Wednesday, July 03, 2013

[rkraqgrb] Small infinite growth

We explore textual representations of small patterns that result in infinite growth in Conway's game of life (link is the source of the images).  All of these patterns become Corderman's switch-engine puffer.

Infinite Life
The 10-cell minimal population pattern as a list of coordinates:
0 1
1 0
1 1
1 2
3 1
3 2
3 3
5 4
5 5
7 5
What is a minimal traveling salesman path through all the points using the Manhattan distance metric?  Then the set can be encoded as 9 delta vectors.

Infinite Life
The 1-cell-thick pattern run-length encoded with live cells alternating with dead cells: 8 1 5 3 3 6 7 1 5.  There are probably shorter instances of infinite growth minimizing textual length of RLE, probably sum of logarithms.

Infinite Life
The 5-by-5 pattern read in rows as binary numbers, then translated to letters from A=0 through Z=25: VWYBX.  We chose an orientation for which values 26 through 31 do not occur.

Infinite Life
The minimal-area pattern, 2 cells thick, as two 12-bit binary numbers converted to decimal: 2495 3033.

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