;     Date: Sat, 18 Jan 2003 11:17:11 -0500
;     From: Jim Muth <jamth@mindspring.com>
;  Subject: [Fractint] FOTD 18-01-03 (Rising mandelbrot [6])
;       Id: <1.5.4.16.20030118112001.0dd75c10@pop.mindspring.com>
; ---------
; FOTD -- January 18, 2003 (Rating 6)
; 
; Fractal visionaries and enthusiasts:
; 
; A formula that draws the 3-D triternion Mandelbrot set was 
; posted yesterday to the Fractint list by Russell Walsmith.  As 
; posted, the formula draws slices in the XY orientation of the 
; 3-D M-set.  After seeing what the formula would do, and being 
; unable to resist experimentation, I made a slight modification 
; to it.  I flipped the value of initial c1 from real to 
; imaginary, and named the modified formula TMan1.  The change 
; enables the formula to draw what I assume is the YZ orientation. 
; Of course, it could be the XZ orientation, or something in 
; between.  I have no idea how triternions work.
; 
; But regardless of the orientation, the revised formula draws 
; slices with intact midgets.  Many of these midgets duplicate 
; scenes in the classic M-set, but some midgets are entirely 
; different, doing strange things even while we watch.  Today's 
; image illustrates one of these new and unusual midgets.
; 
; The midget (or half-midget) appears to be rising above a horizon 
; that consists of part of another, larger midget.  The fragment 
; of a larger midget is stretched, most likely because the larger 
; midget lies in a different plane.  In the 2-D M-set, midgets are 
; oriented in every possible direction. I assume the same thing 
; happens with an even greater degree of freedom in the 3-D M-set. 
; Overlapping features such as those pictured in today's scene are 
; common in the hypercomplex M-set, but I have never seen both 
; stretched and unstretched Mandelbrot features overlapping.
; 
; I need to do much more experimenting with this three-dimensional 
; Mandelbrot set.  For now however, I'll settle for a FOTD image 
; that rates a 6.  The rating reflects the mathematical worth of 
; the image.  The artistic worth barely rates a 4.
; 
; The name "Rising Mandelbrot" was inspired by the impression of 
; one Mandelbrot midget rising above the horizon-like edge of 
; another.  The render time of 10 minutes can be avoided by down-
; loading the completed GIF image from:
; 
;           <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
; 
; or from:
; 
;           <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>
; 
; The fractal weather was cold here at Fractal Central on Friday.  
; With a temperature of 25F -4C, brisk winds, and occasional 
; showers of snow waiting for them, the cats didn't even think of 
; going out.  They were quite contented lying by their radiators.  
; Today is even colder, (the 8am temperature was 7F -14C), so 
; they will be housebound for at least another day.
; 
; As for me, I've got a bit of work to wrap up, then a day with 
; little to do but wander through FractalLand.  If I find anything 
; worthwhile, it will appear as tomorrow's FOTD.  Until then, take 
; care, and when the going gets tough, get a fractal going.
; 
; 
; Jim Muth
; jamth@mindspring.com
; jimmuth@aol.com
; 
; 
; START PARAMETER FILE================================

Rising_Mandelbrot { ; time=0:10:14.45--SF5 on a P200
  reset=2002 type=formula formulafile=triter.frm
  formulaname=TMan1 center-mag=-0.33019260452431920/\
  +0.53369254258170410/2256.431/3.3373/149.75/-15.93\
  32167459564502 params=-0.4/0 float=y maxiter=18000
  inside=0 logmap=94 periodicity=10
  colors=000UKATKASKARKAQKAPKAOKANKAMKBLJCKKDJKEIKGH\
  KHGLIFLKELLDLNCMODMPDMREMSFNUGNVHNWINYJOZKO`LOaMOb\
  NPdNPeOPgPPhQQiRQkSQlTQnURoVRpWRrXRsXRtWSsWSsWSsWT\
  sWTsWTsWTsWUsVUsVUsVVsVVsVVsVVsVWsVWsUWsUWsUXsUXsU\
  XrUYrUYrUYrTYrTZrTZrTZrTZrT_rT_rT_rS`rS`rS`rS`rSar\
  SarSarVbvTatSarR`pQ`nP_lO_jN_hMZfLZdKYbJY`IYZHXXGX\
  VFWUEWSDVQCVOBVMAUK9UI8TG7TE6TC5SA4S83R62R41R33Q55\
  Q77P89PAAOBCODENFGNGHMIJMJLLLNLMOLOQKQSKRUJTWJUXIW\
  ZIX`HZbH`cGaeGcgFdiFflDhjFgiGfhHegIdfJcdKbcLabM`aO\
  _`PZZQYYRXXSXWTWVUVTVUSWTRYSQZRP_QN`PMaOLbNKcMJdLH\
  dKIeLIeLJeLJeMKeMKfMKfMLfNLfNMfNMfNMgONgONgOOgPOgP\
  OhPPhPPhQQhQQhQUfPQhQNiRJjRGkSCmT9nT2oU4qS6pT8pUAp\
  VCpVEpWGpXIpYKp_MpaOpcQpeSpgUpiWpjYpk_plapmcpnepog\
  pphpqiprjpskptlpumpvmpwmpxmpympzmpzmpzmpzmpzmpzmpz\
  mpzmpzmpzmozmozmozmozmozmozmnzmnzmnzmnzmnzmnzmmzmm\
  zmmzmmzmmzmmzmlzmlzmlzmlz }

frm:TMan1 {
c1=flip(real(pixel)),c2=imag(pixel),c3=p1
z1=z2=z3=0:
t1=z1*z1+2*z2*z3
t2=z3*z3+2*z1*z2
t3=z2*z2+2*z3*z1
z1=t1+c1,z2=t2-c2*c2,z3=t3+c3
z=z1+z2+z3
|z| < 8 }

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