# Membership

If $|z|$ gets large enough, it will keep on getting larger and larger.

Colour according to whether the iterations diverge to infinity or not, within a fixed maximum number of iterations $N$ and escape radius $R \ge 2$. The disconnected specks visible in the image turn out to be copies of the whole, and despite appearances the Mandelbrot set is connected.

#include <complex.h>
#include <stdbool.h>

bool m_membership(int N, double R, double _Complex c)
{
    double _Complex z = 0;
    for (int n = 0; n < N; ++n)
    {
        if (cabs(z) > R)
            return false;
        z = z * z + c;
    }
    return true;
}