Ants, Circle Pits & Peter Jackson*

*and tangentially related mathematics

Today's Goals

  1. Understand what self-organisation is
  2. Reason about its evolutionary advantages
  3. Think mathematically about self-organisation
  4. Consume cake
Theorem 1: Pictures > Words

Proof of Theorem 1:

Self-organisation is the spontaneous emergence of large-scale structure from the interactions between individuals.

Moreover, interactions are executed using only local information, without reference to the global pattern.

Today's Goals

  1. Understand what self-organisation is
  2. Reason about its evolutionary advantages
  3. Think mathematically about self-organisation
  4. Consume cake

Benefits of grouping

  • Defence against predation
    • Many-eyes theory
    • Confusion effect
    • Dilution effect
  • Energy conservation
    • Heat conservation
    • Aerodynamics

Dangers of grouping

Dangers of grouping

Dangers of grouping

  • Getting stuck in a circle pit
  • Increased risk of disease and parasitism
  • Being featured in the daily mail

Today's Goals

  1. Understand what self-organisation is
  2. Reason about its evolutionary advantages
  3. Think mathematically about self-organisation
  4. Consume cake

Where does the maths fit in?

  • Model the interactions between individuals using "self-propelled particle models"
  • Interactions include behaviours such as:
    • Repulsion
    • Alignment
    • Attraction
  • Models have shown that complex behaviours can arise from simple interaction rules

Zonal models

Boids (1987)

Peter Jackson & Massive

  • Massive (multiple agent simulation system in virtual enviornment)
  • Developed for Peter Jackon's Lord of the Rings trilogy
  • Used to animate intricate battle scenes

Recent applications

Future goals...

Stephen Regelous, the lead developer of Massive, has since been awarded an Emmy award and an Academy award

Today's Goals

  1. Understand what self-organisation is
  2. Reason about its evolutionary advantages
  3. Think mathematically about self-organisation
  4. Consume cake...
Thanks for (hopefully) listening