. • 1920: Moses Schönfinkel introduces combinators (see page 1121 ) but considers mostly cases specifically constructed to correspond to ordinary logical functions. • 1921: Emil Post looks at a simple tag system (see page 894 ) whose behavior is difficult to predict, but failing to prove anything about it, goes on to other problems. • 1920: The Ising model is introduced, but only statistics of configurations, and not any dynamics, are studied. • 1931: Kurt Gödel establishes Gödel's Theorem (see page 782 ), but the constructions he uses are so complicated that he and others assume that simple systems can never exhibit similar phenomena. • Mid-1930s: Alan Turing , Alonzo Church , Emil Post, etc. introduce various models of computation, but use them in constructing proofs, and do not investigate the actual behavior of simple examples. • 1930s: The 3n + 1 problem (see page 904 ) is posed, and unpredictable behavior is found, but the main focus is on proving a simple result about it. • Late 1940s and 1950s: Pseudorandom number generators are developed (see page 974 ), but are viewed as tricks whose behavior has no particular scientific significance. • Late 1940s and early 1950s: Complex behavior is occasionally observed in fairly simple electronic devices built to illustrate ideas of cybernetics, but is usually viewed as something to avoid. • 1952: Alan Turing applies computers to studying biological systems, but uses traditional mathematical models rather than, say, Turing machines. • 1952-1953: John von Neumann makes theoretical studies of complicated cellular automata, but does not try looking at simpler cases, or simulating the systems on a computer. • Mid-1950s: Enrico Fermi and collaborators simulate simple systems of nonlinear springs on a computer, but do not notice that simple initial conditions can lead to complicated behavior. • Mid-1950s to mid-1960s: Specific 2D cellular automata are used for image processing; a few rules showing slightly complex behavior are noticed, but are considered of purely recreational interest. • Late 1950s: Computer simulations of iterated maps are done, but concentrate mostly on repetitive behavior.

Similar schemes have been popular in quantum cosmology since the early 1990s in connection with studying wave functions for the complete universe.

Several generalizations of linear congruential generators have been considered in which nonlinear functions of n are used at each step.