;     Date: Sat, 28 Dec 2002 09:12:33 -0500
;     From: Jim Muth <jamth@mindspring.com>
;  Subject: [Fractint] FOTD 28-12-02 (Cascade of Bubbles [9])
;       Id: <1.5.4.16.20021228091505.0d67da08@pop.mindspring.com>
; ---------
; FOTD -- December 28, 2002 (Rating 9)
; 
; Fractal visionaries and enthusiasts:
; 
; Somehow, I once again survived the first and biggest of the two 
; seasonal holidays.  (Is it politically correct to use the word 
; 'Christmas'?)  The tree was lovely, the turkey dinner delicious, 
; the presents were exchanged peacefully, the conversation was not 
; controversial, and most importantly, the fractal cats concealed 
; their bad moods.  All this pleasantness left me in a highly-
; charged fractal-finding mode.  (Fractals are really not hard to 
; find.)  The fractal I found appears as today's FOTD image.
; 
; The formula I used is an old one, which has been lying dormant 
; for many years and which for some forgotten reason I had named 
; 'cascade'.  As is the case with most of these old formulae, I 
; have totally forgotten what it was originally intended to do.  
; (Why do I neglect to add comments?)  The formula appears to have 
; some vague relation to the mysterious 'Ikenaga' function, though 
; I wrote it at least one year before I began working with the 
; 'Ikenaga' function.
; 
; The image that I found, with its rating of a very impressive 9, 
; is one of the best of the year.  Like so many works of art that 
; unfold in time, the 2002 series of FOTD images has reached its 
; peak near its end.
; 
; I named the image "Cascade of Bubbles".  I chose this name when 
; I noticed that the bof60 bubbles appear to be cascading down 
; into the depths of the picture.  This cascading effect might be 
; what inspired the original name of the formula, which, unlike 
; most of my formulae, has no variable parameters.  There are as 
; many holly leaves as bubbles in the image, all cascading 
; downward, but bubbles are more poetic, so I chose the bubbles.
; 
; The image renders in exactly 4 minutes on my machine, accurate 
; to 1/100 of a second.  There is nothing unusual in this time.  
; It is simply a coincidence.  After all, a time of exactly 4 
; minutes has just as much chance of coming up as a time such as 
; 0:04:16.37.
; 
; The 4-minute render-time wait can be cut by more than half by 
; downloading the finished GIF image from Paul's web site at:
; 
;           <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
; 
; or from Scott's site at:
; 
;           <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>
; 
; It was a cold week here at Fractal Central, with 4 inches of 
; snow on Christmas day giving the first white Christmas in 33 
; years.  Needless to say, the dynamic duo of fractal cats 
; disapproved of such conditions and needed several treats of 
; left-over turkey to soothe their ruffled tempers.
; 
; As for me, I somehow have managed to get almost all the work 
; caught up, and find myself with little to do but search for the 
; next fractal, which will appear in 24 hours.  It will be hard to 
; find one that equals or exceeds today's image, but I'll try.  
; Check tomorrow to see if I succeed.  Until then, take care and 
; relax.
; 
; 
; Jim Muth
; jamth@mindspring.com
; jimmuth@aol.com
; 
; 
; START PARAMETER FILE================================

Cascade_of_Bubbles { ; time=0:04:00.00--SF5 on a P200
  reset=1950 type=formula formulafile=jim.frm
  formulaname=cascade passes=1 center-mag=+0.2605319\
  14765418/+0.9301176063963406/890.8654/1/162.5/-3.6\
  0000224075562869e-012 float=y maxiter=250
  bailout=100 inside=bof60 logmap=yes periodicity=0
  colors=000zzzzmmwcUqX0mTHkPOjLMiJLhHKgFIfDHeBGd9Fc\
  7Db5C`3BZ4CX5CU5DR6DO6EJ7EJ7EUUtUUtUUoUUoqaapaaoba\
  obanbambalcakcajcajcaidahdaafZUpVNtSFoO8nL8nN8nQzq\
  SpnVmnXdn_anabmdamfcmiclkckndjpehsgftidzkbzn`zqZzu\
  QztCprEhpGbnHSkJViLXgN_ePacQdaSf_UiYWkVYnTZpR`sPbu\
  U_nZWgbT_gPTlMMjPMhSMfVMdYLb`L`cL_fLYhLWkLUnLSqKQt\
  KOwKMzKKxLJuMHsMGqNEnOClPBjP9hQ7eR6cS4aS3ZT1XU4ZS6\
  `R9bPBdOEfMGhKJkJLmHOoFQqETsCVuBYw9_y8`t9ap9bl9chA\
  ddAe`AfXAgTAhPAiLBjHBkDBk9BnKJqVRtdYrdVpeSnePlfMkf\
  JifFggCeg9ch6ah3`h0Zj3Yl6Xm9VoBUpETrHSsKQuMPvP7hh6\
  ce5Zb4U_3PX2KU1FR3WP5mMt8jbFeLN_LUaL_bLfdLleLsgMzi\
  KveIraFnXDjTAfP8bK5ZG9aICcLGfNMTRSEVY0ZZ1Z`2Ya4Yb5\
  Yd6Xe7Xa8VY9TUAQRCONDMJEKFFHBGFDJDENCGQAIT8JW6L_5M\
  b3Oe1Ri9TmGWqOYuV`ybXuaUp_QlZMhYIcWF_VBVT7RS7SO6TK\
  6UH5VD5W9Cz5gOjjadhKolUnocmsmleLpeWqdfrdqsiAhn9`_J\
  nUSkN`iHiffPrgctirwb9o_8n }

frm:cascade {; Jim Muth
z=c=pixel:
a=sqr(z)+(c-1)*z-c
b=3*sqr(z)+c-1
z=z-2*a/b,
.000000000000000000000000000001 <= |a| }

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