This past June I led a team of talented high school students for the summer 2021 Illinois Geometry Lab research program. During the first couple of weeks, we learned some fundamentals of theoretical computer science and numeration systems. Then we read parts of “The critical exponent is computable for automatic sequences” by Schaeffer and Shallit. In the final two weeks, we generalized Corollary 9 in their paper (a certain computability result) to Fibonacci representation, discussed some applications and future directions, and then created the various deliverables for the program including a poster, presentation video, and longer report. This material is collected and organized in an Illinois Wiki page. This was a sophisticated project, and I am very proud of what the students were able to accomplish in such a short time frame!