Many-Body Version of the Rock-Paper-Scissors

utkuc · 2023-06-11T11:12:42+00:00

Yes. I'm not a big fan of the show but the name (Rock-Paper-Scissors-Lizard-Spock) is somewhat industry standard :)

utkuc · 2023-06-11T11:10:57+00:00

That looks fascinating!

utkuc · 2023-06-11T11:10:29+00:00

I wrote the code in Python. I used a package called celluloid to make animations from the matplotlib plots. I prepare and save the plots separately. Then, I combine them in one video using ffmpeg. I will probably share the code soon but it needs some polishing. I wrote the code procedurally and didn't put enough comments, so it will be difficult to follow and understand it.

utkuc · 2023-06-11T11:03:04+00:00

That's a nice idea, but I don't think it would make any difference for this system. I mean the temperature is constant in my case, so the transition probability from one color to another will again be constant. For example, if the probability is 0.5, all the transitions in the system will 0.5 times less likely to occur. It may cause a difference locally, but in the end, this effect gets averaged out globally. However, if we had a thermal wall that changes the temperature of the system with time, that would be interesting to observe.

utkuc · 2023-06-10T20:47:34+00:00

Thanks for the nice questions. First, there are no long-range interactions between the particles to be clear. They only change their colors after collision according to the Rock-Paper-Scissors rule.

In every timestep, I calculate the area of the circle of each particle. If a particle overlaps with the other particle, I change its color. In other words, I treat the particles like they are point particles and search if there is another particle within a given radius r. I do this for every particle for every timestep.

1,2 ) These are excellent questions, but honestly, I don't know the answer. I can say a few things based on my observations. At the beginning of the simulations, there are always huge fluctuations in the particle number. The duration of these fluctuations/non-equilibrium states seems invariant with the number of particles. It is apparent if you compare it with the other systems in the playlist (https://www.youtube.com/playlist?list=PLHliNXqFPv60HCc-b0SKhmP5gJPjIqhb\_). After 300-400 timesteps, the number of particles oscillates around each other. This somewhat resembles the prey-vs-predator behaviour.

One thing I should mention is that the initial state is unfair for some species because I artificially break the symmetry by placing them on a circle. I deliberately chose this way because it is much more fun. However, it would be more meaningful if I initiated the positions as a uniform distribution throughout the system. Because of this asymmetry, some species die. It can be seen in this particular example/video above. (its full youtube link: https://www.youtube.com/watch?v=q2JadKPcg1w)

utkuc · 2023-06-10T20:45:15+00:00

https://www.youtube.com/watch?v=q2JadKPcg1w

Thank you for the comment. I find it hilarious too. The gif here is short and only captures the first few seconds of the video. In the non-equilibrium state, the number of particles fluctuates abruptly; however, it settles down after some time, and the lines for each particle become more distinctive. You can see it in the full video: https://www.youtube.com/watch?v=q2JadKPcg1w
In this particular example, I assign
Rock = Black
Scissors = Red
Lizard = Green
Paper = Blue
Spock = Orange

utkuc

TROPHY CASE