Module 6: Explorables and Discrete Models

Pair Presentations, Cellular Automata and Traffic

This module has two parts. First, you present an interactive model in pairs, the explorables session. Then you switch from continuous fields to fully discrete systems: time, space and state all take discrete values. You study elementary cellular automata, the Game of Life and the Nagel-Schreckenberg model of traffic flow (Wolfram 1983; Nagel and Schreckenberg 1992).

Session Structure

Sessions 27-28: Explorables (double session)

Explorables Presentations Preparation Checklist

Session 29: Modelling with cellular automata

Cellular Automata Wolfram Classes Special Rules and Theorems

Session 30: Laboratory, cellular automata

1D Cellular Automata Space-Time Diagrams Rule Exploration Boundary Conditions Game of Life Random Soups Practice: Cellular Automata

Session 31: Modelling traffic flow and congestion

The Nagel-Schreckenberg Model The Fundamental Diagram

Session 32: Laboratory, traffic models

Traffic Model Flow and Congestion Traffic Extensions Practice: Traffic

Learning Goals

  • Explain a published model to your peers, state its assumptions and add an extension, test or criticism of your own.
  • Encode an elementary cellular automaton rule as an 8-entry lookup table and simulate it with synchronous updates.
  • Build and interpret space-time diagrams, and compare how rule choice and initial condition affect long-run behaviour.
  • Classify space-time diagrams with the four Wolfram classes and discuss the limits of that classification.
  • Explain how boundary conditions and finite lattice size shape long-run behaviour.
  • Implement the Game of Life and identify still lifes, oscillators and gliders.
  • Represent traffic with occupancy and speed arrays, and implement the Nagel-Schreckenberg rules.
  • Measure density and flow, estimate the fundamental diagram, and explain how local agent behaviour creates stop-and-go waves and jams.
  • Decide which model extensions change the fundamental diagram qualitatively.

References

Nagel, Kai, and Michael Schreckenberg. 1992. “A Cellular Automaton Model for Freeway Traffic.” Journal de Physique I 2 (12): 2221–29. https://doi.org/10.1051/jp1:1992277.
Wolfram, Stephen. 1983. “Statistical Mechanics of Cellular Automata.” Reviews of Modern Physics 55 (3): 601–44. https://doi.org/10.1103/RevModPhys.55.601.