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Page's Complex Adaptive Systems

142 paired simulations from Scott E. Page's Model Thinking — Agent-Based Models and System Dynamics for the same families of problems, with a deluxe second pass of visually upgraded variants.

71 ABM · 71 SD · 142 total
Two lenses on emergence. Scott E. Page argues that complex adaptive systems are best understood by deploying many models. Agent-based models grow macro patterns from heterogeneous agents and local rules — useful when discreteness, networks, and individual differences matter. System dynamics use stocks, flows, and feedback to make aggregate behaviour legible — useful when continuous quantities, delays, and reinforcing loops dominate. Both lenses appear repeatedly in Page's curated examples: Schelling tipping, beehive thresholds, sand piles, predator-prey, epidemics, growth, and diffusion. Pair them and the difference between micro mechanism and macro structure becomes visible.

Agent-Based Models

ABM

Heterogeneous agents, local interactions, emergent macro patterns. Page's foundational examples of how simple rules produce surprising aggregates.

01

Schelling Segregation

Mild same-type preferences tip a mixed neighborhood into segregated patches.

ABM
02

Standing Ovation

Heterogeneous quality thresholds and peer effects ignite — or fail to ignite — an ovation.

ABM
03

Granovetter Threshold Riot

Distribution of riot thresholds determines collective participation and tipping.

ABM
04

Conway's Game of Life

Two-state cellular automaton with universal computation lurking in B3/S23 rules.

ABM
05

Bak-Tang-Wiesenfeld Sand Pile

Self-organized criticality: avalanches whose size distribution follows a power law.

ABM
06

Forest Fire (Drossel-Schwabl)

Trees grow, lightning strikes, fires sweep — a canonical SOC model.

ABM
07

Beehive Temperature Regulation

Diverse temperature thresholds keep the hive thermostat tighter than uniform thresholds do.

ABM
08

Beehive Defense Thresholds

Diversity of activation thresholds boosts hive responsiveness to threats.

ABM
09

Axelrod Culture Dissemination

Local imitation produces stable cultural domains — and persistent borders.

ABM
10

Percolation Threshold

Connectivity through a random lattice undergoes a sharp phase transition near p≈0.593.

ABM
11

Spatial SIR Epidemic

Contagion spreads through a 2D contact lattice with recovery and immunity.

ABM
12

Boids Flocking

Reynolds' three rules — separation, alignment, cohesion — produce flocks.

ABM
13

Firefly Synchronization

Pulse-coupled oscillators self-synchronize through phase nudges.

ABM
14

Spatial Prisoner's Dilemma

Cooperators and defectors play neighbors; clusters of cooperation persist.

ABM
15

Sugarscape

Epstein-Axtell agents harvest a regrowing landscape — and inequality emerges.

ABM
16

Voter Model

Each agent copies a random neighbor; opinion domains coarsen toward consensus.

ABM
17

El Farol Bar / Minority Game

Inductive predictors converge on the carrying-capacity equilibrium of a coordination game.

ABM
18

Polya Urn Process

Path-dependent sampling: early draws lock in proportions across runs.

ABM
19

Spatial Rock-Paper-Scissors

Three-strategy cyclic dominance yields rotating spirals — non-transitive coexistence.

ABM
20

Wolf-Sheep-Grass

NetLogo's classic three-trophic ecology with energy budgets and reproduction.

ABM
21

Random Walks & Drunkards

Many random walkers reveal diffusion, first-passage, and the central limit theorem.

ABM

System Dynamics

SD

Stocks, flows, and feedback loops. Page's lens for problems where aggregate continuous variables and delays drive the dynamics.

22

Lotka-Volterra Predator-Prey

Continuous oscillations from coupled ODEs — the SD twin of wolf-sheep.

SD
23

SIR Compartmental Epidemic

Stocks of S, I, R flow with rate equations dβSI/N and γI.

SD
24

SEIR Epidemic

Adds an exposed compartment — incubation delays change the curve shape.

SD
25

Logistic Population Growth

Carrying capacity caps exponential growth via a balancing loop.

SD
26

Bass Diffusion of Innovation

Innovators p plus imitators q produce the classic adoption S-curve.

SD
27

Bathtub Stock & Flow

Inflow vs outflow — Sterman's litmus test for stock-flow intuition.

SD
28

Bullwhip Beer Game

Order delays amplify upstream variance through a four-tier supply chain.

SD
29

Tragedy of the Commons

A renewable resource collapses under unconstrained extraction.

SD
30

Lorenz System

Three coupled ODEs — sensitive dependence on initial conditions made visible.

SD
31

Solow Growth Model

Capital, labour, depreciation and technology in a single feedback diagram.

SD
32

Replicator Dynamics

Strategy frequencies follow fitness gradients — evolutionary game theory in continuous form.

SD
33

Cobweb Market Model

Lagged supply meets present demand — convergence, oscillation, or divergence.

SD
34

Limits to Growth

Population, resources, pollution and capital — Forrester's World3 in miniature.

SD
35

Goal-Seeking with Delays

Closing a gap — slowly. Long perception delays produce overshoot.

SD
36

Romeo & Juliet

Strogatz's love equations: linear feelings, nonlinear courtship.

SD
37

Aging Chain

Cohorts age through stages — demography as serial stocks.

SD
38

Romer Endogenous Growth

Knowledge accumulates and feeds back into productivity.

SD
39

Substance Adoption Loop

Reinforcing peer adoption vs balancing recovery — the addiction archetype.

SD
40

Climate Carbon Cycle

Atmosphere, ocean, biosphere stocks linked by uptake and emission flows.

SD
41

Markov Weather Chain

State-transition probabilities settle into a stationary distribution.

SD
42

Reinforcing & Balancing Loops

Side-by-side anatomy of the two atomic units of every SD model.

SD

Deluxe ABM

ABM ✦

Visually upgraded second-generation ABMs — vibrant colormaps, glow trails, multi-panel layouts, and high-density agents. Networks, continuous CAs, reaction-diffusion, active matter, swarms, and statistical mechanics.

43

Schelling — Continuous Tolerance

Beta-distributed individual tolerances; histogram + segregation timeline.

ABM ✦
44

Schelling on a Network

Watts-Strogatz small-world Schelling — rewiring changes outcomes.

ABM ✦
45

Hegselmann-Krause

Bounded-confidence opinion dynamics fan into clusters.

ABM ✦
46

Watts Threshold Cascade

Cascade size on scale-free networks; click-to-seed.

ABM ✦
47

Voter on Small-World

Network structure modulates time to consensus.

ABM ✦
48

Axelrod Cultural Drift

HSL-mapped cultures with magenta-glow boundaries.

ABM ✦
49

Wolfram 1D CA Explorer

Rules 30, 90, 110, 184, 250 in plasma colormap.

ABM ✦
50

Brian's Brain

3-state CA — electric cyan ON, magenta DYING, glow.

ABM ✦
51

Day & Night CA

B3678/S34678 — symmetric in both binary states.

ABM ✦
52

WireWorld

4-state CA — diodes, oscillators, AND gates; click to draw.

ABM ✦
53

Langton's Ant(s)

Multi-rule ants paint highways from chaos.

ABM ✦
54

Lenia

Continuous space-state generalisation of Conway — orbium organisms.

ABM ✦
55

SmoothLife

Rafler's continuous CA — soft alive blobs that crawl.

ABM ✦
56

Gray-Scott Reaction-Diffusion

Spots, worms, mazes, mitosis, coral, solitons.

ABM ✦
57

FitzHugh-Nagumo Spirals

Excitable medium with rotating spiral waves.

ABM ✦
58

Greenberg-Hastings Cyclic CA

n-state cycle producing rainbow spiral waves.

ABM ✦
59

BZ Hodgepodge Machine

Belousov-Zhabotinsky-like CA — pulsating spirals.

ABM ✦
60

Vicsek Active Matter

1500 self-propelled particles — order/disorder phase transition.

ABM ✦
61

Cucker-Smale Flocking

Distance-weighted alignment converges globally.

ABM ✦
62

Active Brownian MIPS

Motility-induced phase separation in self-propelled disks.

ABM ✦
63

Couzin Schools + Predator

Three-zone fish schooling with escape response.

ABM ✦
64

Boids with Obstacles

Reynolds boids navigating draggable obstacles.

ABM ✦
65

Ant Colony Foraging

Two pheromone fields, glowing trails between nest and food.

ABM ✦
66

Physarum Slime Mold

200K particles weave organic vein networks.

ABM ✦
67

Termite Cemetery Sorting

Stigmergic chip sorting from random scatter to neat piles.

ABM ✦
68

Dictyostelium cAMP Waves

Spiral waves drive slime-mold aggregation.

ABM ✦
69

2D Ising Model

Metropolis dynamics; phase transition at T_c≈2.27.

ABM ✦
70

q-State Potts

Multi-state generalization of Ising — domain coarsening.

ABM ✦
71

XY Model — BKT Vortices

Continuous spins; vortex/antivortex pairs at low T.

ABM ✦
72

Diffusion-Limited Aggregation

Witten-Sander fractal cluster with glowing tips.

ABM ✦
73

Eden Growth

Cluster grows via random boundary additions.

ABM ✦
74

Abelian Sandpile Mandala

Drop thousands of grains at center for fractal symmetry.

ABM ✦
75

Erdős-Rényi G(n,p)

Giant component emerges sharply at p_c=1/N.

ABM ✦
76

Watts-Strogatz Small-World

Rewiring β reveals C(β)/L(β) sweet spot.

ABM ✦
77

Barabási-Albert Growth

Preferential attachment yields scale-free degree distribution.

ABM ✦
78

Bak-Sneppen Evolution

Punctuated equilibria visible as plasma spacetime image.

ABM ✦
79

Network SIR Epidemic

Disease spreading edge-by-edge with flash transitions.

ABM ✦
80

Naming Game

Vocabulary convergence to a single global word.

ABM ✦
81

Sznajd Opinion Model

Aligned dyad converts neighbors — coarsening to consensus.

ABM ✦
82

Galam Majority Rule

Random groups vote; tipping near p_c=0.5.

ABM ✦
83

Hawk-Dove ESS

Population dynamics converge to mixed equilibrium.

ABM ✦
84

Boltzmann Wealth Exchange

Random pooling produces exponential wealth distribution.

ABM ✦
85

Yard-Sale Inequality

Even fair coins concentrate all wealth in one agent.

ABM ✦
86

Minority Game

Challet-Zhang strategy-evolution attendance.

ABM ✦
87

Particle Swarm Optimization

PSO on Rastrigin — particles converge to global best.

ABM ✦
88

Genetic Algorithm

Bit-string evolution with selection, crossover, mutation.

ABM ✦
89

Differential Evolution

DE/rand/1/bin on multimodal landscapes.

ABM ✦
90

3D Boids in a Cube

Depth-coloured flocking with rotating camera.

ABM ✦
91

Aizawa Attractor Swarm

1500 particles trace the Aizawa strange attractor.

ABM ✦
92

Reiter Snowflake CA

Hexagonal dendritic crystal growth with six-fold symmetry.

ABM ✦

Deluxe System Dynamics

SD ✦

Second-generation SD models with multi-panel time-series, phase portraits with vector fields, Poincaré sections, and causal-loop diagrams. Oscillators, chaos, ecology, epidemics, macro, climate, archetypes.

93

Van der Pol Oscillator

Limit cycle from nonlinear damping — sinusoidal to relaxation.

SD ✦
94

Duffing Driven Oscillator

Phase portrait + Poincaré section — chaos at γ=0.30.

SD ✦
95

Rössler Attractor

Single-loop strange attractor with turbo z-coloring.

SD ✦
96

Chua's Circuit

Double-scroll attractor from a piecewise-linear diode.

SD ✦
97

Driven Damped Oscillator

Resonance peak revealed by frequency sweep.

SD ✦
98

Double Pendulum

Lagrangian chaos with phase portrait + Poincaré.

SD ✦
99

Three-Body Orbits

Symplectic integration with figure-8 choreography preset.

SD ✦
100

Logistic Map Bifurcation

Cobweb + iterates + full bifurcation diagram.

SD ✦
101

Hénon Map Attractor

120K-iter glowing strange attractor.

SD ✦
102

Chirikov Standard Map

Tori-to-chaos transition on the (θ,p) torus.

SD ✦
103

Ricker Stock-Recruitment

Period-doubling cascade in fish dynamics.

SD ✦
104

Beverton-Holt

Smooth convergence vs Ricker oscillation.

SD ✦
105

Schaefer Fishery

Surplus production with MSY and overfishing collapse.

SD ✦
106

Two-Species Competition

Four regimes via competitive Lotka-Volterra isoclines.

SD ✦
107

Three-Trophic Chain

Hastings-Powell food web — limit cycles, chaos.

SD ✦
108

SEIRS Waning Immunity

Endemic oscillations; seasonal forcing toggle.

SD ✦
109

SIR with Vaccination

Herd-immunity threshold p_c = 1 − 1/R₀.

SD ✦
110

SIRD with Mortality

Adds D compartment; CFR converges to μ/(μ+γ).

SD ✦
111

Anderson-May Macroparasite

Host density vs mean parasite burden oscillations.

SD ✦
112

Ross-Macdonald Malaria

Vector-borne R₀ = ma²bc / (rμ).

SD ✦
113

Solow + Population Growth

Capital per worker steady state k* with phase line.

SD ✦
114

Solow + Exogenous Tech

Balanced growth path on log axes.

SD ✦
115

Romer R&D Growth

Endogenous knowledge growth from research labour.

SD ✦
116

Goodwin Business Cycle

Predator-prey of employment vs wage share.

SD ✦
117

Kaldor Business Cycle

Endogenous limit cycle from nonlinear investment.

SD ✦
118

Phillips Curve Dynamics

Adaptive expectations break the trade-off.

SD ✦
119

IS-LM Macro Model

Fiscal/monetary shocks shifting equilibrium.

SD ✦
120

Cobweb Adaptive Expectations

Adaptive λ stabilizes the price oscillation.

SD ✦
121

Minsky Financial Fragility

Endogenous boom-bust from debt accumulation.

SD ✦
122

Daisyworld

Black/white daisies thermoregulate the planet.

SD ✦
123

Energy Balance Climate

Snowball-warm bistability from albedo feedback.

SD ✦
124

Permafrost Methane Runaway

Reinforcing thaw loop tips climate.

SD ✦
125

Lake Eutrophication

Clear/turbid alternative stable states with hysteresis.

SD ✦
126

Strong Allee Effect

Critical population threshold A separates extinction from K.

SD ✦
127

Spruce-Budworm Hysteresis

Three fixed points; outbreaks via saddle-node bifurcation.

SD ✦
128

Stommel Ocean Conveyor

Two-box thermohaline circulation collapse under freshwater.

SD ✦
129

Lorenz-84 Atmosphere

Climate-like chaotic attractor of jet vs eddies.

SD ✦
130

Predator-Prey with Refuge

Refuge stabilizes coexistence — closed orbits → spiral.

SD ✦
131

Leslie Matrix Demography

Age-structured Leslie matrix with eigenvalue λ.

SD ✦
132

Demographic Transition

Sigmoidal birth/death rates over development.

SD ✦
133

Kondratieff Long Waves

Coupled K, L, A produce 50-year economic cycles.

SD ✦
134

Innovation S-curve Cascade

Successive Bass diffusions across tech generations.

SD ✦
135

Extended Bass Diffusion

Word-of-mouth + advertising + price + repeat purchase.

SD ✦
136

Tipping Point Hysteresis

Generic fold bifurcation with path-dependent F sweep.

SD ✦
137

Eroding-Goals Archetype

Goals decay to track current state — drift downward.

SD ✦
138

Shifting-the-Burden

Symptomatic fix erodes capacity for fundamental solution.

SD ✦
139

Limits-to-Success

R loop dominates early; B loop dominates later.

SD ✦
140

Capacity Expansion Oscillator

Construction delay produces classic over/undershoot.

SD ✦
141

Inventory Oscillator

Order-fill delay creates beer-game oscillations.

SD ✦
142

Sterman Stock-Flow Cylinder

Three pipelines with delays propagating step/ramp/pulse inflows.

SD ✦