Beauty in maths topic

Emergence and Chaos

Emergence is where simple rules create behaviour that feels unexpectedly rich, chaotic or alive.

live pages

prototype tools

planned ideas

What this area includes

Iteration, feedback and recurrence

Chaos, bifurcation and sensitivity

Cellular automata and local update rules

Patterns that appear without central control

How can a tiny rule generate complex structure?

When does prediction become difficult?

What changes when we move from one object to many?

These are the pages currently available to open from this topic.

Explore one-dimensional rules and patterns from simple local updates.

Iterate a simple recurrence and explore fixed points, cycles and chaos.

Explore still lifes, oscillators, gliders and emergence from local rules.

A portal for connected mathematical explorations: pattern, surprise, structure, nature and emergence.

Rhythm, tuning, symmetry, timing, pattern and musical structure through mathematics.

Self-similarity, recursion, iteration, dimension and patterns that repeat at different scales.

Start by experimenting: change one parameter, watch what survives, and look for the moment the behaviour changes character.