;     Date: Thu, 19 Dec 2002 09:45:11 -0500
;     From: Jim Muth <jamth@mindspring.com>
;  Subject: [Fractint] FOTD 19-12-02 (Corrected Super-Bridges [5])
;       Id: <1.5.4.16.20021219094736.0d97113e@pop.mindspring.com>
; ---------
; FOTD -- December 19, 2002 (Rating 5)
; 
; Fractal visionaries and enthusiasts:
; 
; This is a corrected version of the already-posted FOTD.  I 
; inadvertently left the semicolon out of the comment line of 
; the formula in the first version.
; 
; A few days ago, Tim posted a question about three-part numbers, 
; or triternions.  Shortly thereafter, Morgan posted a basic 
; formula that draws the triternion Mandelbrot set, which, as 
; drawn by the formula, consists of a skewed M-set with its 
; northern part chopped off.  When I ran the formula, I was 
; expecting a somewhat different figure, but I'll take whatever 
; the numbers give.  (Maybe several varieties of three-part 
; numbers are possible, and one of the other varieties would draw 
; a different M-set.)
; 
; Adding a few simple variable parameters to the formula, and 
; giving it a new name, I did a little experimenting, and found 
; that the triternion M-set behaves much like the hypercomplex 
; set.  It seems to consist of overlapping M-sets with straight 
; 'bridges' added.  Unlike the bridges in the odd planes of the 
; Z^2+C Julibrot, which consist of stretched elements and can be 
; unstretched into recognizable figures, the bridges in the 
; triternion set consist of truly one-dimensional elements, which 
; no amount of stretching will make into recognizable figures.
; 
; In the triternion set, as in the hypercomplex set, different 
; elements often overlap, and when this happens, the element with 
; the lowest iteration count will prevail.  Today's image shows 
; triternion bridges overlapping conventional M-set elements, 
; with a Minibrot on the left and a spiral on the right.  The 
; resulting interplay produces some interesting 3-D effects, 
; especially around the spiral.
; 
; I named the image "Super-Bridges" on a whim.  Not knowing quite 
; what to make of the image, I rated it at an average 5.
; 
; Regardless of the rating, the image is a fast one, requiring 
; only 2 minutes to render from the attached parameter file
; 
; The image can also be seen by downloading it from:
; 
;           <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
; 
; or from:
; 
;           <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>
; 
; Partly cloudy skies on Wednesday could not make up for a raw 
; east wind and a temperature that barely rose above freezing.  
; The fractal cat Tippy expressed his displeasure by sulking.  
; Thomas was too busy sleeping by the heat.
; 
; And if I don't soon get busy, a few customers will be sulking.  
; So until next time, which will arrive on schedule in 24 hours, 
; take care, and keep careful watch for the spirit of the season.
; 
; 
; Jim Muth
; jamth@mindspring.com
; jimmuth@aol.com
; 
; 
; START PARAMETER FILE================================

Super-Bridges { ; time=0:02:16.99--SF5 on a P200
  reset=2002 type=formula formulafile=test.frm
  formulaname=triternion passes=1 center-mag=-0.8647\
  1861343083230/-0.33029117615557820/1220.083/1.6718\
  /-135.15/1.65891648238705725 params=0/-0.07/0/-0.2\
  3/0/0.14 float=y maxiter=475 inside=255 logmap=39
  colors=0A0EADEADD9CC9BC8BB8AA79A79C6BB6DK6FN6HP6JR\
  6LT6NV6PW5QX5SY5UZ5W_5Y`5_a5ab5bc5cb7b`8`ZAZXBXVCV\
  SETQFROGPMINKJLHLJFMHDNFBOD9PB8QB7RA6QA6PA5OA5NA4M\
  A4LA3KA3JA5MC6OD7RF8TG9WIAYJB`LDbMEeOFgPGjRHlSIoUJ\
  qVHmTFiREfPCbNB_L9WJ8TH6PF5MD3IB1D72F93GA4IC5JD6LE\
  6MG7OH8PI9RKASLAUNBVOCXPDYRE_SG`TE`TDN8CMDBLIAKN9J\
  S8IX7Ha6Gf5Fk4Ep3Du2Dy5Bv79tA8rC6pF4nH3lLCjPKiTShW\
  _g_gfcoemzbfwd_tfTqhMnjFkl8hn2fo2fo2fo4gm6gl8gkAgj\
  CghEggGgfIgeKgcMgbOgaQg`Sg_UgYWgXYgW_cVagTcgSegRgg\
  QhgPgeRgcTgcVfbXfaYf__eZaeYceXeeWfdUgdTgcShcRhbQhb\
  PiaOiaNi`Mj`Lj`Kj_Jk_IkZHkZGlYFlYElXDmXCmXBmWAnW9n\
  V8nV7oU6oU5oT4pT3pU0oT2pT3pT5pS6pS8qS9qRAqRCqRDrRF\
  rQGrQHrQJsPKsPMsPNsOOtOQtORtOTtNUuNVuNXuMYuM_vM`vL\
  avLcvLdwLfwKgwKhwKjxJkxJmxJnxJoxabatQFsRGsRGrSGrSH\
  rSHqTHqTIqUIpUIpUIoVJoVJoWJnWKnWKnXKmXKmYLlYLlYLlZ\
  MkZMk_Mk_Mj_Nj`NkaFlbFzzz }

frm:triternion { ; adapted from Morgan Owens' formula
c1=real(pixel)+(p1),
c2=imag(pixel)+(p2),
c3=(p3),z1=z2=z3=0:
nz1=z1*z1+z2*z3+z3*z2+c1
nz2=z1*z2+z2*z1+z3*z3+c2
nz3=z1*z3+z2*z2+z3*z1+c3
z1=nz1,z2=nz2,z3=nz3
z=nz1+flip(nz2)
|z-pixel|<100 }

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