Fractal visionaries and enthusiasts:  

Something is indeed wrong with today's scene.  This is why I have given the math a rating of 9, while the art rates only a 7 despite my extra work.  The math is interesting because the minibrot at the center is clearly quadratic, while the elements in the surrounding pattern are of order-6.  As an example of the strangeness, notice the 6 small spirals near the frame edges and the 36 tiny spirals at the next level inward.

I have seen this phenomenon several times before, and it appears no more logical today than it did when I stumbled upon it about 12 years ago.  But such counter-intuitive things in fractal math are what makes fractals so much fun and has kept me fascinated for over 25 years.  By comparison, those who approach fractals with a 'look ma I'm an artist' attitude all too often quickly lose interest.

The parent fractal came about when I subtracted 0.35 part of Z^(4) from Z^(3) and added straight C on each iteration.  This parent resembles a Mandelbrot set rotated 180 degrees, with large open bays at the end of every filament.  The largest bay of all lies at the eastern tip of the main spike.  This bay has a large but unstable valley intruding into it, which is very sensitive to changes in the real(p2) parameter.  Today's scene lies in this valley, very close to the X-axis.

The calculation time of 3 minutes is well within reason, but the viewing can be made even easier by checking the finished image on the web sites.

The weather was rather pleasant here at Fractal Central today, with partly cloudy skies, gentle winds and a temperature of 75F 24C.  The fractal cats passed the time watching the birds in the yard, while the humans took care of the business department.

The next FOTD fractal, for better or worse, will be posted in the near future.  Until then, take care, and some of yesterday's supernatural nonsense has become today's scientific wonders.  I wonder how much of today's supernatural nonsense will become tomorrow's scientific wonders.

Jim Muth
jimmuth@earthlink.net


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

Something_is_Wrong { ; time=0:03:00.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=allinone.frm
  formulaname=MandAutoCritInZ function=ident passes=1
  center-mag=+0.4473682468658692/-0.0008456880636021\
  /2e+007/1/-22/0 params=1/3/-0.35/4/0/0/0/0 float=y
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  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzz }

frm:MandAutoCritInZ {; 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)+(p4)),
k=real(p3)+1, esc=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < esc }

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