Programmable reconfiguration of Physarum machines

📝 Abstract

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 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 active zone (where computation occurs): merge two active zones, multiple 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.

💡 Analysis

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 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 active zone (where computation occurs): merge two active zones, multiple 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.

📄 Content

Programmable reconfiguration of Physarum machines Andrew Adamatzky and JeffJones University of the West of England, Bristol BS16 1QY, United Kingdom {andrew.adamatzky,jeff.jones}@uwe.ac.uk Abstract 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 unique biological substrate that mimics universal storage modification machines, namely the Kolmogorov-Uspensky ma- chine. 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 active zone (where computation oc- curs): merge two active zones, multiple 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. Keywords: Physarum polycephalum, Kolmogorov-Uspensky machine, pattern forma- tion, morphogenesis, graph theory 1 Introduction Physarum polycephalum 1 , commonly known as a true or multi-headed slime mold, is — at one stage of its complicated life cycle – a single cell with many diploid nuclei. This syncytial mass of protoplasm, called plasmodium, looks like amorphous yellowish mass. The plasmodium behaves and moves as a gi- ant amoeba. It feeds on bacteria, spores and other microbial creatures. When 1 Species of order Physarales, subclass Myxogastromycetidae, class Myxomecetes, division Myxostelida Preprint submitted to Elsevier Science arXiv:0901.4556v1 [nlin.AO] 28 Jan 2009 foraging for its food the plasmodium propagates towards sources of food par- ticles, surrounds them, secretes enzymes and digests the food. Typically the plasmodium forms a congregation of protoplasm in a food source it occupies. When several sources of nutrients are scattered in the plasmodium’s range, the plasmodium forms a network of protoplasmic tubes connecting the masses of protoplasm at the food sources. When we think of food sources as nodes and protoplasmic tubes as edges, we say the plasmodium develops a planar graph. Nakagaki et al [16,17,18] showed that the topology of the plasmodium’s proto- plasmic network optimizes the plasmodium’s harvesting on distributed sources of nutrients and makes more efficient flow and transport of intra-cellular com- ponents. Therefore the plasmodium is considered as a parallel computing sub- strate complementary [5] to existing massive-parallel reaction-diffusion chemi- cal processors [2]. Experimental observations suggest that during development of its protoplasmic network the plasmodium undergoes transitions between various classes of proximity graphs [6]. It starts with spanning trees [3] and may complete its protoplasmic network development as a Delaunay triangu- lation [22]. Implementation of a general purpose computing machine is the most remark- able feature of the plasmodium of Physarum polycephalum. In [4] we experi- mentally demonstrated that the plasmodium can implement the Kolmogorov- Uspensky (KUM) machine [13,34], a mathematical machine in which the stor- age structure is an irregular graph. The KUM is a forerunner and direct ‘an- cestor’ of Knuth’s linking automata [12], Tarjan’s reference machine [29], and Sch¨onhage’s storage modification machines [23,24]. The storage modification machines are basic architectures for random access machines, which are the basic architecture of modern-day computers. The plasmodium-based imple- mentation of KUM [4] provides a first-ever biological prototype of a general purpose computer. The key component of the KUM is an active zone [13,34], which may be seen as a computational equivalent to the head in a Turing machine. Physical control of the active zone is of utmost importance because it determines functionality of the biological storage modification machine. In the present paper we show — in laboratory and computer experiments with Physarum polycephalum — how basic operations Add node, Add edge, Remove Edge are implemented in the Physarum machine. We also provide unique results on controlling movement of an active zone. The paper is struc- tured as follows. We provide a very brief introduction to Kolmogorov-Uspensky machine in Sect. 2. Section 3 describes a simple experimental setup for study of plasmodium. A particle-based model of the plasmodium is presented in Sect. 4. In Sect. 5 we discuss results of laboratory experiments and computer 2 Fig. 1. An exemplar snapshot of Physarum machine. Protoplasmic tube connecting flakes a and b represents an edge e(a, b) of KUM. Active zone A(c) emerges in the node c. simulation on reconfiguration of bas

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