Each time I create a design, it takes a mix of analysis, discovery, and creation. The analysis starts and provides a roadmap of the process I will follow. But just as with real maps, the map can provide only a subset of what you encounter; there are many discoveries along the way, some of them helpful, some of them additional and unexpected challenges. At the end, though, there is the result: an act of creation, something new, which never existed before.

The analysis varies enormously by the project. To take one specific example, I've been interested for some time in moveable or 'action' origami, particularly origami that had a lot of moving parts but only a single degree of freedom. I carried out some mathematical analysis of the behavior of individual vertices and the relationships between fold angles and sector angles around a vertex. That allowed me to create a map of how multiple vertices interacted with each other. From that, I was able to construct an algorithm and a computer program for designing an entire family of patterns with the desired single-degree-of-freedom property.

Of course, when writing computer programs, there are many small challenges that arise along the way: bugs in the program to be debugged, or cases that one had not initially considered. Each of those required its own bit of analysis to understand what the problem was, and then rewriting code (or mathematics, or both) to get around the problem.