Do you know of any more of this cool stuff? I've already looked at 'Seven Trees In One' and zippers and want to go further. I'm just learning combinatorics and classes and want to relate it to programming structure.
You can read Huet's seminal paper on zippers [1]. I found that Edward Z Yang's article[2] explains well the more general zippers.
The generic operation of differentiation to create the the type of zipper is explained in this article[3] from Conor McBride.
Another fun fact about zippers is that they have a comonadic structure, ie from a zipper you can build a zipper of zippers that reifies the concept of moving the cursor. That comonadic structure can express "locality of rules" in cellular automata. This classic article[4] by Dan Piponi uses a 1D automaton. As an exercise, I described an implementation of Conway's game of life in a comonadic manner in [5].
