Contraction mapping

A contraction mapping is a mathematical function that brings points closer together each time it's applied. Imagine you have a set of points, and when you use this function on any point, it moves it closer to a specific target point or region. Repeatedly applying the contraction reduces the distance between the points and that target, eventually stabilizing at a single point. This property guarantees that, starting from any initial position, you will find a unique, fixed point where applying the function again doesn't change the point, making contraction mappings essential for solving equations and ensuring convergence in various algorithms.