[Fractint] FOTD 02-06-03 (Burbles [7])

2 Jun 2003

      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 20.0 PAR-FORMULA 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 20.0 PAR-FORMULA FILE==================================