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experimenta 3d julia sets

I made these three images when flying in the airplane from Belgium to Spain in summer 2006. It was an attempt to construct a more symmetrical equations for the iteration of 3D Julia sets. When working with complex numbers (or quaterinions), the iteration formula is quite elegant, but when implemented with real numbers (and that's what computers do), the equations become non-symmetrical. The imaginary parts all get some nice symmetric formulas, but the real part is always an exception. So, I created my own real valued symmetric 3d equations and computed the resulting Julia sets. The results are these (you can click the images to enlarge them):