I seek to define rigorously the concept of an emergent phenomenon in a complex system, together with its implications for explanation, understanding and prediction in such systems. I argue that in a certain fundamental sense, emergent systems are those in which even perfect knowledge and understanding may give us no predictive information. In them the optimal means of prediction is simulation. I investigate the consequences of this for certain decidability and complexity issues, and then explain why these limitations do not preclude all means of doing interesting science in such systems. I touch upon some recent incorporation of this work into the investigation of self-organised criticalities. 1 Motivation and Objectives The calculations were so elaborate it was very difficult. Now, usually I was the expert at this; I could always tell you what the answer was going to look like, or when I got it I could explain why. But this thing was so complicated I couldn't explai...

Abstract. We consider affine systems in Rn constructed from a given integral invertible and expansive matrix R, and a finite set B of translates, σbx: = R−1x + b; the corresponding measure µ on Rn is a probability measure and fixed by the selfsim-ilarity µ = |B|

We show that a wide variety of non-linear cellular automata (CAs) can be decomposed into a quasidirect product of linear ones. These CAs can be predicted by parallel circuits of depth O(log 2 t) using gates with binary inputs, or O(log t) depth if "sum mod p" gates with an unbounded number of inputs are allowed. Thus these CAs can be predicted by (idealized) parallel computers much faster than by explicit simulation, even though they are non-linear. This class includes any CA whose rule, when written as an algebra, is a solvable group. We also show that CAs based on nilpotent groups can be predicted in depth O(log t) or O(1) by circuits with binary or "sum mod p" gates respectively. We use these techniques to give an efficient algorithm for a CA rule which, like elementary CA rule 18, has diffusing defects that annihilate in pairs. This can be used to predict the motion of defects in rule 18 in O(log 2 t) parallel time. PACS Keywords: 02.10, 02.70, 05.45, 46.10 1 Introduction The...

We review cellular automata as a modeling formalism and discuss how it can be used for modeling (spatial) ecological processes. The implications of this modeling paradigm for ecological observation are stressed. Finally we discuss some shortcom-ings of the cellular-automaton formalism and mention some extensions and generaliza-tions which may remedy these shortcomings. 1.

Simulating a cellular automaton (CA) for t time-steps into the future requires t 2 serial computation steps or t parallel ones. However, certain CAs based on an Abelian group, such as addition mod 2, are termed linear because they obey a principle of superposition. This allows them to be predicted efficiently, in serial timeO(t) orO(log t) in parallel. In this paper, we generalize this by looking at CAs with a variety of algebraic structures, including quasigroups, non-Abelian groups, Steiner systems, and others. We show that in many cases, an efficient algorithm exists even though these CAs are not linear in the previous sense; we term them quasilinear. We find examples which can be predicted in serial time proportional to t, t log t, t log 2 t and t α for α < 2, and parallel time log t, log t log log t and log 2 t. We also discuss what algebraic properties are required or implied by the existence of scaling relations and principles of superposition, and exhibit several novel “vector-valued ” CAs. 1 Introduction: CAs

A cellular automaton is a decentralized computing model providing an excellent platform for performing complex computation with the help of only local information. Researchers, scientists and practitioners from different fields have exploited the CA paradigm of local information, decentralized control and universal computation for modeling different applications. This article provides a survey of available literature of some of the methodologies employed by researchers to utilize cellular automata for modeling purposes. The survey introduces the different types of cellular automata being used for modeling and the analytical methods used to predict its global behavior from its local configurations. It further gives a detailed sketch of the efforts undertaken to configure the local settings of CA from a given global situation; the problem which has been traditionally termed as the inverse problem. Finally, it presents the different fields in which CA have been applied. The extensive bibliography provided with the article will be of help to the new entrant as well as researchers working in this field.

A oe-automaton is a simple additive, binary cellular automaton on a graph. For product graphs such as a grids and cylinders, reversibility and periodicity properties of the corresponding oe-automaton can be expressed in terms of a binary version of Chebyshev polynomials. We will give a detailed analysis of the divisibility properties of these polynomials and apply our results to the study of oe-automata. 1 1 Introduction A oe-automaton is a simple, non-uniform, binary cellular automaton on a directed graph. These automata were first studied by Lindenmayer in [7], and later in [1, 9, 12, 13, 2]. Briefly, a oe-automaton consists of a directed graph G = hV; Ei together with a global rule given by oe(X)(v) := X u2N(v) X(u) mod 2: Here X : V ! f0; 1g is a pattern or configuration of the automaton and N(v) denotes the open neighborhood f u 2 V j (u; v) 2 E g of vertex v. If the underlying graph is not obvious from context we will write oe G or oe(G) for emphasis. Note that rule oe i...

Summary. Let ϕ be a one-dimensional surjective cellular automaton map. We prove that if ϕ is a closing map, then the configurations which are both spatially and temporally periodic are dense. (If ϕ is not a closing map, then we do not know whether the temporally periodic configurations must be dense.) The results are special cases of results for shifts of finite type, and the proofs use symbolic dynamical techniques. 1. Introduction and

Cellular Automata (CA) are a class of discrete dynamical systems that have been widely used to model complex systems in which the dynamics is specified at local cell-scale. Classically, CA are run on a regular lattice and with perfect synchronicity. However, these two assumptions have little chance to truthfully represent what happens at the microscopic scale for physical, biological or social systems. One may thus wonder whether CA do keep their behavior when submitted to small perturbations of synchronicity. This work focuses on the study of one-dimensional (1D) asynchronous CA with two states and nearest-neighbors. We define what we mean by “the behavior of CA is robust to asynchronism ” using a statistical approach with macroscopic parameters. and we present an experimental protocol aimed at finding which are the robust 1D elementary CA. To conclude, we examine how the results exposed can be used as a guideline for the research of suitable models according to robustness criteria. 1.

We give basic definitions necessary to understand what are cellular automata, as well as to work with. Some efficient but sometimes problematic concepts as signal, simulation and universality, are pointed out. In particular, different notions of universality are put to light.