The Counting Thread - Page 5

cailin maith · 11th February 2008, 11:12

50

PRC1964 · 11th February 2008, 11:14

Ardesco · 11th February 2008, 11:16

BrilloPad · 11th February 2008, 11:42

PRC1964 · 11th February 2008, 11:45

Rule 54 is one of the elementary cellular automaton rules introduced by Stephen Wolfram in 1983 (Wolfram 1983, 2002). It specifies the next color in a cell, depending on its color and its immediate neighbors. Its rule outcomes are encoded in the binary representation http://mathworld.wolfram.com/images/...54/Inline1.gif.

Starting with a single black cell, successive generations http://mathworld.wolfram.com/images/...54/Inline2.gif, 1, ... are given by interpreting the numbers 1, 7, 17, 119, 273, 1911, 4369, 30583, ... (Sloane's A118108) in binary, namely 1, 111, 10001, 1110111, 100010001, ... (Sloane's A118109). The decimal value of the http://mathworld.wolfram.com/images/...54/Inline3.gifth iteration is given in closed form by

BrilloPad · 11th February 2008, 11:46

PRC1964 · 11th February 2008, 11:48

http://www.56.com/

(May not be sfw)