I wanted to let you know that your "challenge" to me to build the sine wave to sawtooth wave example using my project was the most useful feedback I received last week.

I realized this weekend that the interface was not accomplishing its goal. The construction was still a largely symbolic task, not a spatial task. This became especially evident when the interface was not helpful to us in trying to figure out the "formula" for the construction, or fixing it when we figured out what we had wrong.

I put together a prototype which does a slightly better job. Here's a video.

I realized that there was too much fiddling with the parameters for the arithmetic (+ and *) and that a spatially focused interface instead should ground "arithmetic" in affine transformations rather than addition (translation) and multiplication (rotation/scaling). And more interaction should take place on the graphic rather than the symbols linked to the graphic. My old interface showed the water, but to be truly spatially oriented I need to jump in the water!

Here's the prototype if you want to play with it.

Right now it just adds sine waves but I think I can see how to generalize it to do arbitrary "shader" math. That is, it's at an analogous level of development as the first Recursive Drawing prototype.

Thanks for helping me see this path!

PS: The interface still doesn't help you "discover" how to represent an arbitrary wave form as the sum of sine waves. I've had to look up the formulas for square wave and triangle wave. But at least the iteration speed is decent enough to quickly "check" that a formula works.