Replication of a Binary Image on a One-Dimensional Cellular Automaton with Linear Rules

2018 ◽  
Vol 27 (4) ◽  
pp. 415-430
Author(s):  
U Srinivasa Rao ◽  
Jeganathan L ◽  
Keyword(s):  
Cellular Automaton ◽  
Binary Image ◽  
One Dimensional

scholarly journals Characterization of the Evolution of Nonlinear Uniform Cellular Automata in the Light of Deviant States

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Pabitra Pal Choudhury ◽  
Sudhakar Sahoo ◽  
Mithun Chakraborty
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Boolean Functions ◽  
State Transition ◽  
The State ◽  
Transition Diagram ◽  
One Dimensional ◽  
State Transition Diagram ◽  
Linear Rule

Dynamics of a nonlinear cellular automaton (CA) is, in general asymmetric, irregular, and unpredictable as opposed to that of a linear CA, which is highly systematic and tractable, primarily due to the presence of a matrix handle. In this paper, we present a novel technique of studying the properties of the State Transition Diagram of a nonlinear uniform one-dimensional cellular automaton in terms of its deviation from a suggested linear model. We have considered mainly elementary cellular automata with neighborhood of size three, and, in order to facilitate our analysis, we have classified the Boolean functions of three variables on the basis of number and position(s) of bit mismatch with linear rules. The concept of deviant and nondeviant states is introduced, and hence an algorithm is proposed for deducing the State Transition Diagram of a nonlinear CA rule from that of its nearest linear rule. A parameter called the proportion of deviant states is introduced, and its dependence on the length of the CA is studied for a particular class of nonlinear rules.

scholarly journals ONE DIMENSIONAL nARY DENSITY CLASSIFICATION USING TWO CELLULAR AUTOMATON RULES

1999 ◽  
Vol 10 (05) ◽  
pp. 883-889 ◽  
Author(s):  
H. F. CHAU ◽  
L. W. SIU ◽  
K. K. YAN
Keyword(s):  
Boundary Condition ◽  
Cellular Automaton ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Classification Task ◽  
Dimensional Chain ◽  
One Dimensional

Suppose each site on a one-dimensional chain with periodic boundary condition may take on any one of the states 0,1,…,n-1; can you find out the most frequently occurring state using cellular automaton? Here, we prove that while the above density classification task cannot be resolved by a single cellular automaton, this task can be performed efficiently by applying two cellular automaton rules in succession.

ON THE STRUCTURE OF REAL-VALUED ONE-DIMENSIONAL CELLULAR AUTOMATA

2011 ◽  
Vol 21 (05) ◽  
pp. 1265-1279 ◽  
Author(s):  
XU XU ◽  
STEPHEN P. BANKS ◽  
MAHDI MAHFOUF
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Fixed Points ◽  
Periodic Solutions ◽  
Cellular Systems ◽  
One Dimensional ◽  
Dynamical Behaviors ◽  
New Type ◽  
Complex Patterns

It is well-known that binary-valued cellular automata, which are defined by simple local rules, have the amazing feature of generating very complex patterns and having complicated dynamical behaviors. In this paper, we present a new type of cellular automaton based on real-valued states which produce an even greater amount of interesting structures such as fractal, chaotic and hypercyclic. We also give proofs to real-valued cellular systems which have fixed points and periodic solutions.

scholarly journals CELLULAR AUTOMATON SUPERCOLLIDERS

2011 ◽  
Vol 22 (04) ◽  
pp. 419-439 ◽  
Author(s):  
GENARO J. MARTÍNEZ ◽  
ANDREW ADAMATZKY ◽  
CHRISTOPHER R. STEPHENS ◽  
ALEJANDRO F. HOEFLICH
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Elastic Collision ◽  
Collective Excitations ◽  
Compact Groups ◽  
Dimensional Torus ◽  
Nonlinear Media ◽  
One Dimensional ◽  
Spatially Extended ◽  
Binary Strings

Gliders in one-dimensional cellular automata are compact groups of non-quiescent 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 traveling in a spatially extended nonlinear medium. They can be considered as binary strings or symbols traveling along a one-dimensional ring, interacting with each other and changing their states, or symbolic values, as a result of interactions. We analyze what types of interaction occur between gliders traveling 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 nonlinear media: fusion, elastic collision, and soliton-like collision. Computational outcomes of a swarm of gliders circling on a one-dimensional torus are analyzed via implementation of cyclic tag systems.

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