A Julia set iterates the starting point while keeping its parameter fixed. A Mandelbrot set instead asks which parameters keep the orbit of zero bounded. These pages therefore answer different questions even though both use the quadratic map.
In the Airbrot, Firebrot, and Earthbrot bases, the tricomplex parameter splits into independent real quadratic parameters. The real Mandelbrot interval is exactly [−2, 1/4]. Intersecting the corresponding linear interval constraints produces, respectively, a regular octahedron, a regular tetrahedron, and a cube.
The translucent solid, its vertices, faces, and edge length come from the exact dyadic half-space theorem. Colored points are a finite grid outside it: their hue records how many iterations the orbit survives before escaping. They provide algorithmic context but are not part of the bounded set.