[Fractint] FOTD 01-06-03 (Curlers [5])

1 Jun 2003

      FOTD -- June 01, 2003 (Rating 5)

Fractal visionaries and enthusiasts:

We've been talking about multi-valued functions a lot lately, so 
here's a formula and an image that takes advantage of multiple 
values.  It's not a new formula; I have posted many FOTD images 
created by it in the past.  But it gives an example that good 
things can sometimes come from fractured fractals.

The formula being iterated is Z^(1.06)+C, a formula that 
normally would produce nothing but a tiny featureless dot in the 
center of the screen.  (Change the real (p2) parameter to pi to 
see this dot.) But thanks to those multiple values and today's 
formula, which takes advantage of them, the tiny dot has been 
transformed into an immense cigar with many fields of chaos 
around its edges.  Today's scene is a blow-up of the edge of one 
of those fields of chaos.

I have named the image "Curlers" because of the many loops that 
fill it.  Not really impressed with the image, I have rated it 
at only a 5.

The render time of 1/2 hour is almost entirely expended on the 
top inch or so of the image, so don't be concerned when nothing 
much happens for a while.  Those who prefer not to wait the 1/2 
hour can download the finished image from:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

or from:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

Rain fell off and on all day Saturday here at Fractal Central, 
while the temperature reached 73F 23C.  A thunder-shower at 6pm 
climaxed the day's events as well as the cats' dis-satisfaction. 
Needless to say, a good treat of tuna was needed.

Today is starting cloudy, windy and chilly, with occasional 
bursts of light rain -- not a good sign for fractal cats.  For 
me, it's a sign I might not be able to trim the grass, but may 
have to go along on a shopping trip.  Until next time, take 
care, and don't get broken up over fractured fractals.

Jim Muth
jamth@mindspring.com
jimmuth@aol.com

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

Curlers            { ; time=0:38:53.19--SF5 on a P200
  reset=2002 type=formula formulafile=allinone.frm
  formulaname=MandelbrotBC1 function=floor passes=1
  center-mag=-6.07363/12.6745/0.4719481/1/72.5/-1.23\
  3735336114705e-014 params=1.06/0/121.2/3000 float=y
  maxiter=4200 inside=0 symmetry=none periodicity=10
  colors=0007EXCCZHB`M9bR7dW6f`4hd3je7feAceE`eHYfLVf\
  OSfSPfVLfZIgaFgeCgh9gl6go3dl5bi6`f8Zc9W`BUYCSVEQSF\
  NPHLMIJJKHGLFDMHHPJKSLNVMQXOT_QWbRZdTagVdjWglXgmYf\
  mxSuxRvsSsoSpjTmfTjaUhYUeTVbPV_KWXGWVFYQF_ME`IEbDD\
  c9De5Df1Fc5Ga9H_DIXHJVLKTPLRTMOXNM`OKdPHhQFlRDpSBs\
  PAnM9iJ8dH7_E6VB5Q94L63G32B116D3NP5c`7tZ8qY9oXAmWB\
  kVCiUDgTEeSFcRGaQH_PIYOJWNJUPMTQPSSRSTURUWRWZQX`QZ\
  cP_eP`hObjOcmNdoNbmMalL`jKZiJYhIXfHWeGUcFTbESaDR_C\
  PZBOXANW9MV9OXBPZDQ`ERaGScIUeJVgLWhNXjOYlQZmR_kP`i\
  OagNbeMccLdaKd_JeZLeYNfXPfWRgVThUVhTXiSZiR`jQbkPdk\
  OflNhlMj`VqQcxSerUflWgfYi`ZjW`kQbmKdnEeo9`n8Wn7Sn6\
  Nn5In4En39n24n10n09j4Ig8QdCOeAMf9Kg7Ig6Gh5Ei3Cj2Bj\
  1bl6hn9moCrqFwrItnJrkKphKmdLkaLiZMfVNdSNbPO_LOYIPW\
  FQTBQR8RP5RKGPFRNBaL6lJ2wI4wJ6wJ7wK9wKBwKCwLEwLFwL\
  EvNEuOEtPDsRDrSDqTCpVCoWCnXBmZBl_Bk`AjbAicAhdAheDk\
  cGmbJoaMq_PsZSuYVwX4IT2GU }

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==================================