Julia set (Mathematics)

A Julia set is a complex mathematical shape created by repeatedly applying a simple rule to points on a plane. For each point, you repeatedly substitute its value into an equation involving complex numbers. If the point's value stays bounded and doesn't go off to infinity, it belongs to the Julia set. Different parameters produce intricate, often beautiful patterns that reveal complex structures emerging from simple rules. These sets are important in mathematics for studying chaos and fractals, illustrating how complex, detailed shapes can arise from straightforward iterative processes.