Log Spiral

namespace ct_log_spiral
{
    void iterate_point(
        ct::plot::cairo::plot_2d& plot,
        glm::vec3 oc,
        unsigned long n,
        unsigned long x,
        unsigned long y
    ) {
        ct_complex c = { oc.x, oc.y };
        ct_complex z = c;

        double dis_max = 9999999.0;

        // start i at one
        for (unsigned long i = 1; i < n; ++i)
        {
            //ct_complex zp = z * z + c;

            ct_complex zp = (std::pow(z, 1.3) - (1.0 / (std::log(z) + 0.11))) + 0.42457;
            double slow = 1.2 + (1 / i);
            zp /= slow;

            double dis = std::abs(zp);

            dis_max = std::min(dis_max, dis);

            if (dis > 4.f)
            {
                double icolor = i / (n - 1.f);
                ct::plot::cairo::pixel color = CT_RGBF(icolor * 44., icolor * 15., icolor * 45);
                plot.set_pixel(x, y, color);
                return;
            }

            z = zp;
        }

        ct::plot::cairo::pixel color = CT_RGBF(dis_max * 11.f, 0, 1);
        plot.set_pixel(x, y, color);
    }

    void iterate_plane(
        ct::plot::cairo::plot_2d& plot
    ) {
        std::cout << "ct_log_spiral::iterate_plane\n\n";

        for (unsigned long y = 0; y < plot.m_height; ++y)
        {
            for (unsigned long x = 0; x < plot.m_width; ++x)
            {
                glm::vec3 vc = { plot.m_plane.project_to(x, y), 0.f };

                iterate_point(plot, vc, 123, x, y);
            }

            std::cout << "y = " << y << "\r";
        }

        std::cout << "complete!!!!!!" << "\n";
    }



    void manifest(ct::plot::cairo::plot_2d& plot)
    {
        std::cout << "ct_log_spiral::manifest\n\n";

        iterate_plane(plot);
    }
}