In this article, we give the exact interval of the cross section of the so-called Mandelbric set generated by the polynomial z 3 + c where z and c are complex numbers. Following that result, we show that the Mandelbric defined on the hyperbolic numbers D is a square with its center at the origin. Moreover, we define the Multibrot sets generated by a polynomial of the form Q p,c (η) = η p + c ( p ∈ N and p ≥ 2) for tricomplex numbers. More precisely, we prove that the tricomplex Mandelbric has four principal slices instead of eight principal 3D slices that arise for the case of the tricomplex Mandelbrot set. Finally, we prove that one of these four slices is an octahedron.

In this article, we give the exact interval of the cross section of the Multibrot sets generated by the polynomial z p + c where z and c are complex numbers and p ≥ 2 is an even integer. Furthermore, we show that the same Multibrots defined on the hyperbolic numbers are always squares. Moreover, we give a generalized 3D version of the hyperbolic Multibrot set and prove that our generalization is an octahedron for a specific 3D slice of the tricomplex polynomial η p + c where p ≥ 2 is an even integer.

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In this article, we present a distance estimation formula that can be used to ray trace 3D slices of the filled-in Julia sets and the Multibrot sets generated by the tricomplex polynomials of the form η p + c where p is any integer greater than 1.