static struct colour rainbow(double x)
{
    double red, green, blue;
    struct colour colour;

    red = 4.0 * x - 2.0;
    red = clip(red);

    if (x < 0.5)
        green = 4.0 * x;
    else
        green = (-4.0) * x + 4;
    green = clip(green);

    blue = (-4.0) * x + 2.0;
    blue = clip(blue);

    colour.r = (unsigned char)round(red   * 255.0);
    colour.g = (unsigned char)round(green * 255.0);
    colour.b = (unsigned char)round(blue  * 255.0);

    return colour;
}

static struct colour heat(double x)
{
    double red, green, blue;
    struct colour colour;

    red = sqrt(x);
    red = clip(red);

    green = pow(x,3);
    green = clip(green);

    blue = 1 - pow(x * 4 - 1, 2);
    blue = clip(blue);

    colour.r = (unsigned char)round(red   * 255.0);
    colour.g = (unsigned char)round(green * 255.0);
    colour.b = (unsigned char)round(blue  * 255.0);

    return colour;
}