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Explore the Riemann Zeta function and analytic continuation though turtle graphics and the Logo programming language. This video is as much math art project as it is an explainer. This was my project for the Summer of Math Exposition, hosted by @3blue1brown . Almost this entire video was made and recorded in real-time in Chrome, using techniques and technology from an interactive website about number theory I haven't quite made live yet. The art and music styles come from an older browser-based indie game I worked on but also haven't yet finished. This project kind of got away from me (particularly on the exposition side - I was rushing at the end), but I'm glad #SoME3 gave me a deadline to get some of this stuff out the door. The music is actually pretty interesting in its own right; I was exploring novel algorithmic techniques for composing music way back in 2006-2008, and several of these pieces of music came from that era. I still intend to use them for the unfinished indie game they came from, so I don't have them online anywhere. Actually, at this point, I'm really excited about integrating a lot of what I explored in this video into that game (specifically, using some of these number theory concepts as game mechanics and challenges while maintaining this moody, dreamy tone). So fingers crossed I can figure out some way to get back to working on it.