Jeff Jones

Characteristics of pattern formation and evolution in approximations of physarum transport networks

Most studies of pattern formation place particular emphasis on its role in the development of complex multicellular body plans. In simpler organisms, however, pattern formation is intrinsic to growth and behavior. Inspired by one such organism, the true slime mold Physarum polycephalum, we present examples of complex emergent pattern formation and evolution formed by a population of simple particle-like agents. Using simple local behaviors based on chemotaxis, the mobile agent population spontaneously forms complex and dynamic transport networks. By adjusting simple model parameters, maps of characteristic patterning are obtained. Certain areas of the parameter mapping yield particularly complex long term behaviors, including the circular contraction of network lacunae and bifurcation of network paths to maintain network connectivity. We demonstrate the formation of irregular spots and labyrinthine and reticulated patterns by chemoattraction. Other Turing-like patterning schemes were obtained by using chemorepulsion behaviors, including the self-organization of regular periodic arrays of spots, and striped patterns. We show that complex pattern types can be produced without resorting to the hierarchical coupling of reaction-diffusion mechanisms. We also present network behaviors arising from simple pre-patterning cues, giving simple examples of how the emergent pattern formation processes evolve into networks with functional and quasi-physical properties including tensionlike effects, network minimization behavior, and repair to network damage. The results are interpreted in relation to classical theories of biological pattern formation in natural systems, and we suggest mechanisms by which emergent pattern formation processes may be used as a method for spatially represented unconventional computation.

Towards Physarum Robots: Computing and Manipulating on Water Surface

Plasmodium of Physarum polycephalum is an ideal biological substrate for implementing concurrent and parallel computation, including combinatorial geometry and optimization on graphs. The scoping experiments on Physarum computing in conditions of minimal friction, on the water surface were performed. The laboratory and computer experimental results show that plasmodium of Physarum is capable of computing a basic spanning tree and manipulating of light-weight objects. We speculate that our results pave the pathways towards the design and implementation of amorphous biological robots.

Influences on the formation and evolution of Physarum polycephalum inspired emergent transport networks

The single-celled organism Physarum polycephalum efficiently constructs and minimises dynamical nutrient transport networks resembling proximity graphs in the Toussaint hierarchy. We present a particle model which collectively approximates the behaviour of Physarum. We demonstrate spontaneous transport network formation and complex network evolution using the model and show that the model collectively exhibits quasi-physical emergent properties, allowing it to be considered as a virtual computing material. This material is used as an unconventional method to approximate spatially represented geometry problems by representing network nodes as nutrient sources. We demonstrate three different methods for the construction, evolution and minimisation of Physarum-like transport networks which approximate Steiner trees, relative neighbourhood graphs, convex hulls and concave hulls. We extend the model to adapt population size in response to nutrient availability and show how network evolution is dependent on relative node position (specifically inter-node angle), sensor scaling and nutrient concentration. We track network evolution using a real-time method to record transport network topology in response to global differences in nutrient concentration. We show how Steiner nodes are utilised at low nutrient concentrations whereas direct connections to nutrients are favoured when nutrient concentration is high. The results suggest that the foraging and minimising behaviour of Physarum-like transport networks reflect complex interplay between nutrient concentration, nutrient location, maximising foraging area coverage and minimising transport distance. The properties and behaviour of the synthetic virtual plasmodium may be useful in future physical instances of distributed unconventional computing devices, and may also provide clues to the generation of emergent computation behaviour by Physarum.

Towards Physarum Binary Adders

Plasmodium of Physarum polycephalum is a single cell visible by unaided eye. The plasmodiums foraging behaviour is interpreted in terms of computation. Input data is a configuration of nutrients, result of computation is a network of plasmodiums cytoplasmic tubes spanning sources of nutrients. Tsuda et al. (2004) experimentally demonstrated that basic logical gates can be implemented in foraging behaviour of the plasmodium. We simplify the original designs of the gates and show - in computer models - that the plasmodium is capable for computation of two-input two-output gate x, y-->xy, x+y and three-input two-output x,y,z-->x yz,x+y+z. We assemble the gates in a binary one-bit adder and demonstrate validity of the design using computer simulation.

Programmable reconfiguration of Physarum machines

Plasmodium of Physarum polycephalum is a large cell capable of solving graph-theoretic, optimization and computational geometry problems due to its unique foraging behavior. Also the plasmodium is a unique biological substrate that mimics universal storage modification machines, namely the Kolmogorov–Uspensky machine. In the plasmodium implementation of the storage modification machine data are represented by sources of nutrients and memory structure by protoplasmic tubes connecting the sources. In laboratory experiments and simulation we demonstrate how the plasmodium-based storage modification machine can be programmed. We show execution of the following operations with the active zone (where computation occurs): merge two active zones, multiply active zone, translate active zone from one data site to another, direct active zone. Results of the paper bear two-fold value: they provide a basis for programming unconventional devices based on biological substrates and also shed light on behavioral patterns of the plasmodium.

Sounds Synthesis with Slime Mould of Physarum Polycephalum

This paper introduces a novel application of bionic engineering: a bionic musical instrument using Physarum polycephalum. Physarum polycephalum is a huge single cell with thousands of nuclei, which behaves like a giant amoeba. During its foraging behavior this plasmodium produces electrical activity corresponding to different physiological states. We developed a method to render sounds from such electrical activity and thus represent spatio-temporal behavior of slime mould in a form apprehended auditorily. The electrical activity is captured by various electrodes placed on a Petri dish containing the cultured slime mold. Sounds are synthesized by a bank of parallel sinusoidal oscillators connected to the electrodes. Each electrode is responsible for one partial of the spectrum of the resulting sound. The behavior of the slime mould can be controlled to produce different timbres.

The emergence of synchronization behavior in Physarum polycephalum and its particle approximation

The regeneration process of contractile oscillation in the plasmodium of Physarum polycephalum is investigated experimentally and modelled computationally. When placed in a well, the Physarum cell restructures the body (fusion of small granule-like cells) and shows various complex oscillation patterns. After it completed the restructuring and regained synchronized oscillation within the body, the cell shows bilateral oscillation or rotating wave pattern. This regeneration process did not depend on the well size and all the cases tested here showed similar time course. Phase synchronization analysis based on Hilbert Transform also suggested that the cell can develop a fully synchronized oscillation within a fixed time no matter what the cell size is. A particle-based computational model was developed in order to model the emergence of oscillation patterns. Particles employing very simple and identical sensory and motor behaviors interacted with each other via the sensing and deposition of chemoattractants in a diffusive environment. From a random and almost homogeneous distribution, emergent domains of oscillatory activity emerged. By increasing the sensory radius the model simulated the regeneration process of the real plasmodium. In addition, the model replicated the rotating wave and bilateral oscillation pattern when the sensory radius was increased. The results suggest that complex emergent oscillatory behaviors (and thus the high-level systems which may utilize them, such as pumping and transport mechanisms) may be developed from simple materials inspired by Physarum slime mold.

Are motorways rational from slime mould's point of view?

We analyse the results of our experimental laboratory approximation of motorway networks with slime mould Physarum polycephalum. Motorway networks of 14 geographical areas are considered: Australia, Africa, Belgium, Brazil, Canada, China, Germany, Iberia, Italy, Malaysia, Mexico, the Netherlands, UK and USA. For each geographical entity, we represented major urban areas by oat flakes and inoculated the slime mould in a capital. After slime mould spanned all urban areas with a network of its protoplasmic tubes, we extracted a generalised Physarum graph from the network and compared the graphs with an abstract motorway graph using most common measures. The measures employed are the number of independent cycles, cohesion, shortest paths lengths, diameter, the Harary index and the Randić index. We obtained a series of intriguing results, and found that the slime mould approximates best of all the motorway graphs of Belgium, Canada and China, and that for all entities studied the best match between Physarum and motorway graphs is detected by the Randić index (molecular branching index).

Approximating the Behaviours of Physarum polycephalum for the Construction and Minimisation of Synthetic Transport Networks

The single celled organism Physarum polycephalum efficiently constructs and minimises dynamical nutrient transport networks resembling proximity graphs. We present a model multi-agent population which collectively approximates the network behaviours of Physarum . We demonstrate spontaneous transport network formation and evolution and show that the collective population also exhibits quasi-physical emergent properties, allowing the collective population to be considered as a virtual computing material - a synthetic plasmodium. This material is used as an unconventional method to approximate spatially represented geometry problems. We demonstrate three different methods for the construction, evolution and minimisation of Physarum -like transport networks which approximate Steiner trees, relative neighbourhood graphs, convex hulls and concave hulls. The results span the Toussaint hierarchy of proximity graphs, suggesting that the foraging and minimising behaviours of Physarum reflect interplay between maximising foraging area and minimising transport distance. The properties and behaviours of the synthetic virtual plasmodium may be useful in future physical instances of unconventional computing devices, and may also provide clues to the generation of emergent computation behaviours by Physarum .

On Creativity of Slime Mould

Slime mould Physarum polycephalum is large single cell with intriguingly smart behaviour. The slime mould shows outstanding abilities to adapt its protoplasmic network to varying environmental conditions. The slime mould can solve tasks of computational geometry, image processing, logics and arithmetics when data are represented by configurations of attractants and repellents. We attempt to map behavioural patterns of slime onto the cognitive control vs. schizotypy spectrum phase space and thus interpret slime mould’s activity in terms of creativity.