Complex Fractals

The Mandelbrot Set and various Julia Sets are fractals generated through iterations of complex functions, exhibiting infinitely detailed and self-similar structures.

The Mandelbrot Set is defined by iterating the function \( z_{n+1} = z_n^p + c \), starting from \( z_0 = 0 \) and varying \( c \) over the complex plane. Points \( c \) for which the sequence remains bounded form the set.

The Julia Sets are generated by fixing a value for \( c \) and varying \( z_0 \) over the complex plane. Depending on the value of \( c \), Julia Sets can be connected or completely disconnected, displaying a variety of fractal shapes.