Rendering Non-Euclidean Space in Virtual Reality Using Portals

Simulating non-Euclidean geometry in virtual reality is of interest to a wide variety of fields of research. However it is still quite a challenge. Various methods are already known, but they vary greatly in performance and applicability. This paper compares some methods of rendering a non-Euclidean space. We focus on the order-5 square tiling...

Exploring the Impact of a Procedurally Generated Environment on Immersion in Virtual Hyperbolic Space

Virtual Reality allows for the ultimate immersion in environments not naturally encountered. Still, hyperbolic environments are extremely difficult to get used to. This paper explores whether immersion in virtual hyperbolic environments can be enhanced by introducing a procedurally generated world. We propose a Wave Function Collapse (WFC)...

Shortest Path algorithms for the traversal of an Order-5 square tiling from within a confined space

It is possible to use a different representation of space in a Virtual Reality (VR) game, instead of using the euclidean representation we are used to. The reason why that is interesting is that it opens up the possibility of traversing infinitely far in the virtual space while being confined to a relatively limited space in the real world. But...

Mapping hyperbolic space for the virtual reality game "Holonomy"

Non-Euclidean spaces are spaces that do not satisfy all of Euclid’s postulates. An example of such a space is hyperbolic space. In this paper, a method is discussed to draw a tessellation of hyperbolic space in a manner that fits with the virtual reality game "Holonomy", a game which takes place in hyperbolic space. The main result shows that...

Mini-map positioning for Virtual Reality environments in hyperbolic space

Navigation is a core aspect of exploring virtual environments. To assist players, a mini-map is a commonly used navigational tool. Navigation in an unknown space can be difficult. This difficulty is only increased when a player finds themselves in a non-Euclidean space. This paper explores the effect the mini-map's positioning has on the player...

A cellular automaton for modelling territories

A cellular automaton for simulating territories is presented. In it, cells have a certain amount of markings of two different groups. The amount of markings for each group gets higher based on the amounts of that group in neighboring cells and the amount of markings of the opposite group in the current cell to simulate an avoidance tendency. The...

Implementation and Evaluation of an Order Parameter for the Reaction-Diffusion Model in a Cellular Automaton: How does an order parameter perform on a Reaction-Diffusion model implemented in a Cellular Automata?

This paper describes the process and evaluation methods by which we adapted a Reaction-Diffusion model and an order parameter to monitor its segregation state in a 2D Cellular Automaton model. The model simulates Turing pattern formations, whose behavior will be studied by an order parameter formulated for this project. This order parameter acts...

Effects of City Layout in Gang Territorial Formations

Gang-related violence poses a significant challenge in numerous countries across the world. While previous research have explored modeling formation of gang territories, none of them incorporated a city layout such as roads, water bodies and parks while doing so. Hence, this research explores the effects of city layout in the formation of gang...

Multi species turing patterns in three dimensions

In 1952, Alan M. Turing presented a reaction-diffusion model that described formation of skin patterns. The patterns he predicted have later been found in various natural phenomena, such as in skins of fish or even in vegetation around termite hills. His patterns have even been taken to the micro-level. In 1984, David A. Young proposed a...

Territory patterns created by random walker agents in three dimensions

This research paper proposes a discrete agent-based model to simulate territorial development among micro-organisms. The model involves two species that interact through marker signals left behind by agents as they move through a three-dimensional lattice. The study builds on previous research that established a phase transition from a well...

A Watermark Recognition System: An Approach to Matching Similar Watermarks

Watermarks are historical motifs present in the texture of paper that are commonly used to identify the paper manufacturers. They only become visible when viewed under certain light conditions. Under ideal circumstances, researchers may use watermarks to determine a historical document’s origins and context. To identify a watermark, it is...

“Holonomy”: a non-Euclidean labyrinth game in virtual reality