Using Math equations to create Fractals in Blender

Question

I am trying to recreate something like a Julia spiral fractal in Blender. Where would I begin? I've searched some videos on YouTube and I see there's been some conversation on here about the topic but none of them seem to be achieving something like this. I know it's possible to create fractals with mathematical equations. This image was created with the equation:

fc, c = −0.8 + 0.156i

Is there a way to achieve it inside of Blender?

Edit: I know that we can use planes to create fractals in a 2D space. Is there any way to possibly generate a fractal in a 3D space? Something like a screw modifier?

Answer 1

yes this is possible. CGMatter made a nice tutorial about this. You can find the video here: https://www.youtube.com/watch?v=H8nHxRO7eX0

So all credits of this post go to CGMatter. This setup works in Blender 3.0

Important: Make sure you have Cycles as render engine enabled and CPU, GPU won't work since then you won't have that Open Shading Language checkbox.

This will look like this:

Here is the code as copy paste:

shader fractal(
float creal = 0,
float cimag = 0,
point position = P,
output color fractalcolor = 0
){
float real = position[0];
float imag = position[1];
for(float i = 0; i < 200; i++){
float realtemp = real;
real = real*real - imag*imag + creal;
imag = 2*realtemp*imag + cimag;
if(sqrt(real*real+imag*imag) > 4){
fractalcolor = i/200;
}
}
}