Material approximation of data smoothing and spline curves inspired by slime mould

The giant single-celled slime mould Physarum polycephalum is known to approximate a number of network problems via growth and adaptation of its protoplasmic transport network and can serve as an inspiration towards unconventional, material-based computation. In Physarum, predictable morphological adaptation is prevented by its adhesion to the underlying substrate. We investigate what possible computations could be achieved if these limitations were removed and the organism was free to completely adapt its morphology in response to changing stimuli. Using a particle model of Physarum displaying emergent 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 approximating 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 unwinding of the shape between control points and a preferential adhesion to longer, straighter paths. Interpolating splines could not directly be approximated due to the formation and evolution of Steiner points at narrow vertices, but were approximated after rectilinear pre-processing of the source data. This pre-processing was further simplified by transforming the original data to contain the material inside the polyline. These exemplary results expand the repertoire of spatially represented unconventional computing devices by demonstrating a simple, collective and distributed approach to data and curve smoothing.