Making a forum avatar for alternating backgrounds

furrycat This guide demonstrates how to make a single image...
furrycat ...which achieves passable transparency on two backgrounds.

I wanted to use a single image as my avatar on an internet BBS which uses an alternating light/dark purple background when displaying posts. One way would of course be to put the picture on a solid background but I wanted a transparent look.

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intro | part 1: Preparation | part 2: Layer effects | part 3: Saving for web | part 4: Dithering?