Multi-Armed Spirals and Polar Coordinate Systems

I was playing with spirals, possibly as a prelude to making a spiral photo mosaic, and noticed some interesting aspects of them.

A spiral in a polar coordinate system unwrapped into a rectangular coordinate system becomes a series of diagonals. I figured it would.

A hand drawn, irregular spiral, when unwrapped, still tiles seamlessly. That was interesting.

A tiled, unwrapped spiral re-wraps into a multi-armed galaxy-type spiral. For N tiles there are N arms and each arm wraps N times fewer around the spiral. Also interesting.