Synchronous cell garden
Calculate a new generation without allowing early changes to influence later cells.
Adult planning suggestion: about9–12 · Logic & rule checking
- Players
- 2–4 per group
- Time
- 15–25 minutes
- Materials
- Two 5×5 grids, three large counters, pencil.
Prepare
On the old grid mark B3,C3,D3 alive; all other cells are dead. Use columns A–E and rows 1–5. Cells outside the board are always dead: edges do not wrap. Keep the second grid empty for the next generation.
Play
For each cell count its eight neighbouring positions on the old grid, including diagonals. A live cell survives with two or three live neighbours; otherwise it dies. A dead cell is born with exactly three live neighbours. Write all results on the new grid, never on the grid being counted.
Worked example
The starting horizontal line B3,C3,D3 becomes C2,C3,C4. On the next complete update it returns to B3,C3,D3. C3 survives with two neighbours; C2 is born from three old neighbours. Updating B3 first and counting its changed state for C3 is an error.
Finish and check
Swap old/new only when all 25 cells have been decided. Verify two complete generations and describe the repeating pattern. There is no biological claim and no requirement to search for a stable winning board. Stop after four generations or a repeated whole board.
Adaptation and limits
Use ten trios for thirty learners: counter, writer, auditor. Shade squares rather than use small loose counters when needed. Keep two physically distinct sheets. A simulation rule is not evidence that this activity improves a child’s intelligence or predicts living populations.
Purpose, observation and provenance
Within this activity: Calculate a new generation without allowing early changes to influence later cells.
Ask which generation was used for neighbour counts and include diagonal neighbours.
Our rules, examples and printable diagrams are separately prepared. The earliest inventor of the broader mechanism is not established here.
Math.com — The Game of Life — Rule background for Conway’s cellular automaton; our finite board and worksheet are separately prepared.
Age bands are planning suggestions. Goals describe observable actions, not measured long-term gains or institutional endorsement.
Free alternative: Copy the supplied grids, labels and cards onto reused paper. No specialist product is needed. Adults may prepare pieces or act as a scribe.
Printable materials
Preview at 100% scale, with browser headers and footers off. Cut with suitable help. Keep host keys separate. This is a manual tabletop kit, not an online opponent, automatic judge or solver.
Player materials · Synchronous cell garden
Old generation live: B3 C3 D3. Two blank 5×5 boards follow.
Cell ___ / old live? ___ / old live neighbours ___ / next live? ___ .
Next generation
Player record · keep the host key separate
| Cell | Old state | Old neighbours | New state |
|---|---|---|---|
| ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ |
Host key · separate from players
Generation 1 C2 C3 C4; generation 2 B3 C3 D3. Outside is dead.
Run the round
On the old grid mark B3,C3,D3 alive; all other cells are dead. Use columns A–E and rows 1–5. Cells outside the board are always dead: edges do not wrap. Keep the second grid empty for the next generation.
For each cell count its eight neighbouring positions on the old grid, including diagonals. A live cell survives with two or three live neighbours; otherwise it dies. A dead cell is born with exactly three live neighbours. Write all results on the new grid, never on the grid being counted.
The starting horizontal line B3,C3,D3 becomes C2,C3,C4. On the next complete update it returns to B3,C3,D3. C3 survives with two neighbours; C2 is born from three old neighbours. Updating B3 first and counting its changed state for C3 is an error.
Swap old/new only when all 25 cells have been decided. Verify two complete generations and describe the repeating pattern. There is no biological claim and no requirement to search for a stable winning board. Stop after four generations or a repeated whole board.
Use ten trios for thirty learners: counter, writer, auditor. Shade squares rather than use small loose counters when needed. Keep two physically distinct sheets. A simulation rule is not evidence that this activity improves a child’s intelligence or predicts living populations.