula, which appears in today's parameter file. 
This calculates the Parabolic plane of the iterated expression 
and creates an image that is a rough graph of the expression.  
All that is then necessary is to find the 'Y' coordinates of the 
tips of the three obvious though distorted parabolic curves.  I 
always choose the place where the default red adjoins light 
blue.  The tedious part is continually stretching the curves 
horizontally to determine the exact 'Y' coordinates.  The second 
image, named "Points Revealed", shows the resulting image-graph 
that must be analyzed.

The method is tricky, especially with negative and fractional 
exponents, and sometimes does not work, but it is still better 
than trying to write a formula to do the job or finding the 
points by hand calculation.

The calculation time of 2-2/3 minutes is somewhat slow, and I'm 
not sure the result is worth the wait.  Luckily, the web sites 
can speed up the viewing.

Save time and effort by checking the finished images at:

      <http://www.crosscanpuzzles.com/Archives.html>

<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>

       <http://www.Nahee.com/FOTD/>

  <http://user.xmission.com/~legalize/fractals/fotd/about.html>

A mix of sun and clouds, and a temperature of 88F 31C made today 
quite summer-like here at Fractal Central.  The fractal cat was 
undecided whether to stretch out or curl up, and finally settled 
half stretched in my favorite chair.  The fractal people passed 
the day getting things done.

The next FOTD will soon be posted.  To see how soon, check back 
here frequently, and before you know what happened, the next 
fractal will be here.  Until whenever the fates decide, take 
care, and let's admit it -- according to science, objective 
reality is probably an illusion, which means that our mighty 
scientific method is founded on nothing more than an illusion.

Jim Muth
jimmuth@earthlink.net

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

Spiraling_Onward   { ; time=0:02:40.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandelbrotMix3a function=ident passes=t
  center-mag=-0.511568295107038/+0.05469492019194518\
  /1.23e+010/1/140/0 params=0.1/2/1/3/0.5/6/0.01/-1/\
  0.2246790860663939/0 float=y maxiter=1750 inside=0
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  zzmzzmzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzz }

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 }

Points_Revealed    { ; time=0:00:20.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=CriticalPoints function=ident
  passes=1 center-mag=0/0/0.6666667
  params=0.1/2/1/3/0.5/6/0.01/-1 float=y
  maxiter=500 inside=0 periodicity=6
  colors=00000e0e00eee00e0eeL0eeeLLLLLzLzLLzzzLLzLzz\
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  GBCGBBGCBGDBGFBGGBFGBDGBCGBBGBBGCBGDBGFBGGBFGBDGBC\
  G000000000000000000000000 }

frm:CriticalPoints  {; Jim Muth
z=imag(pixel), c=fn1(real(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):
z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c,
|z| < 10000 }

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