Into Another Dimension: Developing a Simulation of 4D Space by Implementing 4D Rigid Body Dynamics and Ray Marching

Abstract

In recent years, scholars and programmers have developed programs that simulate 4D spaces and allow users to interact with them. Not only do these types of programs serve as great tools for introducing the concepts behind higher-dimensional spaces, they also allude to the many possibilities of gamifying these concepts and incorporating them into other forms of digital entertainment. Nevertheless, despite their benefits, these types of programs are very difficult to implement in practice due to the lack of resources and tools available to do so. In response to this lack of resources, this project outlines and explains the different steps and calculations necessary for implementing a simple 4D simulation that incorporates 4D rigid body dynamics and the ray marching algorithm. Additionally, this project provides a working code implementation of its 4D physics engine and rendering pipeline, both of which may serve as a potential starting point for future related projects.