;; Constants.
width = 30
height = 30
size_pow_two = 16
size = 4
max_iteration = 100 ; How god the algorithm is

for x_pos do width times
    for y_pos do height times

        is_inside_mandelbrot = 1
        x = 0 ; x_math
        y = 0 ; y_math

        for i do max_iteration times
        ;; because the set is so small we need to scale evrything up with scale.

            ;; if x^2 + y^2 > 2^2 * size^2  then outside set.
            if x * x + y * y > 4 * size_pow_two then
                is_inside_mandelbrot = 0
            else
                ;; z = z^2 + c
                ;; z = x + yi
                ;; c = x_pos + i*y_pos
                ;; z^2 = (x + yi)(x + yi) = x^2 -y^2 + 2yxi
                ;; therefore: x = x^2 - y^2 + x_pos, y = 2xy + y_pos
                x = x*x - y  *y + x_pos * size
                y = 2 * x * y +y_pos * size
            end
        end
        if is_inside_mandelbrot == 1 then
            draw_pixel(x_pos,y_pos)
        end
end