• April 14, 2021, 06:12:00 AM

Login with username, password and session length

Author Topic:  Zoomable square set  (Read 583 times)

0 Members and 1 Guest are viewing this topic.

Offline Alef

  • Fractal Fruit Salad
  • *****
  • Posts: 78
  • catalisator of fractals
    • My deviant art page
Zoomable square set
« 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 {
  title="Fractal2" width=640 height=480 layers=1
  caption="Background" opacity=100
  center=-0.5/0 magn=1
  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
  smooth=yes index=0 color=8716288 index=100 color=16121855 index=200
  color=46591 index=300 color=156
  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.

Linkback: https://fractalforums.org/index.php?topic=2653.0
catalisator of fractals

Offline claude

  • 3f
  • ******
  • Posts: 1829
    • mathr.co.uk
Re: Zoomable square set
« 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).

Trees Revisited square version

Started by Dinkydau on Fractal Image Gallery

0 Replies
Last post November 03, 2017, 11:49:38 AM
by Dinkydau
RSS feed item title contains HTML escape code instead of close square bracket

Started by claude on Discuss Fractalforums

2 Replies
Last post September 24, 2017, 05:22:35 PM
by Anon