Material Approximation of Data Smoothing and Spline Curves Inspired by Slime Mould

TL;DR

This paper demonstrates how a particle model inspired by slime mould can perform data smoothing and generate spline curves through emergent collective behavior, offering a novel spatial computation approach.

Contribution

It introduces a minimal collective material computation model that can smooth data and approximate B-spline curves in 1D and 2D datasets using emergent properties.

Findings

Model effectively smooths high-frequency data variations.

Able to approximate various types of B-spline curves.

Displays unique properties like shape unwinding and path adhesion.

Abstract

Using a particle model of Physarum displaying emer- gent morphological adaptation behaviour we demonstrate how a minimal approach to collective material computation may be used to transform and summarise properties of spatially represented datasets. We find that the virtual material relaxes more strongly to high-frequency changes in data which can be used for the smoothing (or filtering) of data by ap- proximating moving average and low-pass filters in 1D datasets. The relaxation and minimisation properties of the model enable the spatial computation of B-spline curves (approximating splines) in 2D datasets. Both clamped and unclamped spline curves, of open and closed shapes, can be represented and the degree of spline curvature corresponds to the relaxation time of the material. The material computation of spline curves also includes novel quasi-mechanical properties including unwind- ing of the shape between control points and a preferential adhesion to longer, straighter paths. Interpolating splines could not directly be ap- proximated due to the formation and evolution of Steiner points at nar- row vertices, but were approximated after rectilinear pre-processing of the source data. This pre-processing was further simplified by transform- ing the original data to contain the material inside the polyline. These exemplar results expand the repertoire of spatially represented uncon- ventional computing devices by demonstrating a simple, collective and distributed approach to data and curve smoothing.