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:

`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.

Linkback: https://fractalforums.org/fractal-mathematics-and-new-theories/28/zoomable-square-set/2653/