hypertext dissertation - by Robyn Stuart


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QUOTE 32 from:
Lucas, C. (1997a) 'Automata - Agents of Life Within' . Available from:, accessed on 6/05/05

Cellular Automata

If we assume automata to be fixed (not mobile) we can equate them with cells in a structure. This structure could be living, molecular, mechanical - any form in fact. This gives us a Cellular Automata (CA), a structure that, whilst static in physical form and space, can exhibit dynamic behaviour in time - emergent <emerge.htm> order.
Let's take a simple case, a board divided into small squares (a lattice). Each square can be in either of two states (black or white). We colour each of the squares initially either black or white at random. For each square, if it starts black then it stays black if two or three of its 8 neighbours (including diagonals) are also black, otherwise it changes to white. If it starts as white then it stays white unless exactly three of the neighbours are black, then it changes to black. We evaluate the current state of all the squares and determine what they will do next, then we change the whole board accordingly. This is called a step (or cycle, or generation). We then repeat the exercise over and over (iterate). The pattern in time that we see of changing square colours proves hard to predict, although every square follows the same simple rules. We can extend such systems to have many individual states per cell, to have transition rules of any complexity and to depend on non-neighbouring events for these rules. All are Cellular Automata.
The Game of Life
The example I gave, despite its simplicity, is one of the most powerful known and is usually called the "Game of Life" after its inventor John Conway. The rules are clearer if we regard the black cells as alive. Thus having 3 alive neighbours allows a new birth (parents + midwife!), having over 3 gives death from overcrowding, and under 2 death from exposure


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