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Fractals like Mandelbrot or Julia have always been fascinating to me. I even implemented some of them during my school time. With the power of modern PCs, there are also 3D fractals possible like this:
For playing around, I am looking for
There is Mandelbulb.
I'm not very familiar with it yet, but here's an example created by me:
There are of course better examples online made by artists who are more familiar with it.
