Tricomplex Distance Estimation for Filled-in Julia Sets and Multibrot Sets

Abstract

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 $1$.

Figures (5)

• Figure 1: Various filled-in Julia sets.
• Figure 2: The Multibrot sets of orders $p=3$, $p=8$ and $p=15$.
• Figure 3: The Tetrabrot sets with $p=3$ and $p=4$.
• Figure 4: The Airbrots with $p=2$ and $p=5$.
• Figure 5: The Arrowheadbrots with $p=3$ and $p=4$.

Theorems & Definitions (30)

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