Julia sets (Mathematics)

Julia sets are complex mathematical shapes generated by iterating a simple formula involving complex numbers. For a given complex number, repeatedly applying this function determines whether it stays bounded or escapes to infinity. The boundary between these behaviors forms intricate, often fractal, patterns known as Julia sets. They are related to the Mandelbrot set, with each point in the Mandelbrot set corresponding to a different Julia set. These sets showcase stunning, infinitely detailed structures that reveal how simple rules can produce complex, self-similar patterns in mathematics.