Andrew Adamatzky

Collision-based computing

Collision-based computing is an implementation of logical circuits, mathematical machines or other computing and information processing devices in homogeneous uniform unstructured media with traveling mobile localizations. A quanta of information is represented by a compact propagating pattern (glider in cellular automata, soliton in optical system, wave-fragment in excitable chemical system). Logical truth corresponds to presence of the localization, logical false to absence of the localization; logical values can be also represented by a particular state of the localization. When two more or more traveling localizations collide they change their velocity vectors and/or states. Post-collision trajectories and/or states of the localizations represent results of a logical operations implemented by the collision. One of the principle advantages of the a collision-based computing medium —hidden in 1D systems but obvious in 2D and 3D media— is that the medium is architecture-less: nothing is hardwired, there are no stationary wires or gates, a trajectory of a propagating information quanta can be see as a momentary wire. We introduce basics of collision-based computing, and overview the collision-based computing schemes in 1D and 2D cellular automata and continuous excitable media. Also we provide an overview of collision-based schemes where particles/collisions are dimensionless.

Physarum machines: Computers from slime mould

A Physarum machine is a programmable amorphous biological computer experimentally implemented in the vegetative state of true slime mould Physarum polycephalum. It comprises an amorphous yellowish mass with networks of protoplasmic veins, programmed by spatial configurations of attracting and repelling gradients. This book demonstrates how to create experimental Physarum machines for computational geometry and optimization, distributed manipulation and transportation, and general-purpose computation. Being very cheap to make and easy to maintain, the machine also functions on a wide range of substrates and in a broad scope of environmental conditions. As such a Physarum machine is a ‘green’ and environmentally friendly unconventional computer. The book is readily accessible to a nonprofessional reader, and is a priceless source of experimental tips and inventive theoretical ideas for anyone who is inspired by novel and emerging non-silicon computers and robots.

DEVELOPING PROXIMITY GRAPHS BY PHYSARUM POLYCEPHALUM: DOES THE PLASMODIUM FOLLOW THE TOUSSAINT HIERARCHY?

Plasmodium of Physarum polycephalum spans sources of nutrients and constructs varieties of protoplasmic networks during its foraging behavior. When the plasmodium is placed on a substrate populated with sources of nutrients, it spans the sources with protoplasmic network. The plasmodium optimizes the network to deliver efficiently the nutrients to all parts of its body. How exactly does the protoplasmic network unfold during the plasmodiums foraging behavior? What types of proximity graphs are approximated by the network? Does the plasmodium construct a minimal spanning tree first and then add additional protoplasmic veins to increase reliability and through-capacity of the network? We analyze a possibility that the plasmodium constructs a series of proximity graphs: nearest-neighbour graph (NNG), minimum spanning tree (MST), relative neighborhood graph (RNG), Gabriel graph (GG) and Delaunay triangulation (DT). The graphs can be arranged in the inclusion hierarchy (Toussaint hierarchy): NNG⊆MST⊆RNG⊆GG⊆DT...

On simultaneous construction of Voronoi diagram and delaunay triangulation by physarum polycephalum

We experimentally demonstrate that both Voronoi diagram and its dual graph Delaunay triangulation are simultaneously constructed — for specific conditions — in cultures of plasmodium, a vegetative state of Physarum polycephalum. Every point of a given planar data set is represented by a tiny mass of plasmodium. The plasmodia spread from their initial locations but, in certain conditions, stop spreading when they encounter plasmodia originated from different locations. Thus space loci not occupied by the plasmodia represent edges of Voronoi diagram of the given planar set. At the same time, the plasmodia originating at neighboring locations form merging protoplasmic tubes, where the strongest tubes approximate Delaunay triangulation of the given planar set. The problems are solved by plasmodium only for limited data sets, however the results presented lay a sound ground for further investigations.

PHYSARUM MACHINE: IMPLEMENTATION OF A KOLMOGOROV-USPENSKY MACHINE ON A BIOLOGICAL SUBSTRATE

We implement a Kolmogorov-Uspensky machine on the Plasmodium of the slime mold Physarum polycephalum. We provide experimental findings on realization of the machine instructions, illustrate basic operations, and elements of programming.

PHYSARUM SPATIAL LOGIC

Plasmodium of Physarum polycephalum is a large single cell capable for distributed sensing, information processing, decentralized decision-making and collective action. In the paper, we interpret basic features of the plasmodium foraging behavior in terms of process calculus and spatial logic and show that this behavior could be regarded as one of the natural implementations of spatial logic without modal operators.

Physarum machines: encapsulating reaction–diffusion to compute spanning tree

The Physarum machine is a biological computing device, which employs plasmodium of Physarum polycephalum as an unconventional computing substrate. A reaction–diffusion computer is a chemical computing device that computes by propagating diffusive or excitation wave fronts. Reaction–diffusion computers, despite being computationally universal machines, are unable to construct certain classes of proximity graphs without the assistance of an external computing device. I demonstrate that the problem can be solved if the reaction–diffusion system is enclosed in a membrane with few ‘growth points’, sites guiding the pattern propagation. Experimental approximation of spanning trees by P. polycephalum slime mold demonstrates the feasibility of the approach. Findings provided advance theory of reaction–diffusion computation by enriching it with ideas of slime mold computation.

Game of Life Cellular Automata

In the late 1960s British mathematician John Conway invented a virtual mathematical machine that operates on a two-dimensional array of square cell. Each cell takes two states, live and dead. The cells states are updated simultaneously and in discrete time. A dead cell comes to life if it has exactly three live neighbours. A live cell remains alive if two or three of its neighbours are alive, otherwise the cell dies. Conways Game of Life became the most programmed solitary game and the most known cellular automaton. The book brings together results of forty years of study into computational, mathematical, physical and engineering aspects of The Game of Life cellular automata. Selected topics include phenomenology and statistical behaviour; space-time dynamics on Penrose tilling and hyperbolic spaces; generation of music; algebraic properties; modelling of financial markets; semi-quantum extensions; predicting emergence; dual-graph based analysis; fuzzy, limit behaviour and threshold scaling; evolving cell-state transition rules; localization dynamics in quasi-chemical analogues of GoL; self-organisation towards criticality; asynochrous implementations. The volume is unique because it gives a comprehensive presentation of the theoretical and experimental foundations, cutting-edge computation techniques and mathematical analysis of the fabulously complex, self-organized and emergent phenomena defined by incredibly simple rules.

Slime Mold Solves Maze in One Pass, Assisted by Gradient of Chemo-Attractants

Plasmodium of Physarum polycephalum is a large cell, visible by unaided eye, which exhibits sophisticated patterns of foraging behaviour. The plasmodiums behaviour is well interpreted in terms of computation, where data are spatially extended configurations of nutrients and obstacles, and results of computation are networks of protoplasmic tubes formed by the plasmodium. In laboratory experiments and numerical simulation we show that if plasmodium of P. polycephalum is inoculated in a mazes peripheral channel and an oat flake (source of attractants) in a the mazes central chamber then the plasmodium grows toward target oat flake and connects the flake with the site of original inoculation with a pronounced protoplasmic tube. The protoplasmic tube represents a path in the maze. The plasmodium solves maze in one pass because it is assisted by a gradient of chemo-attractants propagating from the target oat flake.

Artificial Life Models in Software

The advent of powerful processing technologies and the advances in software development tools have drastically changed the approach and implementation of computational research in fundamental properties of living systems through simulating and synthesizing biological entities and processes in artificial media. Nowadays realistic physical and physiological simulation of natural and would-be creatures, worlds and societies becomes a low-cost task for ordinary home computers. The progress in technology has dramatically reshaped the structure of the software, the execution of a code, and visualization fundamentals. This has led to the emergence of novel breeds of artificial life software models, including three-dimensional programmable simulation environment, distributed discrete events platforms and multi-agent systems. This second edition reflects the technological and research advancements, and presents the best examples of artificial life software models developed in the World and available for users.