This is from an old Roger king post:

Cellular Automata Rhythms

Applying Stephen Wolfram's addition MOD2 rules
to a logical drum instrument allows you to hear
cellular automata patterns. Wolfram's rules:
        0 + 0 = 0
        0 + 1 = 1
        1 + 1 = 0
 apply to neighbor cells of the previous generation.
For an 8 piece instrument you apply Wolfram's
three rules across an 8-bit matrix: You pick an
arbitrary initial state, but keep the lambda
factor in mind, i.e. only three cells in the
initial state of the example are on (1):

time    eight drum sounds
0       0  1  0  0  1  0  0  1
1       1  0  1  1  0  1  1  0
2       0  0  1  1  0  1  1  1
3       0  1  1  1  0  1  0  1
4       1  1  0  1  0  0  0  0
5       1  1  0  0  1  0  0  0
6       1  1  1  1  0  1  0  0
7       1  0  0  1  0  0  1  0
8       0  1  1  0  1  1  0  1
9       1  1  1  0  1  1  0  0
10      1  0  1  0  1  1  1  0
11      0  0  0  0  1  0  1  1
12      0  0  0  1  0  0  1  1
13      0  0  1  0  1  1  1  1

14      0  1  0  0  1  0  0  1
*****The initial state repeats after 13 generations.

I don't understand how the rules are being applied.  If someone could
enlighten me, I would be very grateful.

Cheers
Arne


"The DOLPHIN, desiring to sleep, floats atop the water;having fallen
asleep,he sinks slowly to the floor of the sea;being awakened by striking
the bottom,he rises again to the surface. Having thus risen, he falls
asleep again,descends once more to the bottom, and revives himself anew in
the same fashion. He thus enjoys his rest in motion."

Arne Hanna wrote:
> time    eight drum sounds
> 0       0  1  0  0  1  0  0  1
> 1       1  0  1  1  0  1  1  0
> 2       0  0  1  1  0  1  1  1
> 3       0  1  1  1  0  1  0  1

It looks (though I haven't checked the whole grid) that the update
rule is
        x_i = x_i-1 xor X_i+1
i.e. like this:

> 4       1  1  0  1  0  0  0  0
              \  \/  /
               \ /\ /
> 5       1  1  0  0  1  0  0  0

Kinda strange way to define a rule: when N is even (as here), it
partitions the system into two subgrids (like red and black on a
checkers board) that never interact.

-- 
     Eli Brandt  |  eli+@cs.cmu.edu  |  http://www.cs.cmu.edu/~eli/