A rock-paper-scissors Mandelbrot set
Charlotte Aten
Abstract
The titular object of this paper is an analogue of the Mandelbrot set over the 3-dimensional real algebra whose multiplication is the bilinear extension of the rock-paper-scissors operation. In order to study the dynamics of the mappings x x2+c in this setting, a notion of holomorphy for functions on general finite-dimensional real algebras is introduced. Under a mild assumption it is shown that for such algebras holomorphy is always equivalent to solving a finite system of linear first-order PDEs generalizing the Cauchy-Riemann equations. Code is provided for generating animations of these fractals and for exploring them in a video game format.
Create a lesson
Related papers
High-order discrete differential and integral calculus and Galerkin variational integrators
Jacky Cresson, Khaled Hariz-Belgacem Khaled Hariz-Belgacem, Anna Szafranska
Dynamics of planar integrable Kepler billiards with a focused hyperbolic branch
Daniel Jaud, Lei Zhao
Cyclicity of sliding cycles in regularizations of piecewise linear two-folds
Renato Huzak, Kristian Uldall Kristiansen, Otavio Henrique Perez et al.
The Problem of Stochastic System Prediction in Gait Biomechanics Applications
S. S. Gavryushin, I. A. Meshchihin, S. S. Minkov
Anosov Diffeomorphisms of Finite-Type Surfaces
Raúl Ures, Tongyao Yu
Existence and Regularity of Stable Resonant Spectral Submanifolds and Linearization Maps
Florian Kogelbauer, Rafael de la Llave