Library / Dynamics / Markov Chain
Markov Chain
Next state depends only on now. Run it forward to get the long-run mix.
INTERACTIVE LAB
Tolerance sandbox (original recreation)
happy 76% • avg. similar neighbors 49% • red ring = wants to move
DYNAMICS
When to use / misuse
Use → Mobility, churn, brand switching. Check memorylessness first.
Difficulty → Core
REDCAPE → Predict · Explore
agent: markov-checker family: Dynamics combine_with: [two other families] rule: state failure mode before acting
Free sources: Coursera M5 (Markov Processes)
Attach to a lattice — combines with
Different families, shared jobs. Click to open alongside.
DIFFUSION
SIR Contagion
Susceptible–Infected–Recovered with an R0 tipping point. Same math for flu and pop-star fever.
SHARED JOBS: PREDICT · EXPLORE
DIFFUSIONBass Diffusion (S-Curve)
Innovators plus imitators make the S-curve. Spend early on seeds, later on social proof.
SHARED JOB: PREDICT
LINEARCategorical & Threshold Models
Buckets and cutoffs turn messy attributes into testable if-then rules.
SHARED JOB: PREDICT
More in Dynamics
Random Walk & Markets
Unpredictable steps accumulate; efficient markets leave mostly randomness behind.
Polya Urn / Path Dependence
Early draws rewrite the odds — history locks in QWERTYs, VHSs and dominant cities.
Lyapunov / Equilibrium
An energy-like function proves a system settles down — and bounds how fast.