Promotional shots for Contemporary Music Festival 2014 Eduardo R Miranda, Professor of Computer Music

This page is an explanation of the basic mechanics of Game of Life.

As Miranda describes it, “Game of Life is a two-dimensional cellular automaton created by John Conway, among other descriptions a recognized expert in recreational mathematics.” He quotes Greg Wilson in writing that “Conway was fascinated by the way in which a combination of a few simple rules could produce patterns that would expand, change shape or die out unpredictably. He wanted to find the simplest possible set of rules that would give such an interesting behavior.”

Miranda uses it to generate musical information: “Game of Life can be thought of as an abstract model of an environment with interacting simple life forms … In effect, the only action performed by the Game of Life’s ‘agents’ is to become alive, survive, or die as time progresses, depending upon the conditions of their abstract environment.”

He continues, “My use of it consists of a matrix of 576 cells (24 x 24), each of which can be in one of two possible states: alive (represented by the number one) or dead (represented by the number zero). Living cells are colored black and dead cells are colored white.”

By contrast, for simplicity of explanation, the following examples use a matrix of 9 cells (3 x 3). The state of a cell is determined by so-called transition rules that determine the state of its eight nearest neighboring cells. Here at the examples:

Rule 1.
Birth. In this example, the central cell is dead (white) at time t (the left grid represents time t). According to the transition rule, if exactly three of its neighbors are alive (black), it too becomes alive (black) at time t + 1 (the right grid represents time t + 1).

Example 1Example 1

Rule 2.
Death by overcrowding. In this example, the central cell is alive (black) at time t. According to the transition rule, if four or more of its neighbors are alive, it will die (white) at time t + 1.

Example 2Example 2

Rule 3.
Death by seclusion. In this example, the central cell is alive at time t. According to the transition rule, if it is lonely, i.e. if it has just one or no live neighbors, it will die at time t + 1.

ex4Example 3

Rule 4.
Survival. In this example, the central cell is alive at time t. If it has two or three live neighbors, according to the transition rule it will remain alive at time t + 1.

x4Example 4

How does Miranda use these procedures? He writes, “In order to generate music with Game of Life, I invented a method to represent musical notes as points on a Cartesian plane …”






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Game of Life
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