perhaps a formula worth to implement in 3d ?

[cKleinhuis]

a friend of mine asked me if i could visualise a formula for him:

1. start with a complex ( or triplex ) number

2 if Re(z) not in [-1/2, 1/2] add a int number to bring it back in range

3 if |z| < 1, then z =-1/z  and continue with 1. otherwise end

it terminates always


ultrafractal snippet:

Code:

init:
  z = #pixel
loop:
 complex newz=z;
if |newz| <1
   newz=-1/newz
endif
if real(newz)<-0.5  || real(newz)>0.5
  newz =   real(newz)-floor(real(newz))   +imag(newz)
endif
; y achse
if imag(newz)<-0.5  || imag(newz)>0.5
  newz =   real(newz)  +imag(newz)-floor(imag(newz))
endif
  z = newz
bailout:
   z> @bailout

and some images attached, first 2 are with x/y applied ( as in above snippet ) the later 2 are the algorithm applied just to x axis

[DarkBeam]

Discontinue functions are not quite a candy for raytracing, horrible results.