M2R-Visualisation

This is a code for 2D torus flow simulation and ergodic decomposition theorem visualisation in section 4, and the visualisation of the last part of the section 7 in my M2R group project at Imperial College London. The last theorem is in the last part of my paper, and I approximate 7pi with 5% error here. We can see the ratio is tending to 1 when N (radius) grow bigger, which means that the approximation is good. To calculate the volume of this homogeneous space, I used monte carlo simulation. The idea comes from my group mate Ariff Jazlan.