; April 24, 1997: Solar Symbol 
;
; solar
;
; Fractal visionaries:
;
; Fractals are things of many mysteries.  They raise one question after
; another.  During the ten years I've been working with them, these
; questions have almost constantly been in my mind.
; Perhaps the most immediate question is: how can an infinity of detail be
; encoded in such a simple formula?
;
; This question is relatively easy to answer.  The answer lies in the
; recursive nature of the fractal formula.  The fractal formula as written
; does not contain infinite detail, but the formula tells which way to go
; to see the infinite detail that is waiting there.
;
; Reiterating the Mandelbrot formula is like motoring along a highway.
; The instruction to reiterate the formula Z^2+C for every point of the
; complex plane is the same as the instruction to start at Atlantic City,
; keep traveling west on Route 40, and observe the sights as you go.
; Everyone who follows the same simple fractal instructions will see the
; same glorious fractal scenery for the same reason that everyone who
; follows the same simple highway directions will see the same glorious
; real world scenery.
;
; A more difficult question is: what are fractals -- did they exist before
; computers were invented?
;
; The simplest answer to this question is that fractals are infinitely
; complex images which appear on computer screens when complex formulas
; are reiterated and mapped to the complex plane. Since such images
; obviously did not exist before computers, it could be said that fractals
; did not exist before computers.
;
; But a fractal is not a mere physical image on a computer screen, it is a
; mathematical abstraction, an archetype with no more physical existence
; than the naked number seven without seven objects of some kind to give
; it reality.  Since fractal arche types have no real physical existence,
; it is meaningless to speak of a time before computers, when fractal
; archetypes had even less existence.  The fractal archetypes always
; existed in a kind of virtual state, even as they do now.  We simply were
; unaware of them before computers, because we lacked the means to
; manifest them.
;
; There are even more curious aspects to fractals.  Behind the world of
; fractal images lies the ultimate reality of mathematical formulas.  When
; no one is looking, nothing is there but the fractal formulas.  Behind
; the world of everyday objects lies the ultimate reality of the quantum
; world -- a world of incredibly complex mathematical formulas.  Quantum
; theorists tell us that when no one is looking, nothing is there but the
; quantum formulas.  What does this curious similarity imply?  Could the
; world of everyday objects also be a mere image?
;
; Unfortunately, for now this mystical question must remain unanswered,
; for I'm still pondering it.  Meanwhile, it's time to get to today's
; fractal.
;
; I named the formula and picture Gamut because they covers such a wide
; range of effects.  With six variable parameters to tweak, one could
; spend years before they discovered all this formula can do.  The formula
; is a bit more complex than I prefer, but it creates such unusual
; pictures that it's worth it.  As always, the finished image is posted to
; ABPF for those who prefer not to tie up their machines.  For those who
; wish to watch the picture come to life on their screens, it takes XXXX
; to build on a 486-100mhz.
;
; Jim Muth
; jamth@mindspring.com
;
; START FORMULA===================================================

Solar_Symbol       { ; time=0:00:03.52-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=gamut center-mag=-4.114731896495253/\
  0/131.3539/1/-90/0 params=3/1/0.5/1/-1/5e-031
  float=y maxiter=430 inside=0 periodicity=0
  colors=00013i42U61FXBNR8HK5BE25xxYfcMPKBcgNETFIY77\
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  G710jQ4NDzxBgc7QK31py4Zd6HK9HY8BM85Bh760BcG8YC4HzP\
  LlJGZCAL654b`6QO7DCgotXpy
}

frm:Gamut {; Jim Muth
  z=g=pixel, a=real(p1), b=imag(p1), c=real(p2),
  d=imag(p2), e=real(p3), f=imag(p3):
  h=z^a+(g-b)*z-g
  j=c*z^d+g
  z=z-e*h/j,
  f <= |h|
}

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