I've been trying to figure out how to make a Mandelbulb in Processing for a while and have somewhat given up on google explanations (they usually assume you are using a program someone else wrote to explore the fractal). If you are not familiar with a Mandelbulb here is an image and brief explanation:

and it is a 3D generalization / analogue of the more well known Mandelbrot fractal:

I have two main questions about this:

1. How would I go about making a 3D shape like this? This is fairly easy conceptually speaking for a Mandelbrot (2D version) in the sense that I just use pixels[] to represent what I want to see. The Mandelbrot set uses what is called the complex plane which plots real numbers on the x axis and imaginary numbers on the y axis. For each pixel, the pixel's coordinates in relation to the complex plane are passed through an iterated equation. After some condition is met this iterated equation is escaped (break;) and I end up with a number I can convert and send to pixels[]. Because the Mandelbulb is 3D I would imagine using pixels[] would not make sense. Do I have to create a point cloud and somehow generate triangles to match the information?

2. Another question google did not seem to find the answer to was what the axes (plural of axis) of the Mandelbulb correspond to (I realize this is not a Processing question but I'm hoping someone knows). The Mandelbrot exists on a plane where x values are real numbers and y values are imaginary numbers. Since the Mandelbulb is 3D it would have a x, y, and z value which conceptually does not really make sense to me.

I will keep googling but any help would be greatly appreciated

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