FOTD -- November 08, 2007 (Rating 7.5)

Fractal visionaries and enthusiasts:

The name of today's image, "A Riot of Colors", says it all.  It 
is perhaps the most colorful FOTD image of all time, helped in 
no small degree by myself.  The parent fractal is the Z^(1.75)+C 
Mandeloid as it appears 11 levels up the complex logarithmic 
ladder, which could perhaps be more accurately described as a 
hyper-helix.  As a matter of interest, the formula for calculat-
ing the complex natural logarithm is:

            (1/2)ln(x^2+y^2)+i(atan(y/x)+2kPI)

The logarithmic ladder, or hyper-helix, exists because k can be 
given any value from minus to plus infinity.

Today we are at step +11 of the infinite ladder, where the 
parent appears as a single large oval bay with, strangely 
enough, two large period-2 buds, one on its east side, the other 
more irregular one on its northwest side.  A large area of chaos 
extends north from the irregular bud, and today's scene lies 
just east of a larger minibrot lying near the northern tip of 
this area of chaos.

The image is far too gaudy to earn a superior rating, but it is 
well worth a 7 plus the 1/2 point I gave myself for the little 
extra work I did on the color palette.

The calculation time of 3-1/4 minutes is perhaps a bit slow for 
the total image, but the colors alone will assure that those who 
take the time to run the included parameter file will not be 
totally disappointed.

Iteration frustration may also be avoided by visiting the FOTD 
web site at:

       

and viewing the finished image there.

Typical late autumn conditions prevailed here at Fractal Central 
on Wednesday.  Brisk northwest winds blew, the sunlight alterna-
ted with dark scudding clouds, and the temperature reached only 
43F 6C.  Snug indoors, the fractal cats spent the day by the 
heat, warm as toast, while I kept warm fighting with a job that 
just would not do what the customer wanted.  The next FOTD will 
be posted in 24 hours give or take a few.  Until then, take much 
care, and be at ease with this mysterious world.


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


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

A_Riot_of_Colors   { ; time=0:03:18.17-SF5 on P4-2000
  reset=2004 type=formula formulafile=allinone.frm
  formulaname=MandelbrotBC3 function=floor passes=1
  center-mag=-0.30648810766/+1.86666607889/6240791/\
  1/77.5/-9.14082472e-009 params=1.75/0/11/0 float=y
  maxiter=32000 inside=0 logmap=160 periodicity=10
  colors=000zNQmON`QJNQIBSE0SD0U90U80L40E2680G20D009\
  0080340420600900B00D30J90QG0WO4bWBibGnkNvrUzzZzvUz\
  rQvnNnkJigGbdDX`9QX6LU3GQ09N04J00G00D00900600B00G0\
  0L00Q00W00`00e00k00p00v00z00n2DbDOQNbEZn3kz0vzz0mz\
  0gz2dz6`z9WzDSzIOzLJzOGzUDzX8zb4ze2zi0zn0zr0zv0vv0\
  rv0nv0kv0gv0bv0Zv0Wv0Sv0Ov0Up0Xk0`g0db0zX0kU0nO0rJ\
  0zG0tI0rJ0pJ0nL0zL0mN0kN0iO0gO0eQ0eQ0bO2`O4ZO8XNBW\
  NEUNISLLQLOOLUNJXLJ`JzdIggGZkEZnDLfIBYN4ZN0QS0NY0P\
  b0QzxNztJzpGzmDzi9zd6zZ3zU0tO0nL0iO0eS0`W3WZ6Sb9Nd\
  DJdGGeIDeL9eN4gQ2gS0iW0iX0i`0kb0ke0mg0mk0mm0pg0rb0\
  vX0xS0zN0zI0zD0z86z3Ez0Nz0Wz0dz0mz8vzGzzQzz`zzizzt\
  zzzzzvzznzzgzz`zzUzzNzzOzzdzzvzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzz }

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|

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