From: Morton Goldberg <m_goldberg@...>
Date: 2007-08-11T09:02:52+09:00
Subject: Re: [QUIZ] Cellular Automata (#134)

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On Aug 10, 2007, at 8:53 AM, Ruby Quiz wrote:

> Here's the table for the "rule 30" automaton:
>
> 	+-----------------------------------------------------------------+
> 	| Neighborhood    | 111 | 110 | 101 | 100 | 011 | 010 | 001 | 000 |
> 	+-----------------------------------------------------------------+
> 	| New Center Cell |  0  |  0  |  0  |  1  |  1  |  1  |  1  |  0  |
> 	+-----------------------------------------------------------------+
>
> The first row is the same for this whole family of automata.  It  
> represents the
> "neighborhood" of the cell currently being examined, which includes  
> the cell
> itself and one cell to either side of it.  The current values of  
> those cells,
> ones being on and zeros being off, can be used to determine the new  
> value for
> this cell in the next discreet step of time.
>
> That new value comes from the bottom row.  This row is generated by  
> taking the
> rule number, 30 in this case, in binary form.  11110 is 30 in  
> binary, so we just
> pad the right side with zeros and we have our table.

I'd like to add a little to this quiz description. The cellular  
automaton James describes is sometimes referred to as the Wolfram  
automaton because Stephen Wolfram has studied and written extensively  
on it. There is a good discussion of this problem at

      http://mathworld.wolfram.com/ElementaryCellularAutomaton.html

IIRC, the rule 30 automaton is famous for being chaotic. It looks  
like this.


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Above picture made with Mathematica, not Ruby.

Regards, Morton
--Apple-Mail-9-177410276--