; May 20, 1997: Eternal Triangle 
;
; triangle
;
; Fractal visionaries:
;
; A few days ago Ray Girvan posted a formula that drew distorted Newton's
; images, only to be told that this approach had already been
; investigated.  After trying trying the formula, I realized that the
; images were strangely familiar.  I had seen similar images somewhere
; before.  Examining my Newton's formula file, I discovered a formula that
; contains within itself the ability to duplicate Ray's formula.  The
; formula is attached to the end of this letter.  (Set real p1 to 1, imag
; p1 to 3, real p2 to 3, imag p2 to 1, real p3 to 1, and imag p3 to 0.0001
; and the formula draws the power 3 Newton's figure.)
;
; The formula is still in the testing stage.  When I get it finalized,
; I'll eliminate some of the variables to make it easier to control.  When
; I work with this formula, I start with the above parameters, which draw
; the power 3 figure, and change them one at a time.  Many settings give a
; blank screen.  When this happens, I search out the exact setting where
; the screen goes blank.  Something unusual is almost always found there.
; When I get a blank screen that just won't do anything, I always try the
; bof60 inside fill before giving up.
;
; Today's fractal is all inside fill.  At first glance, it looks nothing
; at all like a Newton's figure.  But it is.  Tomorrow, I'll post another
; fractal made with this formula, which doesn't even look like a fractal.
;
; Before I go, I'd like to pose a challenge.  A while back, I was
; discussing fractals with a non-mathematical co-worker.  The conversation
; drifted to four-dimensional fractals, and this person asked me to
; explain in simple language the difference between quaternions and
; hypercomplex numbers.  I couldn't.  Can anyone out there answer this
; person's question in easy-to-understand layman's terms?
;
; Jim Muth
; jamth@mindspring.com
;
; START PAR FILE FOR 19.6=========================================

Eternal_Triangle   { ; time=0:00:36.30-SF5 on P4-2000
  reset=1960 type=formula formulafile=basicer.frm
  formulaname=NewtonTest26
  center-mag=-0.118626/0.258174/0.5706667/1/-30/0
  params=1/6/3/1/1/2.27e-032 float=y maxiter=90
  bailout=100 inside=bof60 logmap=yes periodicity=0
  colors=000IzAIv9It9Iq8Io8Il7Ik7KgALdDMbFN`IPZKQWNR\
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  N`cP`fR`iTInCInCImBImBIlA
}

frm:NewtonTest26 {; Jim Muth
  a=real(p1), b=imag(p1), c=real(p2),
  d=imag(p2), k=real(p3), f=imag(p3),
  z=(pixel):
  zx=z^b-a
  zy=c*z*z
  z=z-(d*zx/zy)^k,
  |zx| >= f
}

; END PAR FILE FOR 19.6===========================================
;