Metafractals

In multicomplex dynamics, the METATRONBROT is the 8D tricomplex generalization of the Mandelbrot set. Discovered by Vincent Garant-Pelletier & Dominic Rochon in 2009 (Fractals, 17(3):241-255), it can be interpreted as a particular case of dynamics of 4 complex variables.

Any principal 3D slice of the multicomplex Mandelbrot set is equivalent to at least one quadricomplex slice or directly to one of the 8 tricomplex principal slices up to an affine transformation. Hence, the tricomplex space is, in a way, optimal (https://arxiv.org/abs/1809.02020).

The name "Metatronbrot" refers to the 2D geometric shape of the so-called Metatron’s Cube of the Flower of Life, where the same three Platonic Solids (the cube, the tetrahedron & the octahedron) can be found with an orthogonal projection.