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Chapter 7. Cellular Automata

“To play life you must have a fairly large checkerboard and a plentiful supply of flat counters of two colors. It is possible to work with pencil and graph paper but it is much easier, particularly for beginners, to use counters and a board.” —Martin Gardner, Scientific American (October 1970)

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In Chapter 5, I defined a complex system as a network of elements with short-range relationships, operating in parallel, that exhibit emergent behavior. I illustrated this definition by creating a flocking simulation and demonstrated how a complex system ads up to more than the sum of its parts. In this chapter, I’m going to turn to developing other complex systems known as cellular automata.

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In some respects, this shift may seem like a step backward. No longer will the individual elements of my systems be members of a physics world, driven by forces and vectors to move around the canvas. Instead, I’ll build systems out of the simplest digital element possible: a single bit. This bit is called a cell, and its value (0 or 1) is called its state. Working with such simple elements will help illustrate the details behind how complex systems work, and it will offer an opportunity to elaborate on some programming techniques that apply to code-based projects. Building cellular automata will also set the stage for the rest of the book, where I’ll increasingly focus on systems an algorithms rather than vectors an motion—albeit systems an algorithms that I can and will apply to moving bodies.

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In Chapter 5, I defined a complex system as a network of elements with short-range relationships, operating in parallel, that exhibit emergent behavior. I illustrated this definition by creating a flocking simulation and demonstrated how a complex system adds up to more than the sum of its parts. In this chapter, I’m going to turn to developing other complex systems known as cellular automata.

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In some respects, this shift may seem like a step backward. No longer will the individual elements of my systems be members of a physics world, driven by forces and vectors to move around the canvas. Instead, I’ll build systems out of the simplest digital element possible: a single bit. This bit is called a cell, and its value (0 or 1) is called its state. Working with such simple elements will help illustrate the details behind how complex systems operate, and it will offer an opportunity to elaborate on some programming techniques that apply to code-based projects. Building cellular automata will also set the stage for the rest of the book, where I’ll increasingly focus on systems and algorithms rather than vectors and motion—albeit systems and algorithms that I can and will apply to moving bodies.

What Is a Cellular Automaton?

A cellular automaton (cellular automata plural, or CA for short) is a model of a system of “cell” objects with the following characteristics: