; June 17, 1997: Into the Eye 
;
; eye
;
; Fractal visionaries:
;
; When I saw the first fractals that contained complex or imaginary
; exponents of Z in their formula, I was disappointed.  The pictures on my
; screen were split along the negative X-axis.  They looked like part of
; the fractal was missing.  I soon found out that this was indeed the
; case.  Due to the multi-valued nature of the complex log functions, such
; fractals are infinite, and cannot be displayed in their entirety.  But
; enough can be displayed to reveal that they spiral endlessly around the
; origin in a screw motion.
;
; This inability to display the entire fractal was a situation that needed
; to be corrected, so I started experimenting.  I soon noticed that
; changing the sign of the exponent causes a fractal to change the
; direction of its spiral.  What would happen, I wondered, if a formula
; something like (z^x)+(z^(-x)) or (z^x)^(-x) were iterated with x being
; complex or imaginary.  Would the opposite spirals cancel out, leaving a
; fractal with complex or imaginary features, but without the annoying
; X-axis discontinuity?  I wrote a few test formulas, and the answer was
; yes, in some cases the opposite spirals did cancel out, leaving some
; very interesting one-piece complex and imaginary fractals.
;
; Today's fractal, Cyclone, is drawn from one of those test formulas.
; I've added a few frills to the formula to make it more interesting, but
; it's still basically the same idea.  Instead of spiraling off the screen
; into imaginary planes, the fractal spirals endlessly into the origin.  I
; haven't followed the spiral very deep, but it appears to show
; ever-changing features as one goes deeper.
;
; The picture itself is immediately striking -- the way I like a fractal
; to be -- with a brilliant red background blazing through mysterious
; foreground shapes.  The finished image has been posted, of course, to
; a.b.p.f. and a.f.p.
;
; Jim Muth
; jamth@mindspring.com
;
; START COMBINED FILE FOR 19.6===============================

Into_the_Eye       { ; time=0:00:04.99-SF5 on P4-2000
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}

frm:Mytest07  {; Jim Muth
  z=pixel, a=real(p2), b=imag(p2), c=b*(pixel):
  z=(((z^p1)*(z+a))^p3)^(-p3)+c,
  |z|<=100
}

; END COMBINED FILE==========================================
;