// BigCat's Learning Hub

Complexity ScienceLOCAL RULES → GLOBAL BEHAVIOR

The causal chain itself: local rules → global behavior. How simple rules grow into collective behavior, why that behavior resists prediction, and what you can actually do with it. Every issue runs two parallel threads — a decision line and a crossing line.

Two kinds of pages: Main track reads in order (what counts as complex → dynamics → self-organization → networks → adaptation → scale → resilience → method); Reference library holds one page per classic model, linked from the main track and written on demand.

// Main Track

Read in order. Each issue works through one mechanism — how it grows out of local rules, why it resists prediction — and lands it on a decision line (what to do, or stop doing) and a crossing line (where the same mechanism turns up in an unrelated field).

A · WHAT COUNTSWhat Counts as Complex Topic 1–6

T1Complex ≠ complicated — ordered/random/complex · the edge of chaos T2Emergence — weak vs strong · full micro knowledge won't give you macro T3Hierarchy & near-decomposability — Simon's two watchmakers T4Infinity from minimal rules — cellular automata · Life · Rule 110 T5Nonlinearity — thresholds · the failure of superposition T6Feedback loops — delay · stocks and flows · the bullwhip effect

B · DYNAMICSDynamics & Unpredictability Topic 7–12

T7The language of state space — phase portraits · fixed points · attractors T8Chaos — determinism ≠ predictability · Lorenz · chaos ≠ randomness T9Routes to chaos — the logistic map · period doubling · Feigenbaum T10Bifurcation & tipping — saddle-node · bistability · hysteresis T11Two limits of prediction — Lyapunov time · computational irreducibility T12Noise & fluctuation — stochastic resonance · path dependence and lock-in

C · SELF-ORGSelf-Organization & Criticality Topic 13–19

T13Self-organization — Bénard cells · Turing patterns · flocks · autocatalytic sets T14Synchronization — Kuramoto · fireflies · the Millennium Bridge T15Dissipative structures — Prigogine · far from equilibrium · life as an entropy outlet T16Phase transitions & universality — order parameters · why details don't matter T17Percolation & connectivity thresholds — one parameter, sudden spanning T18Self-organized criticality — the sandpile · big events need no big cause T19Power laws & heavy tails — how they differ from normal · the mean may not exist

D · NETWORKSNetworks Topic 20–25

T20Structure drives dynamics — degree/path/clustering · community and modularity T21Small worlds — what six degrees really showed · the strength of weak ties T22Scale-free & preferential attachment — rich get richer, and the pushback T23Robust yet fragile — immune to random failure, undone by targeted attack T24Spreading & contagion — R₀ · thresholds · complex vs simple contagion T25Cascading failure & systemic risk — load redistribution · normal accidents

E · ADAPTATIONAdaptation & Evolution Topic 26–31

T26Complex adaptive systems — Holland · the rules themselves evolve T27Agent-based modeling — Schelling segregation · honest modeling and its traps T28Fitness landscapes — local optima · the NK model · explore vs exploit T29Evolutionary games & the origin of cooperation — ESS · how space rescues cooperation T30Collective intelligence & collective stupidity — independence and diversity are prerequisites T31Coevolution & the Red Queen — arms races · why equilibrium is the rare state

F · SCALEScale Topic 32–35

T32Scale invariance & fractals — self-similarity · fractal dimension · the coastline paradox T33Allometric scaling — the 3/4 power law · why big animals beat slowly T34Scaling in cities and companies — sublinear vs superlinear · cities rarely die T35Limits to growth & the S-curve — exponentials always bend · overshoot and collapse

G · RESILIENCEFragility, Resilience & Early Warning Topic 36–40

T36Critical slowing down & early warning signals — rising variance · slower recovery · and when it fails T37Risk in a heavy-tailed world — extremes aren't outliers · the ergodicity problem T38Resilience & the adaptive cycle — panarchy · redundancy, modularity, diversity T39Antifragility & optionality — convexity · the barbell · and the criticism T40Intervening in complex systems — Meadows' leverage points · Ashby's requisite variety

H · METHODMethod & Limits Topic 41–44

T41Measuring complexity — entropy · Kolmogorov · effective complexity · logical depth

T42Traps in modeling — overfitting and narrative · the "looks like a power law" error

T43The case against complexity science — which charges stick · the honest boundary

T44Intellectual history — cybernetics → general systems theory → Santa Fe

// Reference Library

Standalone pages for classic models and methods, linked on demand from the main track (not meant to be read in order). Each answers the same five questions: what problem it poses → the rules themselves → what you see when it runs → what it explains in the real world → what it cannot explain.

Classic Models

Methods

refIdentifying (and misidentifying) power laws refNetwork centrality measures refBox-counting dimension refAR(1) & the OU process refMonte Carlo & ensemble simulation refConvexity & Jensen's inequality refRenormalization group intuition

Schools

refSanta Fe Institute & its lineage refThe cybernetics lineage