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!
This reminds me of a small experiment I did with a friend, where we asked different people to independently write the HTML and CSS for a website (without communicating), and then put the HTML and CSS files together to see how well they worked. https://kach.github.io/generative-adversarial-web-developmen...
If you liked this, you might enjoy this little trick you can do with moiré patterns -- near the end of the post, I talk a little bit about the math behind the FFT connection. https://hardmath123.github.io/moire.html
You might also like the nearley playground, which lets you write a grammar in BNF and see all possible parsings of an input. You can even press a button and generate a random string that matches your grammar! https://omrelli.ug/nearley-playground/
See also: using differentiable approximations of cellular automata in PyTorch to reverse Conway's Game of Life; in some cases, you can get striking Turing patterns similar to what's described in this paper! http://hardmath123.github.io/conways-gradient.html
How cool! I was on the fence about whether or not to put up the source code— I'm _glad_ I did!
Do you have a recommendation for a good reference that teaches about the various metrics for point-cloud distance? (I only used Chamfer distance because I hazily recalled it from some undergrad class taken a while ago...)