Many years ago, I got the idea for my invertible signature from a book called "Inversions", by Scott Kim. There is no magic formula for doing these inversions (or ambigrams). You simply have to play around with a pencil and graph paper until you come up with something. Some of them can be rotated (like mine), others can be reflected, and some rely on illusions with foreground and background.

In the old days, the only way I could reproduce my signature accurately was to photocopy the original. But once I had a decent computer, I was able to scan the original into a layer in Adobe Illustrator, then use the pen tool to trace out points on the curves and smooth it out. Then I removed the scanned layer, and voila! Now I have a nice resolution independent version which I can resize, rotate, change colors, etc.

To find out more about inversions, ambigrams and Scott Kim, here are some interesting web sites: