You may track the line between this point and a light to check if it's shadowed, or try to compute normal for lighting (there are no typical normals in fractals but you may try to fake it). This means it's not enough to compute some iterations to get the result for current pixel - you may need to do this a lot of times, for every tested point along the ray, and this makes your computations a lot slower.īasically, when you've found the first point that meets your condition and have an iterations count for this point you could color it the same way as in 2D case, but the 3D space gives you more options. You do your iterations for this 3D point, but if you don't meet the condition you advance your point by a small step and recompute everything for this new point. You start with some pixel but now you compute the 3D ray from your eyes to that pixel and pick some starting point close to you (like a near clipping plane). In 3D case most of the computations are the same, just a lot more of them. One thing to notice here is that when you start computing some pixel then after some iterations you'll end up with a result for that pixel - this will be different in 3D case. You may also cycle those colors to fake animation. You may use gradients, bands, grayscale or whatever you want. Having all of this computed for every pixel you map your iterations number to colors, most often I saw the outside painted as black and iterations count mapped to some custom color. If the condition was never met you assume that current pixel is outside of a fractal, if the condition was met you store the iteration count needed to do so. Your numbers may never meet this condition so you add some global counter, let's say 100 iterations per pixel - if it doesn't meet the condition after 100 iterations you assume it never will and stop. If it doesn't you reiterate again, and again. When computing a general (2D) fractal you pick some pixel coordinates and transform them with a function, like = somefunc(x,y) and check if the result meets some condition. But first lets see how you can do a 2D fractal: I don't know the exact math but I do know how you can get from 2D fractal to 3D one.
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