; July 14, 1997: Gritty Endurance 
;
; gritty
;
; Fractal visionaries:
;
; I often ponder such deep questions as, "what is the best Mandelbrot set
; I've ever produced."  A definitive answer might not exist, but today's
; surprising little midget is high on the list.  I've posted it as a
; reward for those few who took the trouble to draw the six views of the
; same lost, misshapen midget that I posted yesterday.
;
; I've always had problems with Newton's method formulas.  I just can't
; seem to get them right.  Today's fractal is a good example.  I was after
; a Newton's image; I got a Mandelbrot set instead.  But the Mandelbrot
; set is so unusual that I still have the formula in my permanent file.
;
; The gravelly texture that fills the image is due to the extremely small
; cutoff value of |a|.  Although the color palette in the attached par
; file does not show it very clearly, the gravelly texture, which appears
; to be infinitely divisible, gives a fair appearance of a PHC image,
; especially when drawn at a high resolution.  Experiment with the colors
; a bit; you'll be surprised at the effects that are possible.
;
; Unlike yesterday's six unfortunate images, today's image has been
; successfully posted to Usenet, where it hangs on a.b.p.f. and a.f.p.  I
; have decided not to post yesterday's images to the binaries groups.  A
; second look convinced me that they are not worth the bandwidth.
;
; For tomorrow's fractal, I'll return to those weird julibrot planes I'm
; fascinated with.  Until then, stay cool or keep warm, depending on which
; hemisphere you're living in.
;
; Jim Muth
; jamth@mindspring.com
;
; START 19.6 FILE=============================================

Gritty_Endurance   { ; time=0:00:18.00-SF5 on P4-2000
  reset=1960 type=formula formulafile=jim.frm
  formulaname=MandNewt06 passes=1 center-mag=-3.281\
  72/0/3.164669 params=8/0/5/0/1.5/0 float=y
  maxiter=200 inside=bof61 logmap=yes symmetry=xaxis
  periodicity=50
  colors=000Ur6_Y3dE0eK2fQ4fW6ga85Fd5Cg49j45m32p53j7\
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}

frm:MandNewt06 {; Jim Muth
  z=c=(pixel*p1):
  a=z^3+(c-p2)*z-c
  b=p3*z^2+c-1
  z=z-1*a/b
  .000000000000000000000000000001 <= |a|
}

; END 19.6 FILE===============================================
;