Metafractals

In multicomplex dynamics, the Tetrabrot is a 3D generalization of the Mandelbrot set. Discovered in 2000 (Fractals, 8(4):355-368), this 3D Fractal shape is a particular case of dynamics of two complex variables and can be interpreted as a 3D slice of the 8D tricomplex Mandelbrot set. The colors on the picture are generated in conformity with the generalized Fatou-Julia Theorem in multicomplex spaces. In particular, each color is related to the topology of the filled-in Julia set corresponding to the 3D point of the Tetrtabrot.