Vesicle computers: Approximating Voronoi diagram on Voronoi automata

TL;DR

This paper introduces a Voronoi automaton model that uses excitable chemical-inspired vesicle arrangements to approximate Voronoi diagrams, demonstrating its effectiveness on arbitrary shapes and shapes' skeletons.

Contribution

It presents a novel automaton-based approach to approximate Voronoi diagrams using chemical-inspired states and interactions, linking precipitate formation to diagram edges.

Findings

Precipitation threshold affects approximation quality.

Model successfully approximates Voronoi diagrams of arbitrary shapes.

Feasibility demonstrated on shape skeletons.

Abstract

Irregular arrangements of vesicles filled with excitable and precipitating chemical systems are imitated by Voronoi automata --- finite-state machines defined on a planar Voronoi diagram. Every Voronoi cell takes four states: resting, excited, refractory and precipitate. A resting cell excites if it has at least one excited neighbour; the cell precipitates if a ratio of excited cells in its neighbourhood to its number of neighbours exceed certain threshold. To approximate a Voronoi diagram on Voronoi automata we project a planar set onto automaton lattice, thus cells corresponding to data-points are excited. Excitation waves propagate across the Voronoi automaton, interact with each other and form precipitate in result of the interaction. Configuration of precipitate represents edges of approximated Voronoi diagram. We discover relation between quality of Voronoi diagram approximation and precipitation threshold, and demonstrate feasibility of our model in approximation Voronoi diagram of arbitrary-shaped objects and a skeleton of a planar shape.