;     Date: Tue, 08 Jun 2004 10:17:45 -0400
;     From: Jim Muth <jamth@mindspring.com>
;  Subject: [Fractint] FOTD 08-06-04 (Iterative Complexity [5])
;       Id: <1.5.4.16.20040608102139.0d2fdcbe@pop.mindspring.com>
; ---------
; 
; FOTD -- June 08, 2004 (Rating 5)
; 
; Fractal visionaries and enthusiasts:
; 
; This morning I was up early with my telescope and sun filter set 
; up in the east-facing attic window of F.C., ready to see the 
; final stages of the transit of Venus across the sun.  
; Unfortunately, fog was in the air at the time the sun rose, 
; obscuring the horizon.  As a result, I saw nothing.  When the 
; sun appeared 2-1/2 hours later, the event had long since ended.  
; Hopefully the luck will be better in 8 years, when the next 
; transit occurs.  If not, it's a wait of 122 years.  I guess I 
; shouldn't be too disappointed.  Those farther west saw nothing 
; at all.
; 
; Today's fractal was created by iterating the expression 
; Z^(2+0.1i) and examining a spurious valley of the resulting 
; chaotic fractal.  The scene is located near a larger midget in 
; the valley.  I named the image "Iterative Complexity" because I 
; could find so little order in it.
; 
; In the classic Mandelbrot set, the features are arranged around 
; the midgets in the series 2,4,8,16...  In the cubic Mandeloid 
; the features follow the series 3,9,27,81...  In Mandeloids of 
; fractional powers, the series follows the same rule.  Thus we 
; have 2.5, 6.25, 15.625, 39.0625...  But what series will a 
; Mandeloid with an imaginary component in its exponent follow?  
; Complex numbers are not counting numbers.
; 
; As today's image shows, the result is total chaos.  There is no 
; order at all in the features surrounding the central midget.  In 
; a way this makes things more interesting.  I rather enjoy an 
; 'anything can happen' fractal.
; 
; I didn't really know what kind of a rating to give to today's 
; image.  When in doubt, I always do the most likely thing, so I 
; ended up giving the image a rating of an average 5.  The render 
; time of close to an hour holds the overall value to a modest 9, 
; but this value can be drastically increased by visiting the FOTD 
; web site at:
; 
;        <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
; 
; and viewing the image there.  But before going to the web site, 
; give Paul a chance to render and post the image.
; 
; Monday was sunny and warm here at F.C., with a high temperature 
; of 81F 27C.  It was a perfect day to keep cats happy.  They 
; spent several hours in the yard, ignoring the cicadas, which 
; are again singing.  When evening arrived, they came indoors with 
; no complaint.  Today looks to be a repeat.  I expect a repeat in 
; the cats' mood also.
; 
; The work is moderate, which means about 4 hours effort will put 
; it behind me.  Then it's on to the world of fractals.  If I'm 
; lucky, tomorrow's fractal will be better than today's.  If not, 
; it will still be interesting.  Until next time, take care, and 
; hope for clear skies in 8 years.
; 
; 
; Jim Muth
; jamth@mindspring.com
; jimmuth@aol.com
; 
; 
; START PARAMETER FILE================================

IterativeComplexty { ; time=0:55:48.13--SF5 on a P200
  reset=2003 type=formula formulafile=allinone.frm
  formulaname=MandelbrotBC2 passes=1
  center-mag=-0.62142028795967830/-0.363045619197981\
  00/4.570629e+010/1/-7.5/-5.02629616519895128e-005
  params=2/0.1/0/0 float=y maxiter=18000
  inside=0 logmap=1430 periodicity=10
  colors=000bMsaNqaNp`On_OmZPlYQjXQiWRgWRfVReUScTSbS\
  T`RT_QTZQUXPUWOVUNVTMVSLWQKWPKXNJXMIXLHYJGYIFZGEZF\
  DYDEZEEZFFZGFZGFZHGZIGZIHZJHZKHZKIZLIZMJZMJZNJZOKZ\
  OKZPLZQLZQLZRMZSMZSMZTN_UN_UO_VO_WO_WP_XP_YQ_YQ_ZQ\
  __R__R_`S_aS_aS_bT_cT_cU_dU_eU_eV_fV_gV_gV_gTbiRdj\
  PfkNilLkmJmoHppFrqDtrCvsCuqCtpCsnCrmCqkCpjCohCnfCm\
  eClcCkbCj`Cj_CiYChWCgVCfTCeSCdQCcPCbNCaLC`KC_ICZHC\
  YFCYEHZIMZMRZQW_T`_Xe_`j`co`gt`ky`nx_nwZnvYnuXntWn\
  sVnsUnrTnqSnpRnoQnnPnnOnmNnlMnkLnjKniJniInhHngGnfF\
  neEndDndCncBnbAna9n`8n_7n_7nV8gR8aN8WJ8QE9JA9D6972\
  914A16B17C19C1BD1CE1EF1FF1HG1JH1KH1MI1OJ1PK1RK1SL1\
  UM1WM1XN1ZO1`P1aP1cQ1dR1fR1hS1iT1kU1mU1nV1pW1qW1pY\
  2pZFp_Io`LoaOobRncUndXne_mfbmgemihmjklknllqlmtknwk\
  ozkpzjqzjrzjszjtziszhszhszgszgszfrzfrzerzerzdrzcqz\
  crzbszbtzauzbvzcwzcxzcyzczzczzczzczzczzczzczzczzcz\
  zczzczzczzczzczzczzczzczz }

frm:MandelbrotBC2   { ; by several Fractint users
  e=p1, a=imag(p2)+100
  p=real(p2)+PI
  q=2*PI*floor(p/(2*PI))
  r=real(p2)-q
  Z=C=Pixel:
    Z=log(Z)
    IF(imag(Z)>r)
      Z=Z+flip(2*PI)
    ENDIF
    Z=exp(e*(Z+flip(q)))+C
  |Z|<a }

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