When I was a freshman in high school, quite enamored by non-mathematical physics, I came across a slick argument about how gravity would differ if the inverse square law differed by some small factor. Namely, by conservation of gravitational flux, lowering the number of dimensions in use decreases the degree of the hyper-sphere (over which the flux is taken), and thus the power of the inverse square law. That is, we go from Gm_1m_2/r^2 ---> Gm_1m_2/r^k, where k = d-1.
Initially, when I came across this, I used this as a pretentious science fair project as a freshman in high school. Namely, I claimed the number of dimensions to be an indepedent variable, and wrote some bad, bad code to simulate the outcome an Earth-Sun orbital system under different constraints. The code was written in Javascript, the only language I knew at the time, and done in CodeAcademy's interpreter. This is written in Python, with a bit of visualization instead!