Inverse Julia IFS Experiment pow 3

struct ifs
{
    struct plane
    {
        complex_t m_cpoint;
        double m_radius;
    };

    complex_t m_jp;

    void plot_plane(
        BMP& bmp,
        plane const& p,
        complex_t jp,
        unsigned int imax,
        double xpow
    ){
        complex_t z = { 0.0, 0.0 };
        double prob = 0.5;

        unsigned int roots = (unsigned int)std::ceil(std::abs(xpow));
        double root_angle = 6.28 / xpow;

        for (unsigned int i = 0; i < imax; ++i)
        {
            double dx = z.real() - jp.real();
            double dy = z.imag() - jp.imag();

            double r2 = std::sqrt(dx*dx + dy*dy);
            double w2 = std::atan2(dy, dx);
            double a = w2 / xpow;
            double r = std::pow(r2, 1.0 / xpow);

            // Hard code at pow 3
            unsigned int random_root = 0;
            double rn = random();
            if (rn < 0.09)
            {
                random_root = 0;
            }

            else if (rn < 0.97)
            {
                random_root = 1;
            }

            else
            {
                random_root = 2;
            }

            double rangle = root_angle * random_root;

            double x1 = r * std::cos(a + rangle);
            double y1 = r * std::sin(a + rangle);

            z.real(x1);
            z.imag(y1);

            unsigned int ix0 = x1 * p.m_radius + p.m_cpoint.real();
            unsigned int iy0 = y1 * p.m_radius + p.m_cpoint.imag();

            unsigned int ix1 = -x1 * p.m_radius + p.m_cpoint.real();
            unsigned int iy1 = -y1 * p.m_radius + p.m_cpoint.imag();



            if (ix0 < bmp.TellWidth() && iy0 < bmp.TellHeight())
            {
                RGBApixel color = bmp.GetPixel(ix0, iy0);

                color.Alpha = 255;
                color.Red = color.Red + 18;
                color.Green = color.Green + 1;
                color.Blue = color.Blue + 3;

                 bmp.SetPixel(ix0, iy0, color);
            }


            if (ix1 < bmp.TellWidth() && iy1 < bmp.TellHeight())
            {
                RGBApixel color= bmp.GetPixel(ix1, iy1);

                color.Alpha = 255;
                color.Red = color.Red + 11;
                color.Green = color.Green;
                color.Blue = color.Blue + 2;

                 bmp.SetPixel(ix1, iy1, color);
            }
        }
    }
};