Pattern · Still life
The Block
Four cells in a 2×2 square. Nothing happens to it, ever, once it forms — and that stability is exactly why the block is the most common still life to emerge from a random soup in Conway's Game of Life.
The Math Behind Its Stability
Each of the block's 4 cells has exactly 3 living neighbors — the other 3 cells that make up the square. Under Conway's rule, a living cell survives with 2 or 3 living neighbors, so all 4 cells survive, every generation, unchanged. Meanwhile, none of the empty cells touching the block's edges or corners have exactly 3 living neighbors (the ones diagonally adjacent have only 2), so none of them are born either. The result is a genuine fixed point: apply the rule, and you get back exactly what you started with.
Why It Matters
The block is the simplest possible demonstration that Conway's Game of Life doesn't force everything into constant motion — stability is baked into the rule just as much as change is. It's also a practical nuisance and a practical tool at once: blocks tend to accumulate as "debris" left behind by more complex interactions, cluttering a simulation, but they're also deliberately used as fixed reference markers or blockers in engineered patterns, specifically because nothing needs to be done to keep them in place.
See It Live
Open the block pre-loaded in Cellscape and press play — watch the generation counter climb while the pattern itself never moves a single cell.
Frequently Asked Questions
Why doesn't the block ever change?
Each of the block's 4 cells has exactly 3 living neighbors (the other 3 cells in the square), satisfying Conway's survival condition (2 or 3 neighbors) every single generation. None of the 4 empty cells directly touching the block have exactly 3 living neighbors, so none of them are born either — the entire configuration is a fixed point of the rule.
Is the block the most common still life?
Yes — it's statistically the most frequently occurring still life to emerge from random starting conditions in Conway's Game of Life, more common than the beehive, loaf, boat, or tub.
Do other Life-like rules also have a stable block?
Only if the rule's survival condition includes 3 (since every block cell has exactly 3 neighbors) and its birth condition excludes 2 (since the block's diagonal-adjacent empty cells have exactly 2 neighbors). Rules that differ on either count will see a block collapse, grow, or transform.
Read more about still lifes and Game of Life mechanics in the complete guide, or browse the full pattern & rule gallery.