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First differences of A267190, which has much more information.

The structure looks like a tree which arises from one of the four spokes of the structure of the cellular automaton of A267190.

a(n) is the total number of ON cells after n-th stage.

For n >> 1 the structure looks like a square which is rotated 45 degrees.

First differs from A161336 at a(17), where A161336 is a version of A161330 (the snowflake cellular automaton).

First differs from A266534 at a(16), where A266534 is a version of A151895.

First differs from A266536 at a(13), where A266536 is a version of A170896 (the Schrandt-Ulam cellular automaton).

From Omar E. Pol, Oct 16 2017: (Start)

The graph of both A266536 and this sequence are very similar.

For n >> 1, it appears that A266534(n) < A161336(n) < a(n) < A266536(n).

The graphs of these four sequences are similar, and the behavior looks like percolation.

It appears that there are no recurrences in these four sequences. Thus it appears that there are no recurrences in A151895, A161330, A267190 and A170896. (End)

The cells are the squares of the standard square grid.

Cells are either OFF or ON, once they are ON they stay ON, and we begin in generation 1 with 1 ON cell.

Each cell has 4 neighbors, those that it shares an edge with. Cells that are ON at generation n all try simultaneously to turn ON all their neighbors that are OFF. They can only do this at this point in time; afterwards they go to sleep (but stay ON).

A square Q is turned ON at generation n+1 if:

a) Q shares an edge with one and only one square P (say) that was turned ON at generation n (in which case the two squares which intersect Q only in a vertex not on that edge are called Q's "outer squares"), and

b) Q's outer squares were not considered (that is, satisfied a)) in any previous generation, and

c) Q's outer squares are not prospective squares of the (n+1)st generation satisfying a).

Originally constructed in an attempt to explain the Holladay-Ulam CA shown in Fig. 2 of the 1962 Ulam article. However, as explained on page 222 of that article, the actual rule for that CA (see A151906, A151907) is different from ours.

A170896 and A267190 are also closely related cellular automata.

A151895 and A267190 first differ at n=17, when A267190 turns (12,2) ON even though its outer square (11,1) was considered (not turned ON) in a previous generation. - David Applegate, Jan 30 2016

The cells are the squares of the standard square grid.

Cells are either OFF or ON, once they are ON they stay ON, and we begin in generation 1 with 1 ON cell.

Each cell has 4 neighbors, those that it shares an edge with. Cells that are ON at generation n all try simultaneously to turn ON all their neighbors that are OFF. They can only do this at this point in time; afterwards they go to sleep (but stay ON).

A square Q is turned ON at generation n+1 if:

a) Q shares an edge with one and only one square P (say) that was turned ON at generation n (in which case the two squares which intersect Q only in a vertex not on that edge are called Q's "outer squares"), and

b) Q's outer squares were not turned ON in any previous generation.

c) In addition, of this set of prospective squares of the (n+1)th generation satisfying the previous condition, we eliminate all squares which are outer squares of other prospective squares.

A151895, A151906, and A267190 are closely related cellular automata.