; May 29, 1997: Brot in a Spot 
;
; spot
;
; Fractal visionaries:
;
; Today's formula is a really strange one.  One minute it's drawing the
; classic Mandelbrot set, the next minute it's drawing a screen full of
; flying fragments.  I devised the formula in an effort to eliminate the
; break along the negative x-axis that appears when complex or imaginary
; powers are calculated.  I got a lot more than I bargained for.
;
; I figured that since positive and negative imaginary powers draw
; fractals that spiral around the origin in opposite directions, if an
; expression something like (Z^2i)^(Z^(-2i)) were calculated, the opposite
; signs would cancel the spiraling out, leaving a fractal with the
; features of an imaginary exponent without the discontinuity along the
; x-axis.
;
; It worked beautifully.  Today's fractal, ringwrld, shows a somewhat
; distorted but still recognizable Mandelbrot set surrounded by rings
; introduced by the imag(1) assigned p3, which is calculated in the
; formula as both positive and negative.
;
; The formula is full of other surprises.  It's one of the most bizarre
; and unpredictable formulas in my collection, but despite its
; versatility, it still runs fast.  So don't hesitate to change the
; parameters and see what surprises you can turn up.
;
; Jim Muth
; jamth@mindspring.com
;
; START PARAMETER-FORMULA FILE FOR 19.6==============================

Brot_in_a_Spot     { ; time=0:00:04.94-SF5 on P4-2000
  reset=1960 type=formula formulafile=basicer.frm
  formulaname=Mytest06 center-mag=-0.729122/0/0.4411
  params=1/0/0.5/0/0/1 float=y bailout=100 inside=253
  logmap=yes symmetry=xaxis periodicity=10
  colors=000OMJUOG_PDeRBkS8qU5wV2wY4w_6wb8xe9xhBxjDx\
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}

frm:Mytest06  {; Jim Muth
  z=c=pixel:
  z=(((z^p1)*(z+p2))^p3)^(-p3)+c,
  |z|<100
}

; END PARAMETER-FORMULA FILE FOR 19.6================================
;