Slime mould computes planar shapes

TL;DR

This paper demonstrates that slime mould Physarum polycephalum can approximate the concave hull of a set of planar points by responding to attractants and repellents, effectively solving a classical computational geometry problem through biological computation.

Contribution

It introduces a novel biological approach to computing planar shapes, specifically the concave hull, using slime mould behavior in laboratory experiments.

Findings

Slime mould can approximate concave hulls of planar point sets.

Physarum responds to attractants and repellents to shape its growth.

Biological computation of geometric shapes demonstrated experimentally.

Abstract

Computing a polygon defining a set of planar points is a classical problem of modern computational geometry. In laboratory experiments we demonstrate that a concave hull, a connected alpha-shape without holes, of a finite planar set is approximated by slime mould Physarum polycephalum. We represent planar points with sources of long-distance attractants and short-distance repellents and inoculate a piece of plasmodium outside the data set. The plasmodium moves towards the data and envelops it by pronounced protoplasmic tubes.