power law
Exponential frequency distribution
A power law is a mathematical relationship where one quantity varies as a power of another—doubling the input might quadruple the output, or cube it.
Power laws appear throughout nature and society: earthquake magnitudes, city populations, wealth distribution, word frequencies.
They produce characteristic patterns where small values are common and large values rare but not impossible: Income follows a power law—many earn little, few earn enormously.
Superscript showing power
- scalingClimbing or resizing
- distributionAllocation across recipients
- long tailExtended rear extremity
- alphaFirst Greek letter
slope · coefficient · regression · curve fitting · 80/20 rule · wealth distribution · word frequency · income inequality
Identical at every magnification
- criticalityState of utmost importance
- phase transitionMatter shifting between states
- universalityApplying to all cases
- percolationLiquid passing through pores
avalanche · sandpile · earthquake magnitude · turbulence · fractals · cascades · emergence
Central focal points
- citationsAcknowledged source mentions
- social networksPlatforms connecting users digitally
- winner-take-allOnly champion receives reward
exponent
Superscript showing power
- scalingClimbing or resizing
- distributionAllocation across recipients
- long tailExtended rear extremity
alpha · slope · coefficient · regression · curve fitting · 80/20 rule · wealth distribution · word frequency · income inequality
self-similarity
Identical at every magnification
- criticalityState of utmost importance
- phase transitionMatter shifting between states
- universalityApplying to all cases
percolation · avalanche · sandpile · earthquake magnitude · turbulence · fractals · cascades · emergence
hubs
Central focal points
- citationsAcknowledged source mentions
- social networksPlatforms connecting users digitally
- winner-take-allOnly champion receives reward
- Rheologyviscosity, non-Newtonian fluid, viscoelasticity, viscometer, creep
- allometryisometry
- corpus linguisticscorpus, word counts, word frequency, concordance, n-grams
- distributionsnormal, uniform, binomial, exponential, bell curve
- tail distributionslong tail, long tails, tail risk, extreme events
- long tailniche markets, niche products, rare items, demand curve