Luxuriant Loxodromes

Brave sailor, you are travelling on the deep dark ocean on a strange planet with bulging orange, green, and purple shapes around the equator. Your bearing is due West-West-West-South-West. Your map is a stereographic projection of the Riemann Sphere rotated by pi over two radians. The north pole is marked in red, the south pole is marked in blue.

Click on the canvas to spwan circle ships!
Click many a time if it please your fancy.
Click to see them follow their baring,
Click and watch the map you sail.
Then watch the ships sink into the south pole sink.