The Random Walk and Its Fractal Limiting Form

John Venn, whose name is immortalized in the “Venn diagram” of logic and set theory (1880) which replaced the more confusing “Euler diagram” previously used for the same purpose, published The Logic of Chance in 1866. The third edition, of 1888, contained much new material, including a chapter “The conception of randomness,” in which Venn illustrated the “truly random character” of the digits of π by using them to generate a discrete random walk in two dimensions. He then discussed the limiting form that such a random walk would take if the direction were drawn from a uniform distribution and the step length made indefinitely small, describing the result in terms which we would now encapsulate in the word “fractal.”