;     Date: Mon, 02 Jun 2003 10:27:47 -0400
;     From: Jim Muth <jamth@mindspring.com>
;  Subject: [Fractint] FOTD 02-06-03 (Burbles [7])
;       Id: <1.5.4.16.20030602102721.2aa7d23e@pop.mindspring.com>
; ---------
; 
; FOTD -- June 02, 2003 (Rating 7)
; 
; Fractal visionaries and enthusiasts:
; 
; The FOTD for June 2 once again takes advantage of the multi-
; valued nature of the complex log function.  The iterated expres-
; sion is a very simple Z^(1.5)+C.  The trick in the MandelbrotBC1 
; formula is that an unlimited number of different images can be 
; produced by the expression Z^(1.5), depending on which of the 
; infinity of returned log values are chosen.  The real(p2) 
; parameter of the formula makes the choice.
; 
; Today's image is part of the particular Z^(1.5) fractal that 
; results when the real(p2) parameter of the MandelbrotBC1 formula 
; is set to -31.  The amorphous thing at the center is a midget of 
; order 1.5.  I have no idea what the jagged-edged colored disks 
; surrounding the midget are.  I have never seen anything quite 
; like them.
; 
; I have named the picture "Burbles".  Those disks reminds me of 
; something bubbling.  The rating of a 7 seems correct for the 
; image, which has more math interest than artistic worth.
; 
; To see these truly unique fractal burbles, run the attached 
; parameter file and wait 5 minutes, or download the finished GIF 
; image from:
; 
;           <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
; 
; or from:
; 
;           <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>
; 
; Sunday started blustery and chilly here at Fractal Central, but 
; by afternoon, the sun appeared, the wind slacked off, and the 
; temperature rose to 66F 19C.  The cats had a good day.
; 
; This morning is starting much better.  The cats will likely have 
; another good day.  For me, it's several hours work before my day 
; will be good.  Until next time, take care, and keep blowing 
; those burbles.
; 
; 
; Jim Muth
; jamth@mindspring.com
; jimmuth@aol.com
; 
; 
; START PARAMETER FILE================================

Burbles { ; time=0:05:06.76--SF5 on a P200
  reset=2002 type=formula formulafile=allinone.frm
  formulaname=MandelbrotBC1 function=floor passes=1
  center-mag=+0.72523926124837650/+0.172183551614105\
  20/488923/1/-62.5/9.1405363139562823e-010
  params=1.5/0/-31/0 float=y maxiter=12000 inside=0
  logmap=105 symmetry=none periodicity=10
  colors=000GstKptNmuQkuThvXev_cwb`weYxiWxlTyoQyrOyo\
  NvmNskMpiMmgMjeLgcLdaLa_KZYKWWJTUJQSJNQIKOIHMIEOJG\
  QJISJJUJLVJMXJOZJQ`KRbKTcKUeKWgKYiKZkK`lKajRdhYgfd\
  jdkmbrp`xsYvrWtrUsqRqqPppNnpKmoIkoGjnDhnBgm9em6dl4\
  bl2al3bk3cj3di3ei4fh4gg4hf4hf5ie5jd5kc5lc6mb6na6o`\
  6o`5la5ia5fa5ca5`a5Yb5Vb5Sb5Pb5Mb9PcDSdGVeKYfN`gRc\
  hVfiYijalkdolhrmlunoxoszpvzpozahyNaw9aw9aw9aw9aw9b\
  vAbuBbuBctCctDcsDcsEdrFdrFdqGdqHepHepIepIeoJeoJfnK\
  fnLfmLfmMglNgkNgkOgjPhjPhiQhiQhhRihSigSigTifUjfUje\
  VjeWjdWkdXkcYkcYkbZla_la_l``m`am_am_bmZcnZcnYdnYen\
  XeoXfoWfoWgoVhpVhpUipUjpTjqSkqSlqRlqRmrQnrQnrPorPp\
  sOpsOqsNrsNrtMstMttLttLuuKvuKvuJwuJwsJwqKwoLwmMwkN\
  wiOwgPweQweRweSwfTwfTwgSwgSwgSwgSuhRwiRwiRwjQwjQwk\
  QwkQwkPwlPwlPwmOwmOwnOwnNwnNwoNwoNwpMwpMwqMwqLwrLw\
  rLwrLwsKwsKwtKwtJwuJwuJwvJxvJywJzwJzxJzxJzyJzyJzzJ\
  zzJzzJzzJzzJzzJzzJzzJzzJz }

frm:MandelbrotBC1   { ; by several Fractint users
  e=p1, a=imag(p2)+100
  p=real(p2)+PI
  q=2*PI*fn1(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==================================
;