scholarly journals Faster Methods for Identifying Nontrivial Energy Conservation Functions for Cellular Automata

2010 ◽  
Vol DMTCS Proceedings vol. AL,... (Proceedings) ◽  
Author(s):  
Leemon Baird ◽  
Barry Fagin
Keyword(s):  
Cellular Automata ◽  
General Theory ◽  
Energy Conservation ◽  
Linear Algebra ◽  
Solution Space ◽  
Basis Set ◽  
Complete List ◽  
Energy Functions ◽  
Game Of Life ◽  
International Audience

International audience The biggest obstacle to the efficient discovery of conserved energy functions for cellular auotmata is the elimination of the trivial functions from the solution space. Once this is accomplished, the identification of nontrivial conserved functions can be accomplished computationally through appropriate linear algebra. As a means to this end, we introduce a general theory of trivial conserved functions. We consider the existence of nontrivial additive conserved energy functions ("nontrivials") for cellular automata in any number of dimensions, with any size of neighborhood, and with any number of cell states. We give the first known basis set for all trivial conserved functions in the general case, and use this to derive a number of optimizations for reducing time and memory for the discovery of nontrivials. We report that the Game of Life has no nontrivials with energy windows of size 13 or smaller. Other $2D$ automata, however, do have nontrivials. We give the complete list of those functions for binary outer-totalistic automata with energy windows of size 9 or smaller, and discuss patterns we have observed.

scholarly journals On the analysis of ''simple'' 2D stochastic cellular automata

2010 ◽  
Vol Vol. 12 no. 2 ◽  
Author(s):  
Damien Regnault ◽  
Nicolas Schabanel ◽  
Eric Thierry
Keyword(s):  
Cellular Automata ◽  
Time Step ◽  
Energy Functions ◽  
Stochastic Cellular Automata ◽  
Von Neumann ◽  
Rich Variety ◽  
Moore Neighborhood ◽  
International Audience ◽  
Definition Of ◽  
New Phenomena

International audience Cellular automata are usually associated with synchronous deterministic dynamics, and their asynchronous or stochastic versions have been far less studied although significant for modeling purposes. This paper analyzes the dynamics of a two-dimensional cellular automaton, 2D Minority, for the Moore neighborhood (eight closest neighbors of each cell) under fully asynchronous dynamics (where one single random cell updates at each time step). 2D Minority may appear as a simple rule, but It is known from the experience of Ising models and Hopfield nets that 2D models with negative feedback are hard to study. This automaton actually presents a rich variety of behaviors, even more complex that what has been observed and analyzed in a previous work on 2D Minority for the von Neumann neighborhood (four neighbors to each cell) (2007) This paper confirms the relevance of the later approach (definition of energy functions and identification of competing regions) Switching to the Moot e neighborhood however strongly complicates the description of intermediate configurations. New phenomena appear (particles, wider range of stable configurations) Nevertheless our methods allow to analyze different stages of the dynamics It suggests that predicting the behavior of this automaton although difficult is possible, opening the way to the analysis of the whole class of totalistic automata

scholarly journals Larger than Life: Digital Creatures in a Family of Two-Dimensional Cellular Automata

2001 ◽  
Vol DMTCS Proceedings vol. AA,... (Proceedings) ◽  
Author(s):  
Kellie M. Evans
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Nearest Neighbor ◽  
Two Dimensional ◽  
Game Of Life ◽  
Large Neighborhood ◽  
International Audience ◽  
Parameter Values

International audience We introduce the Larger than Life family of two-dimensional two-state cellular automata that generalize certain nearest neighbor outer totalistic cellular automaton rules to large neighborhoods. We describe linear and quadratic rescalings of John Conway's celebrated Game of Life to these large neighborhood cellular automaton rules and present corresponding generalizations of Life's famous gliders and spaceships. We show that, as is becoming well known for nearest neighbor cellular automaton rules, these ``digital creatures'' are ubiquitous for certain parameter values.

A New Highway Safety Model Based on Cellular Automata

2014 ◽  
Vol 989-994 ◽  
pp. 2340-2343
Author(s):  
Li Xing Li
Keyword(s):  
Cellular Automata ◽  
Energy Conservation ◽  
Traffic Safety ◽  
Conservation Law ◽  
Highway Safety ◽  
Traffic Density ◽  
New Model ◽  
The Road ◽  
The Right ◽  
Energy Conservation Law

With the growth of the total mileage of highway. There is great importance in studying highway safety. At the present time, there are little research on traffic safety with the consideration of the Keep-Right-Except-To-Pass Rule, which requires drivers to drive in the right-most lane unless they are passing another vehicle. Based on Cellular Automata, this paper constructs a new model of highway safety with the consideration of the particular Rule. To evaluate the safety of the road, the model proposes a new index based on energy conservation law. After the simulation, the result shows the best traffic density to balance the safety and traffic flux is 20.1133veh/km.

scholarly journals MPI implementations of Conways Game of Life and Kohomoto-Oono cellular automata

2010 ◽  
Vol 2 (3) ◽  
pp. 319-322
Author(s):  
Anna Yur'evna Subbotina ◽  
Nikolai Igorevich Khokhlov
Keyword(s):  
Cellular Automata ◽  
Game Of Life
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