Related papers: Cellular Automata and Discrete Geometry
Spontaneous self-replication in cellular automata has long been considered rare, with most known examples requiring careful design or artificial initialization. In this paper, we present formal, causal evidence that such replication can…
In recent years the modelling of traffic flow using methods from statistical physics, especially cellular automata models have allowed simulations of large traffic networks faster than real time. In this paper, we study a probabilistic…
The paper proposes a simple formalism for dealing with deterministic, non-deterministic and stochastic cellular automata in a unifying and composable manner. Armed with this formalism, we extend the notion of intrinsic simulation between…
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…
In this paper we introduce a new quantum computation model, the linear quantum cellular automaton. Well-formedness is an essential property for any quantum computing device since it enables us to define the probability of a configuration in…
A detail study on the In-degree Distribution (ID) of Cellular Automata is obtained by exact enumeration. The results indicate large deviation from multiscaling and classification according to ID are discussed. We further augment the…
Computing the configuration of any one-dimensional cellular automaton at generation $n$ can be accelerated by constructing and running a composite rule with a radius proportional to $\log n$. The new automaton is the original one, but with…
There exists an index theory to classify strictly local quantum cellular automata in one dimension. We consider two classification questions. First, we study to what extent this index theory can be applied in higher dimensions via…
Particle-like objects are observed to propagate and interact in many spatially extended dynamical systems. For one of the simplest classes of such systems, one-dimensional cellular automata, we establish a rigorous upper bound on the number…
Based on computer simulations Wolfram presented in several papers conjectured classifications of cellular automata into 4 types. He distinguishes the 4 classes of cellular automata by the evolution of the pattern generated by applying a…
Cellular automata (CA) can be viewed as maps in the space of probability measures. Such maps are normally infinitely-dimensional, and in order to facilitate investigations of their properties, especially in the context of applications,…
Parameter choosing in classical edge detection algorithms can be a costly and complex task. Choosing the correct parameters can improve considerably the resulting edge-map. In this paper we present a version of Edge Drawing algorithm in…
We present a method for construction of approximate orbits of measures under the action of cellular automata which is complementary to the local structure theory. The local structure theory is based on the idea of Bayesian extension, that…
This article surveys some theoretical aspects of Cellular Automata (CAs) research. In particular, we discuss on maximal length CA. An n-cell CA is a maximal length CA, if all the configurations except one form a single cycle. There is a…
We consider the typical asymptotic behaviour of cellular automata of higher dimension (greater than 2). That is, we take an initial configuration at random according to a Bernoulli (i.i.d) probability measure, iterate some cellular…
A general mathematical method is presented for the systematic construction of coupled map lattices (CMLs) out of deterministic cellular automata (CAs). The entire CA rule space is addressed by means of a universal map for CAs that we have…
Physical universality of a cellular automaton was defined by Janzing in 2010 as the ability to implement an arbitrary transformation of spatial patterns. In 2014, Schaeffer gave a construction of a two-dimensional physically universal…
In three spatial dimensions, communication channels are free to pass over or under each other so as to cross without intersecting; in two dimensions, assuming channels of strictly positive thickness, this is not the case. It is natural,…
Cellular Automata (CA) have been extensively used to implement symmetric cryptographic primitives, such as pseudorandom number generators and S-boxes. However, most of the research in this field, except the very early works, seems to be…
This talk advocates intrinsic universality as a notion to identify simple cellular automata with complex computational behavior. After an historical introduction and proper definitions of intrinsic universality, which is discussed with…