Calculating Voronoi Diagrams Using Chemical Reactions

Abstract

This chapter overviews work on the use of simple chemical reactions to calculate Voronoi diagrams and undertake other related geometric calculations. This work highlights that this type of specialised chemical processor is a model example of a parallel processor. For example increasing the complexity of the input data within a given area does not increase the computation time. These processors are also able to calculate two or more Voronoi diagrams in parallel. Due to the specific chemical reactions involved and the relative strength of reaction with the substrate (and cross-reactivity with the products) these processors are also capable of calculating Voronoi diagrams sequentially from distinct chemical inputs. The chemical processors are capable of calculating a range of generalised Voronoi diagrams (either from circular drops of chemical or other geometric shapes made from adsorbent substrates soaked in reagent), skeletonisation of planar shapes and weighted Voronoi diagrams (e.g. additively weighted Voronoi diagrams, multiplicatively weighted crystal growth Voronoi diagrams). The chapter also discusses some limitations of these processors. These chemical processors constitute a class of pattern forming reactions which have parallels with those observed in natural systems. It is possible that specialised chemical processors of this general type could be useful for synthesising functional structured materials.