Constant Block

In Conway's Game of Life, there are live (marked black) and dead (marked white) cells on an infinite board.

The cells transform themselves to the next moment by interacting with its eight neighbors, according to the following rules:

  • (Underpopulation) Any live cells with less than 2 live neighbors die.
  • (Continuation) Any live cell with 2 or 3 live neighbors continue to live.
  • (Overpopulation) Any live cell with more than 3 live neighbors die.
  • (Reproduction) Any dead cell with exactly three neighbors becomes alive.

A Demonstration of The Rules A Demonstration of The Rules

Can there be a block of cells, not all dead, which does not change over time?

Yes No

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2 solutions

Phillip Temple
Jul 28, 2017

A 2x2 square of live cells will only ever always have three live neighbors, and thus won't change.

You've made a typo haha

Rian Hasiando Silaen - 3 years, 10 months ago

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Updated Answer: Minor Text Fixes.

Phillip Temple - 3 years, 10 months ago
Hasmik Garyaka
Sep 8, 2017

The most common still life (i.e. that most likely to be generated from a random initial state) is the block. A pair of blocks placed side-by-side (or bi-block) is the simplest pseudo still life. Blocks are used as components in many complex devices, an example being the Gosper glider gun. The second most common still life is the hive (or beehive).

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