Also, you may notice in the final image that the reflections do not draw the backfaces of the spheres. This is because the framebuffer can only store one color value per pixel, the front pixel. Since we are accessing the framebuffer to get the reflected color, it will not find anything for the back pixel.
One interesting thing to point out is there is a cool shadowing effect on some of the walls. I'm not totally sure how this happens at the moment, but it is definitely cool.
Clearly there is a lot more work to be done in terms of visual quality and speed, but at least my results resemble proper reflections.