# Domain Size

Atom domain size estimation (2013) derives the atom domain size estimate for a nucleus $c$ of period $p$ as:

$$r = \left|\frac{F^q(0, c)}{\frac{\partial}{\partial c} F^p(0, c)}\right|$$

where $1 \le q < p$ minimizes $\left|F^q(0, c)\right|$. The atom domain size is approximately $4$ times the radius of circle-like components, and typically a lot larger for cardioid-like components.

#include <complex.h>

double m_domain_size(double _Complex c, int p)
{
    double _Complex z = c;
    double _Complex dc = 1;
    double abszq = cabs(z);
    for (int_t q = 2; q <= p; ++q)
    {
        dc = 2 * z * dc + 1;
        z = z * z + c;
        double absz = cabs(z);
        if (absz < abszq && q < p)
            abszq = absz;
    }
    return abszq / cabs(dc);
}