Library / Distributions / Power Law / Long Tail

Power Law / Long Tail

Rich-get-richer: a few huge winners, many tiny players. Straight line on log-log.

few giantsmany tiny
log–log: straight line · recreated schematic
INTERACTIVE LAB

Tolerance sandbox (original recreation)

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

DISTRIBUTIONS

When to use / misuse

Use → City sizes, book sales, network degrees. Never average it like a normal.

Difficulty → Starter

REDCAPE → Explain · Predict

agent: power-law-checker
family: Distributions
combine_with: [two other families]
rule: state failure mode before acting

Free sources: SFI Fractals & Scaling • Wikipedia: Power law (CC BY-SA)

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Attach to a lattice — combines with

Different families, shared jobs. Click to open alongside.

GROWTH
Exponential & Solow Growth
Compounding plus capital, labor and ideas explain why some economies stall.
SHARED JOBS: EXPLAIN · PREDICT
NETWORKS
Granovetter Threshold
Each person has a riot threshold; cascades depend on the distribution, not the average.
SHARED JOBS: EXPLAIN · PREDICT
DIFFUSION
Percolation / Tipping Points
Sparse links suddenly gel into a giant component — bank networks and blackouts tip fast.
SHARED JOBS: EXPLAIN · PREDICT

More in Distributions

Normal Distribution
Bell-curve averaging: many small independent effects sum to a predictable center with thin tails.
Poisson Arrivals
Counts of rare independent events per window: calls, mutations, clicks.
← Normal DistributionPoisson Arrivals →