;     Date: Fri, 26 Sep 2003 09:22:03 -0400
;     From: Jim Muth <jamth@mindspring.com>
;  Subject: [Fractint] FOTD 09-04-98 (Pink Midget)
;       Id: <1.5.4.16.20030926092248.29efbeda@pop.mindspring.com>
; ---------
; 
; F.O.T.D., April 09, 1998 (Pink Midget)
; 
; Fractal visionaries:
; 
; I had planned on discussing in today's FOTD the ultimate ques-
; tion of life, and the way it relates to the realm of fractal 
; geometry.  But I just couldn't muster the proper degree of 
; profundity that one must feel before tackling such a life-
; altering topic.  So instead, I dredged up a picture of a baby 
; Mandelbrot.
; 
; The guilty formula is my MandelbrotMix4, which automatically 
; calculates a critical point of the formula and sets that value 
; as the starting point of Z.  The actual equation being iterated 
; is (4*Z^3)+(2*Z)+C.  These values draw a small Mandelbrot set 
; rotated 90 degrees, with a curious tail dropping down from the 
; cleft of East (Elephant) Valley, which has now become a South 
; Valley.
; 
; The main Mandelbrot figure is fairly conventional, but the East 
; Valley tail is filled with cut-off bits and pieces that demand 
; further investigation.  Only a slight magnification is needed 
; to reveal the tell-tale patterns that lead to hidden midgets.
; 
; At first glance, today's image appears to have come from a 
; spiral in Elephant Valley itself.  A quick examination, how-
; ever, will show that the pattern around the midget is more 
; delicate, with more fine, hairline detail than that which 
; appears around the midgets in Elephant Valley.  Also, the 
; features are broken rather than connected, as they are in the 
; valley.
; 
; I gave the image a pastel-like palette of colors, which empha-
; sizes the more delicate nature of this midget.  The tendrils 
; curving away from the central midget are themselves filled with 
; midgets, but alas, these midgets are beyond the reach of conven-
; tional DP math.  (Hint, hint . . . Fractint developers, 
; wouldn't it be great if arbitrary precision math could be 
; applied to formula type fractals?)
; 
; Today's harmless little midget has been posted to the usual 
; sites -- alt.fractals.pictures and alt.binaries.pictures.fractals
; It is also available at Paul Lee's web site at:
; 
;       http://home.att.net/~Paul.N.Lee/FotD/FotD.html
; 
; and Scott's site at:
; 
;       http://sdboyd.dyndns.org/~sdboyd/fotd/index.html
; 
; Tomorrow, I might gather my profundity and discuss the ultimate 
; question of life, or then again, I might blather on about some-
; thing of little consequence, but whatever I do, I will have 
; another fractal ready and waiting.  Until then, take care, and 
; the next time you see a fractal, view it with reverence, for 
; that fractal might encode the answer to the riddle of the 
; universe.
; 
; 
; Jim Muth
; jamth@mindspring.com
; 
; 
; START PARAMETER FILE===========================

Pink_Midget { ; 7min on a P200, SF5
  reset=1960 type=formula formulafile=apr-98.par
  formulaname=MandelbrotMix4 passes=1 function=ident
  center-mag=-0.00218445795113323/-0.2346673882601\
  9790/9.192243e+010/1/-160/1.5611329691467279e-005
  params=4/3/2/1/0/0 float=y maxiter=6000 bailout=9
  inside=0 logmap=123 colors=00016727929A2CB2EC2FD\
  3HF3IG3KH3LI3MJ4NL4OM4PN4QO4SP4SQ4SR5TT5TU5TV9VX\
  DXZHZaL`cPbeUehYhlbkognrlqupsxstxutyuqvuottlrukq\
  ujpvhnvgmwflxckxajyZhyXgzVfzUewUbuU`rUYoVVmUTjUQ\
  gTNeTLbRI`OGYMDVJATH8QG5OF3PE4QD5SE6TF7VG8WH9YIA\
  ZJB_KC_LD`PE_TFbVFcXFeYFe_FV`FVaFVbFVcFVcFTdEReD\
  PfCOfBMhALjAJl9Hm8Fp7Dr6Cs6Au59w47w35w24v2KncQam\
  VQxO9xOCvOEsNHqNJnNMlNPjNRgNUeMWbMZ`M`YMcWMfUMhR\
  LkPLmMLpKFeOWV_bLia5obAobFocKpcOpdTpeYpebpfgpflq\
  gpqguqhzqcvn_qjVmgRhdMdaI_YDWV9WSEXZI`dMdkQhqRco\
  R_lSVjSRgTMeTHbUD`U8YU4WT3UT3TS3SS3RR3QR3PQ3OQ3N\
  P2MP2LO2KO2JN2IN2HM2GM2FM2EN4FO6FO7FP9FQGFRIFSKF\
  SMFTOFUQFVSFVUFWWFXXFYZFY`FZbF_dF`fF`hFajFblFcnF\
  cqFbrJ`sO_tSYuXXv`VwdUxiSymUymVymXymZym`ylaylcyl\
  eylgylhzljzllzlnzlozlqzkszkuzkvzkxzkuzlrzmoznlzo\
  izofzpczq`zrXzsUztRzuOzvLzvIzwFzxCzyEzyGzyIzyKzy\
  MzxOzxQzxSzxEzz0zz0zz1zz1zz }

frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l }

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