Warp wrote:
>   I'm a bit puzzled here. The thread starts with ellipses and then, all
> of a sudden and out of nowhere, some completely obscure and unexplained
> references are made about some mysterious "Rule 30" and something called
> a "CA", whatever that means, without nobody explaining what they mean or
> what they are referring to.

I'm pretty sure we discussed it before, but unless you're into this sort of 
math, I can see where it would be confusing.

CA = cellular automata.
Rule 30 is an encoding of a linear CA's rules as a binary number. You can 
take the rules of a linear CA and express them as a truth table, then read 
the result of each combination as a binary state, giving you one bit for 
each possible input combination the CA will consider. The rule number (30 in 
this case) tells you if you interpret the CA's result as a binary number, it 
turns out to have the value 30.

For a similar example, "not" is rule 2, "AND" is rule 1, OR is rule 7, and 
XOR is rule 6.

XOR:
0 x 0 = 0
0 x 1 = 1
1 x 0 = 1
1 x 1 = 0
rule 6 -^

Wolfram constructed a pattern that uses rule 30 to emulate a turing machine 
if you read the results down the page as the linear CA calculates across the 
page. That's cool, except he has to put an infinite number of "clock bit" 
patterns on the line first. I'm not sure that's legit, since rule 30 doesn't 
actually generate its own clock pulses. If he had a rule that created the 
clock pulses on an otherwise uniform starting state and which then changed 
over to rule 30 afterwards, I'd have no complaints.

But it's like saying "I have this Turing machine that emulates in only 2 
states all other turing machines. But only if you start out on a tape where 
each prime numbered cell has a non-empty symbol on it first."

-- 
Darren New, San Diego CA, USA (PST)
   Forget "focus follows mouse." When do
   I get "focus follows gaze"?

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