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Convergent Julia Renderz^z+c smoothed with paramsz^z+c zoom
z^z+c smoothed with params
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Description: z^z+c smoothed with params

Bailout 256

As is obvious the z^z+c is very similiar in style to the exponential types e.g. exp(z)+c.

The detail only shows when the bailout is large enough - i.e. the proof that if the magnitude sqrt(x^2+y^2)  exceeds 2 then the point is outside *is only valid* for the standard Mandelbrot form i.e. either just z^2+c or maybe z^p+c or possibly any "plain" polynomial form - and certainly not true when one starts using more complicated functions.

However using the "auto-power" method to calculate the divergence at bailout it's still possible to get smooth iteration colouring - and of course a smooth iteration fraction.

Params for this image:

Code:

Fractal1 {
fractal:
  title="Fractal1" width=928 height=696 layers=1
  credits="Dave Makin;6/12/2012;D J Makin;12/20/2011;Dave Makin;10/5/2\
  011;David Makin;6/15/2008;Frederik Slijkerman;7/23/2002"
layer:
  caption="Layer 1" opacity=100 method=multipass
mapping:
  center=1.5/0 magn=0.8
formula:
  maxiter=1000 percheck=off filename="Standard.ufm" entry="Mandelbrot"
  p_start=0/0 p_xmod=2.0 p_ymod=2.0 p_power=2/0 p_bailout=256
inside:
  transfer=none
outside:
  density=300 transfer=cuberoot filename="mmf3.ucl"
  entry="MMF3f-ExtCilia" p_method="Standard Div." p_bailout=256
  p_dauto=yes p_power=2/0 p_usedfudge=no p_fudge=1.0 p_fudge1=1.0
  p_ciliamode="Just iteration" p_split=2.0 p_olditer=No p_iterval=0.0
  p_iterweight=50.0 p_logiter=Ident p_skew=0.0 p_rot=0.0 p_fixrot=no
  p_rpwr=5.0 p_fixskew=no p_smallbail=1E-5 p_cauto=yes p_cpower=2/0
  p_usecfudge=no p_fudgec=1.0 p_fudge1c=1.0 p_cfixed=no
  p_cfixedval=1/0 p_cciliamode=Sawtooth p_csplit=2.0 p_fixconv=yes
  p_colditer="1 older" p_citerval=0.0 p_iterweightc=50.0
  p_logiterc=Ident p_cskew=0.0 p_crot=0.0 p_cfixrot=no p_crpwr=5.0
  p_cfixskew=no p_convoffset=0.0 p_zbasin=Off p_zscale=0.1 p_ip=1.0
gradient:
  smooth=yes rotation=1 index=77 color=6588220 index=156
  color=13331306 index=238 color=16777197 index=357 color=6662911
opacity:
  smooth=no index=0 opacity=255
}

Stats:
Total Favorities: 0 View Who Favorited
Filesize: 125.09kB
Height: 696 Width: 928
Keywords: z^z smooth colouring 
Posted by: David Makin June 12, 2012, 11:49:03 AM

Rating: *** by 1 members.

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