3Dfractals.com - Gallery 1

"The 8 Fantastic" by Guillaume Brouillette & Dominic Rochon, 2018. Illustration of the eight principal 3D slices of the Metatronbrot representing the equivalence classes in the tricomplex case.

2D Mandy vs 3D Mandy by Dominic Rochon, 2019. Deep zoom on a "3D Mandy" inside the Tetrabrot. A "3D Mandy" can be defined as a 3D Mandelbrot set inside the same 3D set. In multicomplex dynamics, the Tetrabrot is a 3D generalization of the Mandelbrot set. Discovered in 2000, this 3D Fractal shape can be interpreted as a 3D slice of the 8D tricomplex Mandelbrot set.

Deep zoom on a Tetrabrot "inside" the Tetrabrot with the MBE8D Software by Dominic Rochon, 2019. In multicomplex dynamics, the Tetrabrot is a 3D generalization of the Mandelbrot set. Discovered in 2000, this 3D Fractal shape can be interpreted as a 3D slice of the 8D tricomplex Mandelbrot set. The first "3DMandy" appears explicitly on page 84 of this Conference Document in 2006.

The Tetrabrot - Power 3. The Tetrabric is a principal 3D slice of the family of the Tricomplex Multibrots. The colors on the picture are generated in conformity with the generalized Fatou-Julia Theorem in multicomplex spaces. Each color is related with the topology of the filled-in Julia set corresponding to the 3D point of the Tetrabric.

THE METABROT (Pseudo-OCTAHEDRON with fractal corners) by André Vallières & Dominic Rochon, 2018. The Metabrot is a principal 3D slice of the Metatronbrot.

Tricomplex Dynamics - 8D Mandelbrot set by Dominic Rochon, 2018. Genealogical schematization of the METATRONBROT. In multicomplex dynamics, the Metatronbrot is the 8D tricomplex generalization of the Mandelbrot set. 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.

Illustration of the principal 3D slices related to the biduplex, bicomplex and tricomplex Mandelbrot set.

The Tetrabrot with the hyperbolic bifurcation diagram by Raphaël Gervais Lavoie, Samuel Lemay and Dominic Rochon.

Cosmic Tetrabrot by Étienne Beaulac and Dominic Rochon, 2018.

Rochon's Tetrabrot with various filled-in Julia sets by Pierre-Olivier Parisé, 2017.

The Tetrabrot

Animation of the Tetrabrot rendered using ray tracing with the Bicomplex Distance Estimation develloped by Étienne Martineau and Dominic Rochon.

The Tetrabrot
self-digest

Here is the animation of different slices from

of the generalized Mandelbrot set for bicomplex numbers.

The Tetrabrot
bottom

Here is an animation made from successive approximations of the bottom of the Tetrabrot.

Tetrabrot explorations made from the TetraBrot Explorer, 2005.

Julia-Tourbil

Bicomplex Filled-in Julia Set Exploration #01

c = (0.26)e_1+(-1.754878)e_2

Julia-Soleil

Bicomplex Filled-in Julia Set Exploration #02

c = (-1.754878)e_1+(-1.754878)e_2

Julia-Loli

Bicomplex Filled-in Julia Set Exploration #03

c = (0.27)e_1+(0.27)e_2

Fractal art compositions from bicomplex filled-in Julia sets. Artwork by Alec Bourque and Dominic Rochon, 2001.