# visualization of 3D probability flow

I have a master equation for $P(N_A^+,N_B^+,N_C^+,t)$, with $N_A^+,N_B^+,N_C^+$ all discrete. The numerical integration is done by this Matlab program using Euler's method. Despite the crude Euler's method, the results from numerical integration are in agreement with the simulation, so the correctness of the program is not the focus.

I want to see how $P(N_A^+,N_B^+,N_C^+,t)$ evolves over time. Since $P(N_A^+,N_B^+,N_C^+,t)$ has 3 more coordinates in addition to time, it is really hard to visualize the changes. Ideally, I want to have something like

But I cannot find any function in Matlab that can does something similar. The closest thing I can find is Matlab's contourslice function.

By running the Matlab program mentioned above with

ABC_driver(0.5,100,20,200,10,true);


you will get something like the following:

You can guess what happens to $P(N_A^+,N_B^+,N_C^+,t)$, but it is nowhere as obvious as the atomic orbital graph.

My question is, how can I plot $P(N_A^+,N_B^+,N_C^+,t)$ in way similar to the atomic orbital density plot? Or can anyone suggest better way to visualize the time evolution of $P(N_A^+,N_B^+,N_C^+,t)$?

• Cool plot! Where did that come from? – meawoppl Mar 2 '14 at 19:29
• @meawoppl, the upper plot comes from here, the lower 6 plots are from contourslice in Matlab. – wdg Mar 3 '14 at 3:11
• dead link, fixed one here – bhbr Aug 14 '19 at 20:22