What is the cellular automaton shown as loading screen on Wolfram Alpha?

Question

When entering a query in Wolfram Alpha you usually see an animation shown for a couple of seconds before the result is displayed. It seems to be a cellular automaton with 3 distinctive states.

I would like to know what this particular automaton is called, and where I can find informations about it. Thank you!

Answer 1

It's a cellular automaton with 5 states. The rule is 3457/357/5 using Golly's notation.

It has 5 states: 0, 1, 2, 3, 4. In each step, cells behave as follows:

• 0 -> 1 if 3, 5 or 7 of its eight neighbors are 1, or 0 otherwise
• 1 -> 1 if 3, 4, 5 or 7 of its eight neighbors are 1, or 2 otherwise
• 2 -> 3
• 3 -> 4
• 4 -> 0

Here is an oscillator with period 15:

Here is a puffer with period 24:

Answer 2

It's Conway's Game of Life. There's a very good wikipedia article on it, I suggest you go take a look there.

Answer 3

Here is a very fast matlab implementation of Wolfram Alpha's cellular automation:

rng(38); % 31 lasts a while / 38 has two oscillators / 39 lasts longer /42 lasts muuuuch longer
X = randi([0 4],30,40);

[a,b] = size(X);

initialFig = figure('toolbar','none','menubar','none');
[x,y]      = meshgrid(1:b,1:a);
scathandle = scatter(x(:),y(:),20*X(:)+1,X(:)+1,'filled');
colormp    = linspace(1,0.4,5)'*[1 1 1]; colormap(colormp);
axis([0 b+1 0 a+1]); axis off; set(gca,'position',[0 0 1 1]); set(gcf,'toolbar','none','menubar','none','color','w','numbertitle','off','name',''); axis equal;

n = [a 1:a-1]; % The previous row
s = [2:a 1];   % The next row
e = [2:b 1];   % The next column
w = [b 1:b-1]; % The previous column

[A,B,C] = meshgrid(1:a,1:b,[0 1]);

Xnew = X;
while 1
    N = (X(n,:)==1) + (X(s,:)==1) + (X(:,e)==1) + (X(:,w)==1) + (X(n,e)==1) + (X(n,w)==1) + (X(s,e)==1) + (X(s,w)==1); % Look for the total number of nieghbours == 1

    Xnew(X>=2) = mod(X(X>=2)+1,5); % if state is greater or equal to 2, increment 1 modulo 5
    Xnew(X==0) = (N(X==0)==3 | N(X==0)==5 | N(X==0)==7); % if state is 0, turn to 1 when neighbours equal 3,5 or 7. Leave 0 otherwise.
    Xnew(X==1) = 2 - (N(X==1)==3 | N(X==1)==4 | N(X==1)==5 | N(X==1)==7); % if state is 1, turn to 2 unless neighbours equal 3, 4 or 5. In the latter case, leave 1.
    X = Xnew;
    set(scathandle,'cdata',X(:)+1,'sizedata',20*X(:)+1);
    drawnow;

    if ~ishandle(initialFig)
        return
    end
end

I guess that, at any moment, someone will find this useful (somehow).