Statistical Complexity of Boolean Cellular Automata with Short-Term Reaction-Diffusion Memory on a Square Lattice

2019 ◽  
Vol 28 (3) ◽  
pp. 357-391
Author(s):  
Zakarya Zarezadeh ◽  
Giovanni Costantini ◽  
Keyword(s):  
Cellular Automata ◽  
Reaction Diffusion ◽  
Square Lattice ◽  
Short Term ◽  
Statistical Complexity

MODELING THE SINOATRIAL NODE BY CELLULAR AUTOMATA WITH IRREGULAR TOPOLOGY

2010 ◽  
Vol 21 (01) ◽  
pp. 107-127 ◽  
Author(s):  
DANUTA MAKOWIEC
Keyword(s):  
Cellular Automata ◽  
Sinoatrial Node ◽  
Single Cells ◽  
Square Lattice ◽  
Proper Function ◽  
System Control ◽  
Cyclic Activity ◽  
Cellular Dynamics ◽  
Horizontal Connections ◽  
Intercellular Connections

The role of irregularity in intercellular connections is studied in the first natural human pacemaker called the sinoatrial node by modeling with the Greenberg–Hastings cellular automata. Facts from modern physiology about the sinoatrial node drive modeling. Heterogeneity between cell connections is reproduced by a rewiring procedure applied to a square lattice. The Greenberg–Hastings rule, representing the intrinsic cellular dynamics, is modified to imitate self-excitation of each pacemaker cell. Moreover, interactions with nearest neighbors are changed to heterogeneous ones by enhancing horizontal connections. Stationary states of the modeled system emerge as self-organized robust oscillatory states. Since the sinoatrial node role relies on a single cell cyclic activity, properties of single cells are studied. It appears that the strength and diversity of cellular oscillations depend directly on properties of intrinsic cellular dynamics. But these oscillations also depend on the underlying topology. Moderate nonuniformity of intercellular connections are found vital for proper function of the sinoatrial node, namely, for producing robust oscillatory states that are able to respond effectively to the autonomic system control.

scholarly journals EVOLVING LOCALIZATIONS IN REACTION-DIFFUSION CELLULAR AUTOMATA

2008 ◽  
Vol 19 (04) ◽  
pp. 557-567 ◽  
Author(s):  
ANDREW ADAMATZKY ◽  
LARRY BULL ◽  
PIERRE COLLET ◽  
EMMANUEL SAPIN
Keyword(s):  
Cellular Automata ◽  
Chemical Species ◽  
Reaction Diffusion ◽  
Discrete Systems ◽  
Chemical Systems ◽  
Transition Functions ◽  
Phenomenological Studies ◽  
Spatially Extended ◽  
Limited Diffusion

We consider hexagonal cellular automata with immediate cell neighbourhood and three cell-states. Every cell calculates its next state depending on the integral representation of states in its neighbourhood, i.e., how many neighbours are in each one state. We employ evolutionary algorithms to breed local transition functions that support mobile localizations (gliders), and characterize sets of the functions selected in terms of quasi-chemical systems. Analysis of the set of functions evolved allows to speculate that mobile localizations are likely to emerge in the quasi-chemical systems with limited diffusion of one reagent, a small number of molecules are required for amplification of travelling localizations, and reactions leading to stationary localizations involve relatively equal amount of quasi-chemical species. Techniques developed can be applied in cascading signals in nature-inspired spatially extended computing devices, and phenomenological studies and classification of non-linear discrete systems.

Creativity and ALife

2015 ◽  
Vol 21 (3) ◽  
pp. 354-365 ◽  
Author(s):  
Margaret A. Boden
Keyword(s):  
Genetic Algorithms ◽  
Cellular Automata ◽  
Reaction Diffusion ◽  
Evolutionary Programming ◽  
Diffusion Models ◽  
Do So

Three forms of creativity are exemplified in biology and studied in ALife. Combinational creativity exists as the first step in genetic algorithms. Exploratory creativity is seen in models using cellular automata or evolutionary programs. Transformational creativity can result from evolutionary programming. Even radically novel forms can do so, given input from outside the program itself. Transformational creativity appears also in reaction-diffusion models of morphogenesis. That there are limits to biological creativity is suggested by ALife work bearing on instances of biological impossibility.

scholarly journals Reaction-diffusion cellular automata model for the formation of Leisegang patterns

1994 ◽  
Vol 72 (9) ◽  
pp. 1384-1387 ◽  
Author(s):  
Bastien Chopard ◽  
Pascal Luthi ◽  
Michel Droz
Keyword(s):  
Cellular Automata ◽  
Reaction Diffusion ◽  
Cellular Automata Model

scholarly journals ON MEMORY AND STRUCTURAL DYNAMISM IN EXCITABLE CELLULAR AUTOMATA WITH DEFENSIVE INHIBITION

2008 ◽  
Vol 18 (02) ◽  
pp. 527-539 ◽  
Author(s):  
RAMÓN ALONSO-SANZ ◽  
ANDREW ADAMATZKY
Keyword(s):  
Cellular Automata ◽  
Short Term Memory ◽  
Temporal Dynamics ◽  
Short Term ◽  
Resting Cell ◽  
Fixed Topology ◽  
Dynamical Topology ◽  
Novel Complex ◽  
Spatio Temporal ◽  
Update Rules

Commonly studied cellular automata are memoryless and have fixed topology of connections between cells. However by allowing updates of links and short-term memory in cells we may potentially discover novel complex regimes of spatio-temporal dynamics. Moreover, by adding memory and dynamical topology to state update rules we somehow forge elementary but nontraditional models of neurons networks (aka neuron layers in frontal parts). In the present paper, we demonstrate how this can be done on a self-inhibitory excitable cellular automata. These automata imitate a phenomenon of inhibition caused by hight-strength stimulus: a resting cell excites if there are one or two excited neighbors, the cell remains resting otherwise. We modify the automaton by allowing cells to have few-steps memories, and create links between neighboring cells removed or generated depending on the states of the cells.

scholarly journals PERCOLATION-LIKE PHASE TRANSITION IN A NONEQUILIBRIUM STEADY STATE

2001 ◽  
Vol 12 (02) ◽  
pp. 247-256
Author(s):  
INDRANI BOSE ◽  
INDRANATH CHAUDHURI
Keyword(s):  
Steady State ◽  
Finite Size ◽  
Reaction Diffusion ◽  
Universality Class ◽  
Critical Value ◽  
Square Lattice ◽  
Finite Size Scaling ◽  
Average Cluster Size ◽  
A Site ◽  
Average Cluster

We study the Gierer–Meinhardt model of reaction-diffusion on a site-disordered square lattice. Let p be the site occupation probability of the square lattice. For p greater than a critical value pc, the steady state consists of stripe-like patterns with long-range connectivity. For p < pc, the connectivity is lost. The value of pc is found to be much greater than that of the site percolation threshold for the square lattice. In the vicinity of pc, the cluster-related quantities exhibit power-law scaling behavior. The method of finite-size scaling is used to determine the values of the fractal dimension df, the ratio, γ/ν, of the average cluster size exponent γ and the correlation length exponent ν. The values appear to indicate that the disordered GM model belongs to the universality class of ordinary percolation.

Sign in / Sign up

Export Citation Format

Share Document