Navigating Higher Dimensional Spaces using Hyperbolic Geometry

TL;DR

This paper presents a new interactive visualization method for higher-dimensional grids using hyperbolic geometry, enabling clear and comprehensive visualization of complex spaces for applications like data visualization and game design.

Contribution

The paper introduces a novel hyperbolic geometry-based visualization technique that overcomes previous limitations in visualizing higher-dimensional spaces.

Findings

Visualized objects are adjacent if and only if they are in adjacent grid cells.

The method avoids overlapping and disjointed representations of higher-dimensional spaces.

Applicable in data visualization, user interfaces, and game design.

Abstract

Higher-dimensional spaces are ubiquitous in applications of mathematics. Yet, as we live in a three-dimensional space, visualizing, say, a four-dimensional space is challenging. We introduce a novel method of interactive visualization of higher-dimensional grids, based on hyperbolic geometry. In our approach, visualized objects are adjacent on the screen if and only if they are in adjacent cells of the grid. Previous attempts do not show the whole higher-dimensional space at once, put close objects in distant parts of the screen, or map multiple locations to the same point on the screen; our solution lacks these disadvantages, making it applicable in data visualization, user interfaces, and game design.