That simulation that was running while I was in Vegas was as good as the time I had there. After reducing the simulation from 2D to 1D and pushing into ultra high resolution, the deviation between the simulation and my theory is now less than 10%. This agreement is astonishing for these kind of simulations that involve millions of particles in a complicated structure. On top of that the result is clean, noise-free and as smooth as Laetitia's curves.
I will now proceed to simulate the full length of our run, which is 3 times longer (I had to simulate shorter lengths because until now the noise was growing fast).
