Examples Of Cellular Automata Research Articles

CHARACTERIZATION OF ONE DIMENSIONAL PERIODIC BOUNDARY CELLULAR AUTOMATA

In this paper, we investigate one dimensional cellular automata under periodic boundary conditions. We use matrix algebra for calculating over on Zp. We obtain a formula for finding the reversibility of cellular automata. Finally, we give some important examples of cellular automata.

Mean-Field Analysis with Random Perturbations to Detect Gliders in Cellular Automata

Cellular automata are mathematical models that represent systems with complex behavior through simple interactions between their individual elements. These models can be used to study unconventional computational systems and complexity. One notable aspect of cellular automata is their ability to create structures known as gliders, which move in a regular pattern to represent the manipulation of information. This paper introduces the modification of mean-field theory applied to cellular automata, using random perturbations based on the system’s evolution rule. The original aspect of this approach is that the perturbation factor is tailored to the nature of the rule, altering the behavior of the mean-field polynomials. By combining the properties of both the original and perturbed polynomials, it is possible to detect when a cellular automaton is more likely to generate gliders without having to run evolutions of the system. This methodology is a useful approach to finding more examples of cellular automata that exhibit complex behavior. We start by examining elementary cellular automata, then move on to examples of automata that can generate gliders with more states. To illustrate the results of this methodology, we provide evolution examples of the detected automata.

The Transition Rules of 2D Linear Cellular Automata Over Ternary Field and Self-Replicating Patterns

In this paper we start with two-dimensional (2D) linear cellular automata (CA) in relation with basic mathematical structure. We investigate uniform linear 2D CA over ternary field, i.e. ℤ3. Present work is related to theoretical and imaginary investigations of 2D linear CA. Even though the basic construction of a CA is a discrete model, its macroscopic level behavior at large times and on large scales could be a close approximation to a continuous system. Considering some statistical properties, someone may also study geometrical aspects of patterns generated by cellular automaton evolution. After iteratively applying the linear rules, CA have been shown capable of producing interesting complex behaviors. Some examples of CA produce remarkably regular behavior on finite configurations. Using some simple initial configurations, the produced pattern can be self-replicating regarding some linear rules. Here we deal with the theory 2D uniform periodic, adiabatic and reflexive boundary CA (2D PB, AB and RB) over the ternary field ℤ3and the applications of image processing for patterns generation. From the visual appearance of the patterns, it is seen that some rules display sensitive dependence on boundary conditions and their rule numbers.

Critical Self-Organized Self-Sustained Oscillations in Large Regulatory Networks: Towards Understanding the Gene Expression Initiation

In this paper, a new model of self-organized criticality is introduced. This model, called the gene expression paradigm, is motivated by the problem of gene expression initiation in the newly-born daughter cells after mitosis. The model is fundamentally different in dynamics and properties from the well known sand-pile paradigm. Simulation experiments demonstrate that a critical total number of proteins exists below which transcription is impossible. Above this critical threshold, the system enters the regime of self-sustained oscillations with standard deviations and periods proportional to the genes’ complexities with probability one. The borderline between these two regimes is very sharp. Importantly, such a self-organization emerges without any deterministic feedback loops or external supervision, and is a result of completely random redistribution of proteins between inactive genes. Given the size of the genome, the domain of self-organized oscillatory motion is also limited by the genes’ maximal complexities. Below the critical complexity, all the regimes of self-organized oscillations are self-similar and largely independent of the genes’ complexities. Above the level of critical complexity, the whole-genome transcription is impossible. Again, the borderline between the domains of oscillations and quiescence is very sharp. The gene expression paradigm is an example of cellular automata with the domain of application potentially far beyond its biological context. The model seems to be simple enough for staging an experiment for verification of its remarkable properties.

Asynchronous, irregular automata nets: the path not taken

This is a prelude to, and an extension of the original paper Artificial tissue models (Stark, R., 1994. The topology and analysis of asynchronous processes. http://www.math.usf.edu/∼stark/documents). However, this exposition is designed for a broader audience — anyone working in biological information processing. A primary objective is to demonstrate that irregular asynchronous automata nets, as opposed to cellular automata, are a realistic approach to modeling biological information processing. Also, new material is presented. Sections 1 and 2 review the early history of von Neumann’s attempt explore biological information processing and finally the emergence of cellular automata. The history is guided by the question of why John von Neumann knowingly (we believe) compromised his investigation of biological information processing by falling back to the model we now know as cellular automata. Section 3 defines and explores examples of cellular automata and artificial tissue. Sections 4 and 5 contain philosophical observations which unify our paper, and propose an answer to the original question. A new model for Turing’s leopards’ spot problem is presented. The asynchronous models are defined by a cell program and a local commumications protocol only. Computational freedom comes from asynchronous activity, while global organization emerges from the entropy reducing nature of the cell programs.

Finite Size Scaling in Three-Dimensional Bootstrap Percolation

We consider the problem of bootstrap percolation on a three-dimensional lattice and we study its finite size scaling behavior. Bootstrap percolation is an example of cellular automata defined on the $d$-dimensional lattice ${1,2,\ldots,L^d}$ in which each site can be empty or occupied by a single particle; in the starting configuration each site is occupied with probability $p$,occupied sites remain occupied forever, while empty sites are occupied by a particle if at least $\ell$ among their 2$d$ nearest neighbor sites are occupied. When $d$ is fixed, the most interesting case is the one $\ell=d:$ this is a sort of threshold, in the sense that the critical probability $p_c$ for the dynamics on the infinite lattice $\mathbb{Z}^d$ switches from zero to one when this limit is crossed. Finite size effects in the three-dimensional case are already known in the cases $\ell\leq2$; in this paper we discuss the case $\ell=3$ and we show that the finite size scaling function for this problem is of the form $f(L) =const/lnlnL$.We prove a conjecture proposed by A.C.D. van Enter.

On the law of entropy increase of some cellular automata on Zd

We consider some time-reversible cellular automata on thed-dimensional integral latticeZ d and study their time evolution properties. We show first that a Boltzmann-type entropy can be defined which is not less than its initial value for initial States which have no spatial correlation. For monotonic increase of the entropies for such initial States we need an additional condition which we call renewality. Under the renewality condition entropy is monotonic nondecreasing. We give some examples of cellular automata which satisfy the renewality condition

The topological entropy of cellular automata is uncomputable

AbstractThere is no algorithm which will take a description of a celluar automaton and determine whether it has zero topological entropy, or for any fixed ε > 0 compute its topological entropy to a tolerance e. Furthermore a set of aperiodic Wang tiles arising from Penrose's kite and dart tiles is used to demonstrate specific examples of cellular automata with a single periodic point but non-trivial non-wandering sets, which furthermore can be constructed to have arbitrarily high topological entropy.

Discrete logarithms a parallel pseudorandom pattern generator analysis method

The phaseshifts between the bitstreams emitted from various stages of one-dimensional linear finitestate machines are analyzed. An operational calculus involving ashift operator is developed. The concept of discrete lograithms of binary polynomials is introduced to calculate phaseshifts. The analysis technique is applied to various examples of cellular automata and LFSRs. Phaseshift end effects are observed in cellular automata due to rule configurations. Modified LFSR generators are shown to have potentially more useful outputs than cellular automata, lower circuit complexity, and equivalent phaseshift statistics.