Zoomable square set

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Offline Alef

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« on: February 27, 2019, 05:07:06 PM »
This is nothing new. But I think it hadn't recieved deserved attention.

Pure split complex mandelbrot (i*i=1 ; i<>1) is just solid square. With few modifications it becomes zoomable complex geometric figure just like mandelbrot set but mostly based on right angles and parabolas. 

Zuzubrot or Quadratic General formula. It need some better name than that.
x=abs( x*x+y*y +Cx )
y=abs( 2*x*y   +Cy )

With starting seed of (0.5,0) and bailout >= 50.

Ultra fractal parameter:
Code: [Select]
UF_Basic {
fractal:
  title="Fractal2" width=640 height=480 layers=1
layer:
  caption="Background" opacity=100
mapping:
  center=-0.5/0 magn=1
formula:
  maxiter=250 percheck=off filename="em.ufm" entry="Zuzubrot"
  p_settype=Mandelbrot p_switchsettype=Julia p_bailout=128
  p_inverted=no p_function=Abs p_talisfactor=0.4 p_julia=-1.6/0
  p_start=0.5/0 f_func_post=ident
inside:
  transfer=none
outside:
  transfer=linear
gradient:
  smooth=yes index=0 color=8716288 index=100 color=16121855 index=200
  color=46591 index=300 color=156
opacity:
  smooth=no index=0 opacity=255
}

This formula is pretty simple for Kalles Fractaler but it probably don't needs it's advanced capabilities.
No images just an artistic render.

catalisator of fractals

Offline claude

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« Reply #1 on: February 27, 2019, 10:32:50 PM »
I rendered a slightly different formula (abs before instead of after each step) in 'et', coloured by atom domains and distance estimation.
Code: [Select]
z := ((x^2+y^2) + i |2xy|) + cAuto-skew was used to unstretch the 3rd image.  Seed was 0+0i.

If you're happy with the modification of the formula (KF needs a +c at the outside), decide on a name and I can add it to the next KF release, even though deep zooming might not be so interesting (I didn't find mini-sets yet).


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