Re: Low FPS webcam - here's an approach that attempts to analyze coin tossing data from the _sound_ rather than the _video_, since sound is typically recorded at a much higher sampling rate (high enough to "hear" the spinning of the coin). https://cs.stanford.edu/~kach/can-one-hear-the-fate-of-a-coi...
A lot of replies here are missing the key idea behind Penrose: that the "substance" and "style" of any mathematical diagram are separable. For example, the "substance" of a diagram might be a collection of sets with known subset relationships:
Set A, B, C
IsSubset(B, A)
IsSubset(C, A)
That same substance can then be rendered in many different styles, e.g. as a Venn diagram or as a tree diagram (substance vs. style is a lot like HTML vs. CSS). Importantly, Penrose's vision is that experts will author libraries of domains and styles, and end-users need only express the substance of their diagrams (i.e. the three lines of code above).
The second beautiful idea in Penrose is that diagram generation is expressed as a constrained optimization problem. This lets you easily experiment with layouts by writing constraints and sampling a variety of potential diagrams via stochastic search.
These two ideas set Penrose apart from most other diagram software out there. I really hope it gains wider adoption. Give it a try!