Nawaf M Albadia

Introduction. Components. Behavior & Characteristics. Classes & Rules. Grid Dimensions. Evolving Cellular Automata using Genetic Algorithms. Applications. Conclusion. References. 2

Some of the contents of this presentation is assembled and adopted from multifarious resources, see the references for more details 3

What are Cellular Automata? A cellular automaton (plural: cellular automata) is a discrete model studied in computability theory, mathematics, theoretical biology and microstructure modeling CA are discrete dynamic systems. CA's are said to be discrete because they operate in finite space and time and with properties that can have only a finite number of states. CA's are said to be dynamic because they exhibit dynamic behaviors. Basic Idea: Simulate complex systems by interaction of cells following easy rules. 4

Original concept of CA is most strongly associated with John von Neumann. von Neumann was interested in the connections between biology and the new study of automata theory Stanislaw Ulam suggested that von Neumann use a cellular automata as a framework for researching these connections. The original concept of CA can be credited to Ulam, while the early development of the concept is credited to von Neumann. Ironically, although von Neumann made many contributions and developments in CA, they are commonly referred to as “non-von Neumann style”, while the standard model of computation (CPU, globally addressable memory, serial processing) is know as “von Neumann style”. 5

Grid Mesh of cells. Simplest mesh is one dimensional. Cell Basic element of a CA. Cells can be thought of as memory elements that store state information. All cells are updated synchronously according to the transition rules. Rules 6

Local interaction leads to global dynamics. One can think of the behavior of a cellular automata like that of a “wave” at a sports event. Each person reacts to the state of his neighbors (if they stand, he stands). 7

Rule Application Next state of the core cell is related to the states of the neighborhood cells and its current state. An example rule for a one dimensional CA: 011->x0x All possible states must be described. Next state of the core cell is only dependent upon the sum of the states of the neighborhood cells. For example, if the sum of the adjacent cells is 4 the state of the core cell is 1, in all other cases the state of the core cell is 0. 8

9 John H. Conway developed “the Game of Life” in the 1970’s.

First Generation

Second Generation

Discrete lattice of cells. Homogeneity – all of the cells of the lattice are equivalent. Discrete states – each cell takes on one of a finite number of possible discrete states. Local interactions – each cell interacts only with cells that are in its local neighbourhood. 12

CA typically fall into 4 classes: Class 1: system freezes into a fixed state after a short time. Class 2: system develops periodic behaviours, which repeat continuously. Class 3: system becomes a periodic, in which it continuously changes in unpredictable ways. Class 4: system can develop in highly patterned but unstable ways. 13

14  A computational Model with discrete cells updated synchronously. ……….. output Input Combination al Logic Clock From Left Neighbor From Right Neighbor 0/1 2 – State, 2- Neighborhood, 3 -CA Cells

Combinational Logic can be of 256 types each type is called a rule Each cell can have 256 different rules ……… cell CA with different rules at each cell 15

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18 von Neumann neighborhood Moore neighbourhood.

19 The cyclic cellular automaton is a cellular automaton rule developed by David Griffeath

20 Melanie Mitchell, working on sophisticated micro level structures designed at network. Inspired by complex natural systems like insect colonies. Mitchell and collaborators have applied Genetic Algorithms to evolve patterns in cellular automata. In their results they were able to show that the GA discovered rules that gave rise to sophisticated emergent computational strategies.

Cryptography use, Rule 30 Simulations Gas behaviour. Forest fire propagation. Urban development. Traffic flow. Air flow. Crystallization process. Alternative to differential equations 21

Natural biotic types. Chemical types. Computer processors CAM-6 Error correction coding 22

Discrete dynamical system simulator. Allow for a systematic investigation of complex phenomena. Original models of fundamental physics. Instead of looking at the equations of fundamental physics, consider modelling them with CA. Can mimic complex operations Problem – How to find the exact CA rules which will model a particular application 23

Introduction to Cellular automata, Derek Horton “Cellular Automata”, April 14, 2003 Jean-Philippe Rennard Ph.D. ز "Introduction to Cellular automata", 12/2000 Wikipedia, “Cellular automaton” Wikipedia Rule 30, Wikipedia Rule 110,

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