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Great work! I was just about to build something very similar in Python using a 10 dimensional projective geometric algebra described here https://youtu.be/VYZHdEkLgC0?si=admkfiQwxIjHBa3Y?&t=90

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Nice, there is a guy here live coding a tesseract on a string in javascript using geometric algebra. The code is general enough that you just have to adjust the dimension n=2,3 or 4. The rest of the code is identical.

https://youtu.be/5R2sv9GCwz0?t=685

Interesting stuff!

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