Independent Study Ideas: Physics and Programming

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TheDemx27
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I have the option for independent study at school, and I am open to any ideas for projects either pertaining to physics or programming. (I've thought about making a web bot.)

Anything is helpful.
 
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How about a look into Monte Carlo simulations? They're fairly approachable at a beginner level if you have the proper pre-reqs, and are heavily used the physics.