Plotting algorithms for the Mandelbrot set

Plotting algorithms for the Mandelbrot set involve a set of mathematical processes used to visualize the boundary of this famous fractal. The Mandelbrot set is defined in the complex plane and consists of complex numbers \( c \) for which the iterative sequence \( z_{n+1} = z_n^2 + c \) remains bounded (i.e., does not tend to infinity) when starting from \( z_0 = 0 \).