FOTD 06-11-13 (The Shadow Arises [A-8.5,M-7])

6 Nov 2013

      FOTD -- November 06, 2013 (Rating A-8.5,M-7)

Fractal visionaries and enthusiasts:

Today's stellar but slightly ominous image lies in the East 
Valley of the parent fractal that comes about when the 
expression Z^(2.01)+C is iterated 1.5 levels up the complex 
logarithmic hyperladder with no function applied.  At this 
not-very-impressive height the parent resembles a Mandelbrot set 
rotated almost 180 degrees so that East Valley falls close to 
the negative X-axis, and its beat-up main bud and main spike lie 
near the positive X-axis.

In today's parent, East Valley has been broadened into a wedge, 
with fractal debris scattered along the sharp northern edge of 
this wedge.  Today's image lies in this debris.  I'll check the 
beat-up main bud and spike in a future FOTD.

Strangely, there is very little in the image to reveal that it 
lies in an East Valley.  Instead, we see finely-divided arcs and 
crescents surrounding the central minibrot.  I rated the art 
worth at a superior 8.5, mostly because of my coloring, most of 
which was created randomly by the Fractint program.  I rated the 
math interest at a 7, which might be a bit liberal for a math 
trick ten years old.

The name "The Shadow Arises" does not imply the return of that 
old radio character who could make himself invisible.  It refers 
to the unusually shadowy appearance of the dark green elements 
surrounding the minibrot.

The calculation time of 1-1/5 minutes is reasonably fast, but a 
trip to one of the web sites will make the brief wait even 
briefer.

The finished image is available at:

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

with clever variations at:

<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 little sun, lots of clouds and a high temperature of 61F 16C 
brought rather pleasant conditions to Fractal Central today.  
The fractal cats had a quiet day except for the time Jasmine 
sneaked up on Nico and took a swipe at his tail.  In return, he 
took a harmless swipe at her to warn her away.  The fractal 
humans had a near average day.

The next FOTD will be posted within a certain time.  To find out 
how certain, check back at regular intervals.  Until whenever, 
take care, and if it can be scientifically demonstrated to be a 
fact, it might even be true.

Jim Muth
jimmuth@earthlink.net

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

The_Shadow_Arises  { ; time=0:01:12.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandelbrotBC3 function=ident
  center-mag=-0.261378641122/-0.001444041117/\
  1.593933e+007/1/161/0 params=2.01/0/1.5/0 float=y
  maxiter=1500 inside=0 logmap=165 periodicity=6
  colors=00045H5Gg65_70f85Y95RA5TB5VC5XD5ZE5`F5bG5dH\
  5fH3hL7eP7cT7`X7Z`6Vc6Sg6Ok6Lo5Hs5EA5zA5wA6t98qBAn\
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  7z46z35z34z23z12zqLzqKzqK }

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=========================================

Jim Muth

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