Julia sets

Julia sets are complex mathematical objects derived from iterating functions in complex numbers. Essentially, they demonstrate how simple equations can create intricate and beautiful shapes. Starting with a point in the complex plane, you repeatedly apply a specific function; some points stay close to a certain value, while others escape to infinity. The boundary of the points that don’t escape forms the Julia set, which can display stunning fractal patterns. Each unique equation produces a different Julia set, revealing endless variations in design, often illustrated in vibrant colors, making them appealing both mathematically and artistically.