Iterated Function Calculator

Explore the fascinating world of iterated functions. Enter your function, starting value, and number of iterations to see the magic unfold.

Function Details

Function f(x)

Enter a valid mathematical function using 'x' as the variable.

Initial Value x₀

The starting value for iteration.

Number of Iterations (n)

How many times to apply the function.

Result

f⁽ⁿ⁾(x₀) =

Iteration Steps

Iteration (i)	Value (x_i)

What is Function Iteration?

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.