# 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;
}