Continuous Conformal Mandelbrots

[fractalrebel]

Last one for tonight. This is a rotation of the Conformal Julia with the Stone Face. In this case we get a Cathedral.

[kram1032]

wow, that stone face is creepy!
Great

A 3D-print anyone?

[fractalrebel]

I had to keep playing with these formulas. I added the inversion code to the Conformal code, set up options to do the Box, Rotate and Inversion operations in any order, and set up a loop so that the set of operations could be performed 1, 2, ... times per iteration (the default for Conformal is 2). I am still testing and tweaking the code, but this interesting image, which I call Courtyard Ruins popped out. It uses a loop count of 2 and an operation order of Rotate Box Invert.

[cKleinhuis]

i played around with the unity function

ORIGINAL FRACTINT CODE:

Code:

unity {
init:
  float ddelmin = 2 / (#magn * #width)
  float x = 0
  float y = 0
  float one = 0
  z = pixel
  
loop:
  x = real(z)
  y = imag(z)
  one = |z|
  y = (2 - one) * x
  x = (2 - one) * y
  z = x + flip(y)
  
bailout:
  (one <= 2.0) && (abs(one - 1) >= ddelmin)

default:
  title = "Unity"
  maxiter = 149
}

this is easily extendable to 3d:

length=length(triplex)
triplex.x=(2-length)*triplex.z
triplex.y=(2-length)*triplex.x
triplex.z=(2-length)*triplex.y

normal bailout/iteration method as in standard mandelbrot

have not rendered it yet, just examined 2d slices of it :

[Timeroot]

Tglad, that wouldn't give quite the same thing, since |z| here doesn't mean length(), but rather length()^2. Did you remember to include this fact when drawing it?

[cKleinhuis]

oh, no, have to correct it
i always mix it, i have adjusted the formula and rendered some more slices

it isa surely not as interesting as the amazing fractal, but it could make a nice seashell object

[ericruijun]

What Software do you use when making those?. I tried lots of softwares, but they all suck