Fractal of the Day
by Jim Muth

In a Remote Valley © (#2)
Jim Muth's fractal image in GIF format (640x480).

FOTD -- August 09, 2006   (Rating 7)

Fractal visionaries and enthusiasts:

Today's FOTD image takes us to the fractal that is created when various negative portions of Z^(-1.7) and Z^(-5.7) are combined and (1/C) is added.   This parent fractal consists of a sprawling area of filamentary threads and loops, with two large open Mandeloid bays.   Today's image lies in a valley of the smaller and westernmost Mandeloid.

Judging by the pattern around the midget, the valley appears to have a mixture of Seahorse and East Valley nature, with maybe a slightly stronger East Valley nature.   But the brain-like features usually associated with East Valley are anything but brain like.   They look more like a carnival booth surrounded by energetic lightning, or perhaps the brain of a super-genius.

The rating of a 7 seems about right for today's fractal.   The name "In a Remote Valley" describes the location of the fractal in its parent.   The render time of 7-1/3 minutes is brief enough to avoid total boredom, but still long enough for hints of impatience to arise.   These twinges of impatience may be avoided by downloading the completed image from the FOTD web site at:
The absolutely perfect weather here at Fractal Central on Tuesday raised hopes in the fractal cats of going outdoors.   Unfortunately, those hopes were dashed and the duo had to settle for an afternoon of playing with and finally wrecking the daily newspaper.   In the evening, Nicholas enjoyed his treat of New York sharp cheddar cheese, which he prefers to tuna, while Cassie satisfied herself with a simple dish of tuna.

Tuesday was uneventful in my department, though I expect the next week or so to be quite busy.   So do not be surprised if the FOTD for tomorrow fails to appear when it should.   In fact, we might miss a couple FOTD's between now and August 16.   Until the next time, take care, and the answer to the riddle of the universe might be encoded in the depths of these fractals, if only we had the eyes to see and recognize it.

Jim Muth

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

In_a_Remote_Valley-2 { ; time=0:07:20.17--SF5 on a P200
  reset=2004 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=recip
  params=-1/-1.7/-0.2/-5.7/0/0 float=y maxiter=2400
  inside=0 logmap=277 periodicity=10
  pzzizzbzzZzzYzzXzz2zzAzzH }

frm:MandelbrotMix4 {; 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,
  k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
  |z| < l }

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

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