iPhone: How to Dynamically Color a UIImage

In my recent work on Sphericle, there were a few instances where I wanted to use the same image over and over, but colored differently each time. For example, I want to show spheres of different colors on a map; there are 360,000 spheres, each having its own color. I didn't want to draw the sphere algorithmically; I wanted the picture of a sphere to be based on an image, but then colored appropriately. The solution: use a grayscale image of a sphere, then draw a color over it using a color burn blend mode. That's what I want to show you today.