This week I learned how to animate fractals! Iāll briefly go into how I learned this. As for the construction of the initial, static Mandelbulb, there are fortunately a lot of great resources online that can help, and the equation for the Mandelbulb is fairly well known. What I really wanted to do, though, was to animate it, as I felt that it would be fascinating to see how the computer creates these structures in real time. This was more difficult to find. After looking around a bit, I found a comment that linked to a pretty old website that talked about adding an offset, or phase, to the equation, without specifying where exactly. For reference, this is the exact text I found.
ā{x,y,z}^n = r^n*{cos(phi)*cos(theta), cos(phi)*sin(theta), sin(phi)}
r=sqrt(x²+y²+z²), theta=n*atan2(y,x), phi=n*asin(z/r)+phase
where the phase varies continuously from goes from 0 to 2piā
After fixing this up so it worked in VEX (Houdiniās code language), I created the phase variable as a channel and specified that the value could only ever go between 0 and 2š, as specified in the text. This allows me to key animate on that channel or possibly even write a function so that I donāt have to go back into the wrangle node. Iām very excited about this as Iāve been wanting to use fractals for a while and now that itās actually possible to do, I can look into ways of further streamlining the process!