Mesoscale disordered materials are ubiquitous in industry and in the environment. Any fundamental understanding of the transport and mechanical properties of such materials must follow from a thorough understanding of their structure. However, in the overwhelming majority of cases, experimental characterization of such materials has been limited to first- and second-order structural correlation functions, i.e., the mean filling fraction and the structural autocorrelation function. We report here the successful combination of synchrotron x-ray microtomography and image processing to determine the full three-dimensional real-space structure of a model disordered material, a granular bed of relatively monodisperse glass spheres. Specifically, we determine the center location and the local connectivity of each granule. This complete knowledge of structure can be used to calculate otherwise inaccessible high-order correlation functions. We analyze nematic order parameters for contact bonds to characterize the geometric anisotropy or fabric induced by the sample boundary conditions. Away from the boundaries we find short-range bond orientational order exhibiting characteristics of the underlying polytetrahedral structure.

Plasmodium of Physarum polycephalum is a single cell visible by unaided eye. During its foraging behavior the cell spans spatially distributed sources of nutrients with a protoplasmic network. Geometrical structure of the protoplasmic networks allows the plasmodium to optimize transport of nutrients between remote parts of its body. Assuming major Mexican cities are sources of nutrients how much structure of Physarum protoplasmic network correspond to structure of Mexican Federal highway network? To find an answer undertook a series of laboratory experiments with living Physarum polycephalum. We represent geographical locations of major cities by oat flakes, place a piece of plasmodium in Mexico city area, record the plasmodium's foraging behavior and extract topology of nutrient transport networks. Results of our experiments show that the protoplasmic network formed by Physarum is isomorphic, subject to limitations imposed, to a network of principle highways. Ideas and results of the paper may contribute towards future developments in bio-inspired road planning

Rule 54, a two state, three neighbor cellular automaton in Wolfram's systems of nomenclature, is less complex that Rule 110, but nevertheless possess a rich and complex dynamics. We provide a systematic and exhaustive analysis of glider behavior and interactions, including a catalog of collisions. Many o f t h e m s h o ws promise are computational elements.

We study a binary-cell-state eight-cell neighborhood two-dimensional cellular automaton model of a quasi-chemical system with a substrate and a reagent. Reactions are represented by semi-totalistic transitions rules: every cell switches from state 0 to state 1 depending on if the sum of neighbors in state 1 belongs to some specified interval, cell remains in state 1 if the sum of neighbors in state 1 belong to another specified interval. We investigate space-time dynamics of 1296 automata, establish morphology-bases classification of the rules, explore precipitating and excitatory cases and scrutinize collisions between mobile and stationary localizations (gliders, cycle life and still-life compact patterns). We explore reaction–diffusion like patterns produced as a result of collisions between localizations. Also, we propose a set of rules with complex behavior called Life 2c22.

In cellular automata with memory, the unchanged maps of the conventional cellular automata are applied to cells endowed with memory of their past states in some specified interval. We implement Rule 30 automata with a majority memory and show that using the memory function we can transform quasi-chaotic dynamics of classical Rule 30 into domains of travelling structures with predictable behaviour. We analyse morphological complexity of the automata and classify dynamics of gliders (particle, self-localizations) in memory-enriched Rule 30. We provide formal ways of encoding and classifying glider dynamics using de Bruijn diagrams, soliton reactions and quasi-chemical representations.

Since their inception at Macy conferences in later 1940s complex systems remain the most controversial topic of inter-disciplinary sciences. The term 'complex system' is the most vague and liberally used scientific term. Using elementary cellular automata (ECA), and exploiting the CA classification, we demonstrate elusiveness of 'complexity' by shifting space-time dynamics of the automata from simple to complex by enriching cells with memory. This way, we can transform any ECA class to another ECA class -without changing skeleton of cell-state transition function -and vice versa by just selecting a right kind of memory. A systematic analysis display that memory helps 'discover' hidden information and behaviour on trivialuniform, periodic, and non-trivial -chaotic, complex -dynamical systems.

Gliders in one-dimensional cellular automata are compact groups of nonquiescent and non-ether patterns (ether represents a periodic background) translating along automaton lattice. They are cellular-automaton analogous of localizations or quasi-local collective excitations travelling in a spatially extended non-linear medium. They can be considered as binary strings or symbols travelling along a one-dimensional ring, interacting with each other and changing their states, or symbolic values, as a result of interactions. We analyse what types of interaction occur between gliders travelling on a cellular automaton 'cyclotron' and build a catalog of the most common reactions. We demonstrate that collisions between gliders emulate the basic types of interaction that occur between localizations in non-linear media: fusion, elastic collision, and soliton-like collision. Computational outcomes of a swarm of gliders circling on a one-dimensional torus are analysed via implementation of cyclic tag systems.

Purpose -Studies in complexity of cellular automata do usually deal with measures taken on integral dynamics or statistical measures of space-time configurations. No one has tried to analyze a generative power of cellular-automaton machines. The purpose of this paper is to fill the gap and develop a basis for future studies in generative complexity of large-scale spatially extended systems. Design/methodology/approach -Let all but one cell be in alike state in initial configuration of a one-dimensional cellular automaton. A generative morphological diversity of the cellular automaton is a number of different three-by-three cell blocks occurred in the automaton's space-time configuration. Findings -The paper builds a hierarchy of generative diversity of one-dimensional cellular automata with binary cell-states and ternary neighborhoods, discusses necessary conditions for a cell-state transition rule to be on top of the hierarchy, and studies stability of the hierarchy to initial conditions.Research limitations/implications -The method developed will be used -in conjunction with other complexity measures -to built a complete complexity maps of one-and two-dimensional cellular automata, and to select and breed local transition functions with highest degree of generative morphological complexity. Originality/value -The hierarchy built presents the first ever approach to formally characterize generative potential of cellular automata.