Zipfian Distributions as Emergent Geometries

This paper offers a new explanation for Zipf’s Law, showing that the familiar 1/r distribution seen in language, cities, websites, and other systems is not a coincidence or statistical trick. Instead, it emerges naturally when systems reinforce past choices while working under limited resources. As certain elements are chosen more often, they become easier to access—creating a feedback loop that shapes the whole system into a predictable curve. Zipf’s Law is not just observed—it’s the natural geometry of repeated decisions under pressure.