For those that aren't aware, the uncertainty principle goes pretty deep. You can actually define the uncertainty principle as an inequality involving the integral of a function vs the function's Fourier transform: https://en.wikipedia.org/wiki/Uncertainty_principle#Harmonic... . And in a quantum system you can construct the momentum of a particle as the Fourier transform of the position (up to a constant) and the uncertainty principle falls out because of this. This article doesn't state that super explicitly. So the real interesting thing being done here is getting a Fourier transform that works on fractal spaces.