Other

In addition to sandpile torsors and tilings, I also have worked on several other combinatorial projects. You can read about everything on the research + CV subpage, but I wanted to use this page to highlight some additional animations that I am especially proud of (currently, I have one short video).

Toggle Groups.avi

For the 2022 FPSAC, each group presenting a poster was required to submit a 1 minute preview video with no other guidelines. I challenged myself to show the idea for our topic without using words. This restriction helped me discover a "growing and shrinking disk" perspective to demonstrate the rules for sequentially toggling independent sets on a cycle graph. Audio cues also help draw a link between the toggling operation and the orbit table which keeps track of when nodes are live. The repetition in the audio also suggests the importance of the period of the table. Finally, the appearance of snakes at the end of the video hint at the structure of the table. Even though this video does not state any results, it is meant to spread ideas and inspire curiosity.

Software Recommendations:

SageMath is a free open-source Python-based programming language which is popular among mathematicians. I use it to create most of the objects in my animations.
VSDC is a free video editing software (with a $20 a year pro version). It is incredibly versatile but has a bit of a learning curve. It is excellent for combining objects, text, and/or video, and is what I use to turn objects into a full video.
Blender is a free open-source computer animation software that is popular among professional animators. Its potential to make beautiful 3D animations is unmatched, but it takes some time to get used to.
Manim is a community maintained python library specifically for mathematical animations that was created by Grant Sanderson of 3Blue1Brown. I never worked with it since I want to develop my own style, but videos using it tend to look incredible.
Notability is a free iPad note app which also allows for an appealing alternative to a traditional slideshow.

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