Function iteration is the process of applying a function repeatedly to an initial value. Starting with a value x₀, we calculate x₁ = f(x₀), then x₂ = f(x₁), and so on.

This calculator helps you explore this concept by computing x_n = f⁽ⁿ⁾(x₀), which means applying the function f, n times to the initial value x₀.

Function iteration is used in various fields of mathematics, computer science, and chaos theory to study the behavior of systems over time or repeated operations. For example, in chaos theory, iterated functions can lead to complex and unpredictable patterns.