Library / Dynamics / Polya Urn / Path Dependence

Polya Urn / Path Dependence

Early draws rewrite the odds — history locks in QWERTYs, VHSs and dominant cities.

+1 same color
draws rewrite odds · recreated schematic
INTERACTIVE LAB

Tolerance sandbox (original recreation)

happy 76% • avg. similar neighbors 49% • red ring = wants to move

DYNAMICS

When to use / misuse

Use → Audit increasing returns; intervene early or standardize late.

Difficulty → Advanced

REDCAPE → Explain

agent: polya-checker
family: Dynamics
combine_with: [two other families]
rule: state failure mode before acting

Free sources: Coursera M8 (Path Dependence)

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◍ Ask mentor about this →See REDCAPE playbook →

Attach to a lattice — combines with

Different families, shared jobs. Click to open alongside.

GROWTH
Capital Share (Piketty-style)
When returns on capital outrun growth, wealth concentrates without any villain.
SHARED JOB: EXPLAIN
DIFFUSION
Cellular Automata & Game of Life
Tiny local rules aggregate into gliders, blinkers and chaos. Emergence needs no boss.
SHARED JOB: EXPLAIN
GAMES
Coordination & Culture
Pure coordination games plus memory harden into culture as equilibrium.
SHARED JOB: EXPLAIN

More in Dynamics

Random Walk & Markets
Unpredictable steps accumulate; efficient markets leave mostly randomness behind.
Markov Chain
Next state depends only on now. Run it forward to get the long-run mix.
Lyapunov / Equilibrium
An energy-like function proves a system settles down — and bounds how fast.
← Markov ChainLyapunov / Equilibrium →