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.

THE CRITICAL BEHAVIOR OF THE 2D SPIN-1 ISING MODEL WITH THE BILINEAR AND POSITIVE BIQUADRATIC NEAREST NEIGHBOR INTERACTIONS ON A CELLULAR AUTOMATON

2004 ◽  
Vol 15 (10) ◽  
pp. 1425-1438 ◽  
Author(s):  
A. SOLAK ◽  
B. KUTLU
Keyword(s):  
Cellular Automaton ◽  
Phase Boundary ◽  
Critical Behavior ◽  
Nearest Neighbor ◽  
Finite Size ◽  
Square Lattice ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Creutz Cellular Automaton ◽  
Beg Model

The two-dimensional BEG model with nearest neighbor bilinear and positive biquadratic interaction is simulated on a cellular automaton, which is based on the Creutz cellular automaton for square lattice. Phase diagrams characterizing phase transitions of the model are presented for comparison with those obtained from other calculations. We confirm the existence of the tricritical points over the phase boundary for D/K>0. The values of static critical exponents (α, β, γ and ν) are estimated within the framework of the finite size scaling theory along D/K=-1 and 1 lines. The results are compatible with the universal Ising critical behavior except the points over phase boundary.

A STUDY OF BIFURCATIONS IN A CIRCULAR REAL CELLULAR AUTOMATON

1993 ◽  
Vol 03 (02) ◽  
pp. 293-321 ◽  
Author(s):  
JÜRGEN WEITKÄMPER
Keyword(s):  
Hopf Bifurcation ◽  
Dynamical Systems ◽  
Cellular Automata ◽  
Cellular Automaton ◽  
Parallel Computers ◽  
Discrete Dynamical Systems ◽  
Two Dimensional ◽  
Bifurcation Structure ◽  
Logistic Mapping ◽  
Henon Mapping

Real cellular automata (RCA) are time-discrete dynamical systems on ℝN. Like cellular automata they can be obtained from discretizing partial differential equations. Due to their structure RCA are ideally suited to implementation on parallel computers with a large number of processors. In a way similar to the Hénon mapping, the system we consider here embeds the logistic mapping in a system on ℝN, N>1. But in contrast to the Hénon system an RCA in general is not invertible. We present some results about the bifurcation structure of such systems, mostly restricting ourselves, due to the complexity of the problem, to the two-dimensional case. Among others we observe cascades of cusp bifurcations forming generalized crossroad areas and crossroad areas with the flip curves replaced by Hopf bifurcation curves.

scholarly journals Selection of Pairings Reaching Evenly Across the Data (SPREAD): A simple algorithm to design maximally informative fully crossed mating experiments

2014 ◽  
Author(s):  
Kolea Zimmerman ◽  
Daniel Levitis ◽  
Ethan Addicott ◽  
Anne Pringle
Keyword(s):  
Nearest Neighbor ◽  
Simple Algorithm ◽  
Two Dimensional ◽  
Neighbor Distance ◽  
Crossing Experiments ◽  
The Mean ◽  
Parameter Values ◽  
Selection Of ◽  
Novel Algorithm ◽  
Trait Space

We present a novel algorithm for the design of crossing experiments. The algorithm identifies a set of individuals (a ?crossing-set?) from a larger pool of potential crossing-sets by maximizing the diversity of traits of interest, for example, maximizing the range of genetic and geographic distances between individuals included in the crossing-set. To calculate diversity, we use the mean nearest neighbor distance of crosses plotted in trait space. We implement our algorithm on a real dataset ofNeurospora crassastrains, using the genetic and geographic distances between potential crosses as a two-dimensional trait space. In simulated mating experiments, crossing-sets selected by our algorithm provide better estimates of underlying parameter values than randomly chosen crossing-sets.

CHARACTERIZING THE ABILITY OF PARALLEL ARRAY GENERATORS ON REVERSIBLE PARTITIONED CELLULAR AUTOMATA

1999 ◽  
Vol 13 (04) ◽  
pp. 523-538 ◽  
Author(s):  
KENICHI MORITA ◽  
SATOSHI UENO ◽  
KATSUNOBU IMAI
Keyword(s):  
Pattern Recognition ◽  
Cellular Automata ◽  
Cellular Automaton ◽  
Inverse System ◽  
Two Dimensional ◽  
Turing Machines ◽  
Recognition Mechanism ◽  
Parallel Array ◽  
Parallel Pattern ◽  
Monotonic Constraint

A PCAAG introduced by Morita and Ueno is a parallel array generator on a partitioned cellular automaton (PCA) that generates an array language (i.e. a set of symbol arrays). A "reversible" PCAAG (RPCAAG) is a backward deterministic PCAAG, and thus parsing of two-dimensional patterns can be performed without backtracking by an "inverse" system of the RPCAAG. Hence, a parallel pattern recognition mechanism on a deterministic cellular automaton can be directly obtained from a RPCAAG that generates the pattern set. In this paper, we investigate the generating ability of RPCAAGs and their subclass. It is shown that the ability of RPCAAGs is characterized by two-dimensional deterministic Turing machines, i.e. they are universal in their generating ability. We then investigate a monotonic RPCAAG (MRPCAAG), which is a special type of an RPCAAG that satisfies monotonic constraint. We show that the generating ability of MRPCAAGs is exactly characterized by two-dimensional deterministic linear-bounded automata.

scholarly journals Representing Reversible Cellular Automata with Reversible Block Cellular Automata

2001 ◽  
Vol DMTCS Proceedings vol. AA,... (Proceedings) ◽  
Author(s):  
Jérôme Durand-Lose
Keyword(s):  
System Theory ◽  
Cellular Automata ◽  
Cellular Automaton ◽  
Linear Time ◽  
Fixed Size ◽  
Mathematical System ◽  
Reversible Cellular Automaton ◽  
International Audience ◽  
Infinite Lattices ◽  
Reversible Cellular Automata

International audience Cellular automata are mappings over infinite lattices such that each cell is updated according tothe states around it and a unique local function.Block permutations are mappings that generalize a given permutation of blocks (finite arrays of fixed size) to a given partition of the lattice in blocks.We prove that any d-dimensional reversible cellular automaton can be exp ressed as thecomposition of d+1 block permutations.We built a simulation in linear time of reversible cellular automata by reversible block cellular automata (also known as partitioning CA and CA with the Margolus neighborhood) which is valid for both finite and infinite configurations. This proves a 1990 conjecture by Toffoli and Margolus <i>(Physica D 45)</i> improved by Kari in 1996 <i>(Mathematical System Theory 29)</i>.

Emergent Structures

2010 ◽  
pp. 83-113
Author(s):  
Eleonora Bilotta ◽  
Pietro Pantano
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Initial Conditions ◽  
Natural Sciences ◽  
Forward Problem ◽  
Second Step ◽  
Large Collection ◽  
Parameter Values

There are two classes of problem in the study of Cellular Automata. The forward. problem is the problem of determining the properties of the system. Solutions often consist of finding quantities that are computable on a rules table and characterizing the behavior of the rule upon repeated iterations, starting from different initial conditions. Solutions to the backwards problem begin with the properties of a system and find a rule or a set of rules which have these properties. This is especially useful in the application of Cellular Automata to the natural sciences, when researchers deal with a large collection of phenomena (Gutowitz, 1989). Another approach is to identify the basic structures of a Cellular Automaton (Adamatzky, 1995). Once these are known it becomes possible to develop specific models for particular systems and to detect general principles applicable to a wide variety of systems (Wolfram, 1984; Lam, 1998). According to Adamatzky, the identification of a system consists of two related steps, namely specification and estimation. In specification we choose a useful and efficient description of the system: perhaps an equation and a set of parameters. The second step involves the estimation of parameter values for the equation: exploiting measures of similarity.

scholarly journals Molecular ping-pong Game of Life on a two-dimensional DNA origami array

2015 ◽  
Vol 373 (2046) ◽  
pp. 20140215 ◽  
Author(s):  
N. Jonoska ◽  
N. C. Seeman
Keyword(s):  
Cellular Automata ◽  
Molecular Interactions ◽  
Molecular Species ◽  
Environmental Control ◽  
Dna Origami ◽  
Two Dimensional ◽  
Laser Illumination ◽  
Game Of Life ◽  
Array Platform ◽  
Ping Pong

We propose a design for programmed molecular interactions that continuously change molecular arrangements in a predesigned manner. We introduce a model where environmental control through laser illumination allows platform attachment/detachment oscillations between two floating molecular species. The platform is a two-dimensional DNA origami array of tiles decorated with strands that provide both, the floating molecular tiles to attach and to pass communicating signals to neighbouring array tiles. In particular, we show how algorithmic molecular interactions can control cyclic molecular arrangements by exhibiting a system that can simulate the dynamics similar to two-dimensional cellular automata on a DNA origami array platform.

scholarly journals Real Linear Automata with a Continuum of Periodic Solutions for Every Period

2019 ◽  
Vol 29 (06) ◽  
pp. 1930016
Author(s):  
Xu Xu
Keyword(s):  
Cellular Automata ◽  
Boundary Conditions ◽  
Cellular Automaton ◽  
Periodic Solutions ◽  
Periodic Points ◽  
Two Dimensional ◽  
Dynamical Features ◽  
Real Linear

Interesting dynamical features such as periodic solutions of binary cellular automata are rare and therefore difficult to find, in general. In this paper, we illustrate an effective method in identifying fixed and periodic points of traditional one- and two-dimensional [Formula: see text]-valued cellular automaton systems, using cycle graphs. We also show that when the binary or [Formula: see text]-valued cellular states are extended to real-values and when defined as doubly-infinite vectors, there exists a continuum of periodic solutions for every period, even when the governing local rules are simply linear. In addition, we demonstrate the important effect that boundary conditions have on systems’ dynamical structures.

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