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WillTeachMaths

Thinking-first maths tools

Emergence and cellular automata

Conway's Game of Life turns tiny local rules into living-looking behaviour.

This MVP explores a two-dimensional cellular automaton. Each cell only knows how many neighbours it has, yet the whole grid can produce still lifes, oscillators, gliders and patterns that feel organised.

The aim is not to win a game. It is to notice how local rules can create global behaviour, and to enjoy the strange process of trying, watching, adjusting and trying again.

Conway's Game of Life

Local rules. Global behaviour.

Every cell follows the same tiny rule: survive with two or three neighbours, be born with exactly three, otherwise become empty.

0

generation

5

live cells

180

ms per step

Starting patterns

What to notice

Still lifes settle and stop changing.

Oscillators repeat after a fixed number of generations.

Gliders move across the grid without any cell deciding to move.

Joy in the process

The point is not just to finish. It is to notice, test and return.

These tools are invitations to explore. A good mistake, a surprising pattern or a question you cannot yet answer is part of the work, not a failure of it.

The challenge is deliberate: the site should support thinking, not remove the need for it.

Predict the fate of a pattern before running it.
Try to create a stable pattern that does not change.
Try to create a repeating pattern that stays in one place.
Look for behaviour that appears to move even though no cell itself moves.

Guided exploration

Treat each pattern as a small mathematical experiment.

Before pressing run, predict whether the pattern will die, stabilise, repeat or travel.
Click a few cells by hand. How small can a pattern be and still do something interesting?
Compare a blinker and a glider. Why does one stay in place while the other travels?
Run the Gosper glider gun and look for the repeated structure that creates moving gliders.

Future extensions

Add wrapping boundaries so the grid behaves like a torus.
Add a pattern library with still lifes, spaceships and oscillators.
Add generation history and population graphs.
Add a challenge mode where students design a target behaviour.