July 2018
Beginner
198 pages
4h 33m
English
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Chapter 5. Cellular Automatons
A cellular automaton (CA) is a model of a world with very simple physics. “Cellular” means that the world is divided into discrete chunks, called cells. An “automaton” is a machine that performs computations—it could be a real machine, but more often the “machine” is a mathematical abstraction or a computer simulation.
This chapter presents experiments Stephen Wolfram performed in the 1980s, showing that some cellular automatons display surprisingly complicated behavior, including the ability to perform arbitrary computations.
I discuss implications of these results, and at the end of the chapter I suggest methods for implementing CAs efficiently in Python.
A Simple CA
Cellular automatons1 are governed by rules that determine how the state of the cells changes over time.
As a trivial example, consider a cellular automaton (CA) with a single cell. The state of the cell during time step i is an integer, xi. As an initial condition, suppose .
Now all we need is a rule. Arbitrarily, I’ll pick , which says that during each time step, the state of the CA gets incremented by 1. So this CA performs a simple calculation: it counts.
But this CA is atypical; normally the number of possible states is finite. As an example, suppose a cell can only have one of two states, 0 or 1. For a 2-state CA, we could write a rule like , where % is the remainder (or modulus) operator.
The behavior of this CA is simple: it blinks. That is, the state of ...
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I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.