One might intuitively expect that a slight change in input produces a slight change in output, with this function, the logistic map, the output wiggles dramatically.

This is a recursive equation, each value of x depends on the previous one. The value n_max is the number of recursions before plotting the final result. Slight changes to the initial value, x₀, do not produce smooth changes in the graph.

This graph plots for a single value of x₀, the one below plots a range of values.

Simple mathematical models with very complicated dynamics (May, Robert M. (1976)).

The logistic map. This graph automatically plots for all values of x₀ between 0 and 1. The graph above plot for a single value of x₀.