;     Date: Mon, 07 Oct 2002 10:39:12 -0400
;     From: Jim Muth <jamth@mindspring.com>
;  Subject: [Fractint] FOTD 07-10-02 (Monarch Butterfractal [5])
;       Id: <1.5.4.16.20021007104039.2a0f94ae@pop.mindspring.com>
; ---------
; FOTD -- October 07, 2002 (Rating 5)
; 
; Fractal visionaries and enthusiasts:
; 
; To produce today's fractal, I took Z^(-1.25) and subtracted 
; Z^(-2.75) from it before adding 1/C.  With the bailout radius 
; set to 210, this formula draws a parent fractal with a spade-
; shaped bay whose point faces east.  Though the bay is filled 
; with various forms of fractal debris, little of interest lies 
; in this debris.  Today's scene is located just north of the 
; eastern point of the parent fractal, where two lacy arms 
; converge.
; 
; When I saw the image, I was reminded of a monarch butterfly 
; that I had noticed fluttering in the garden earlier in the day.  
; I immediately named the picture "Monarch Butterfractal", and 
; then rated the image an average 5.
; 
; Like fractals, those butterflies have long been a puzzle to me.  
; They appear every year in late summer and autumn, fluttering 
; around the flowers, storing energy for their migration to the 
; recently-discovered remote mountain valley in Mexico, where they 
; spend the winter in a state of torpor.  But how does a single 
; butterfly survive a journey of nearly 5,000 kilometers?  Not 
; even considering the hazards along the way, the time needed to 
; complete such a journey would far exceed the life span of a 
; single butterfly.
; 
; Perhaps the butterflies make the trip in the same manner 
; humanity is supposed to explore interstellar space.  The 
; individuals who arrive at the destination are the remote 
; descendants of those who set out on the journey.  Or maybe the 
; whole monarch migration story is as much a myth as the idea that 
; humanity one day actually will reach the distant stars.
; 
; Forgetting butterflies and space exploration, perhaps the best 
; feature of today's image is its lightning speed.  It renders in 
; less than one minute on my tired old machine, even in single-
; pass mode.  And as always, the completed image is available on 
; Paul's web site at:
; 
;           <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
; 
; and on Scott's site at:
; 
;           <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>
; 
; And despite recent speculation on another list, Paul is quite 
; alive and active.
; 
; The fractal weather Sunday here at Fractal Central was crisp and 
; fall-like, with deep blue skies and a temperature of 72F 22C.  
; The cats enjoyed the day lazing all afternoon in the sun on the 
; porch.  Unfortunately, with the sun's angle growing lower every 
; day, the holly trees are beginning to cast their shade onto the 
; porch, and soon the cats will have no sun to bask in during the 
; afternoons.
; 
; Right now, I've got to get busy on a convention program which is 
; a big rush.  But then convention programs are usually rush jobs. 
; Well, the best way I know to eliminate the rush is to get busy.  
; Until next time in 24 hours, take care, and before a problem can 
; be solved, it must be understood.
; 
; 
; Jim Muth
; jamth@mindspring.com
; 
; 
; START PARAMETER FILE================================

MonarchButtrfractl { ; time=0:00:48.61--SF5 on a P200
  reset=2002 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=2.70058/0.0691111/58.96007/1/-120/-5.05\
  012698326368081e-014 params=1/-1.25/-1/-2.75/0/110
  float=y maxiter=270 inside=0 logmap=11 periodicity=9
  colors=000RIVNETJARF6PB2NPEWaQcn`kjV_fPOcKDkXAwi8z\
  v6wo5rh4mb3hW2cP1ZJ1WE7e9Co4Hx0MNxrLupJrnHolFlkDii\
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  p3zo4zn5zm5zmBzeGzZMzRRzKIzM9zO1zQEzXRzbbzh4zU7zaA\
  ziDzqGzxJzsLznNziPzdSzgUzjWzljzrxzwnzsdzoVzkLzgQza\
  UzXYzSbzNfzIjzDnz8izJdzU`zccz`fzZizXkzVnzTqzRtzPvz\
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  czS`zSYzRVzRSzRPzRQzYQzdRzkRzrRzxTznUzdVzWHzg4zr6z\
  i8z`AzSCzJEzAGz1Fz2Ez2Dz2Dz2mzqfzr_zsTzsMztFzu8zuG\
  ztOzsWzsczrkzqszqvzsyztJzALzEMzINzMOzQQzURzYSzaTze\
  dzQozBgzI`zPTzVMzaEzh7znMz``zNoz9jzBezCazDXzFTzGOz\
  HKzIhzVizWjzXkzYkzYfz`VzX }

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==================================
; 
;