Social systems produce emergent complexity from simple agent rules —
bank runs from rational fear, segregation from mild preference, city
growth from local density incentives. These eight simulations show the
hidden mechanics of economic and social phenomena.
8
simulations
4
sub-topics
ABM
core method
EN + UK
languages
Financial Systems & Market Dynamics
Financial crises are rarely caused by fundamentally insolvent
institutions — they are often coordination failures. In the bank run
model, each depositor's decision to withdraw depends on their
expectation of what others will do, creating a self-fulfilling
prophecy that is impossible to prevent with purely economic tools.
Agents observe queue length at a bank. When withdrawal queues
exceed a psychological threshold, rational agents join the queue —
a coordination game with two Nash equilibria. Vary reserve ratio
and information transparency.
SHA-256 hash difficulty in real time. Adjust the number of miners
and difficulty target; the simulation shows hashrate, expected
block time and how difficulty retargeting keeps the 10-minute
interval stable.
Proof-of-work · hash distribution
Key insight: Nash Equilibrium in Bank Runs
There are two Nash equilibria: all depositors wait (stable bank) or
all withdraw simultaneously (run). Which equilibrium occurs depends
entirely on the initial coordination signal — sunspot theory
explains why genuine crises can start with no fundamental cause.
Urban Growth & Spatial Society
Cities are far-from-equilibrium systems. Small differences in early
population distribution create path-dependent spatial structures. The
city growth cellular automaton uses only local density rules but
produces organic-looking urban cores, suburbs and sprawl patterns that
match real satellite imagery statistics.
Each cell becomes urban if a quorum of its eight Moore neighbours
are urban. Vary the threshold from 2 to 6 and watch the city
crystallise slowly (high threshold) or explode into sprawl (low
threshold).
Why buses arrive in pairs. A single bus running slightly late
picks up more passengers, slows down further, and the next bus
picks up fewer — a positive feedback loop that bunches the fleet
despite a rigid timetable.
ABM · positive feedback
Decision Theory & Game Theory
Decision trees and game-theoretic models underlie every strategic
interaction from voting to auctions. The decision tree simulation
implements a CART-style learner that builds a binary classification
tree from labelled data, and lets you probe where the decision
boundary sits.
Interactive binary classifier built in real time. Choose a dataset
(moons, circles, blobs), drag training points, and watch the
Gini-impurity-minimising tree restructure. Visualises information
gain at each node split.
Monte Carlo simulation of basic strategy vs. dealer. Run 100,000
hands to measure the house edge (typically −0.5%) and verify
optimal stand/hit/double decisions that match the four-deck basic
strategy table.
Animated walkthrough of public-key agreement: Alice and Bob
exchange colours (modular exponentiation) in the open without
revealing the shared secret. The discrete logarithm problem is
what makes it hard to reverse.
Encrypt and decrypt text with shift (Caesar) or polyalphabetic
(Vigenère) ciphers. Frequency analysis visualisation shows why
Caesar is trivially breakable while Vigenère survives longer — but
not indefinitely.
Substitution cipher · frequency analysis
Core Algorithms in Economics & Society Simulations
Emergent complexity: Every simulation in this
category produces macro-level phenomena (bank panics, segregated
cities, traffic bunching) from micro-level rules that contain no
mention of the macro phenomenon. This is the central insight of
agent-based modelling — and it cannot be understood from the
equation alone.