Efficient visualisation in Python

I have data (generated by an algorithm I wrote for it) for a random process which consists of coalescing and branching random walks on a finite space that I would like to visualize using python and probably something from matplotlib.

The data look like this:

A list of lists the of states of the process at times when something changes (a walk moves to an empty spot, coalesces with another one or a new particle is born), so something like this (let's say the process lives on {0,1,2,3,4}:

[[0,1,2,0,2],...,[1,0,2,2,0]], so at the beginning I start with the process having particles at positions 1,2 and 4 (there are two different kinds of particles so that "1" indicates the presence of a first type and "2" of the second, whole "0" means nothing there)

And I have also the list of events that alter the process, so a list of lists of the form

[place,time,type]

so I know what happens where and at what time (which corresponds to writing appropriate marks in the graphical representation, for example an arrow to the left if the event was that a particle moved to the left).

I wrote something like this :

import pylab as P
P.plot(-spacebound,0,spacebound,maxtime)
while something in the process:
    current=listofevents.pop(0)
    for i that are nonempty at current time:
        P.arrow() in a way corresponding to the data

P.show()

This works, but it is extremely slow so that if I have a big process it takes an enormous amount of time to make this visualization (while generating the process data takes a few seconds at most for rather extreme parameters - a big space, time and a high rate of particle births which means a a lot of events changing the process often).

I am pretty sure using arrows like this is pretty idiotic, but since I've only visualized things in R so far (I could of course simply export my data from python and visualize them in R but I want to avoid that) I am also very green at doing this in Python.

I tried some googling, found out about matplotlib and looked at some tutorials there and apart from the arrows I also tried just visualizing the states of the process (without the events) by looping plt.scatter() over all the states, but while this is slightly faster, it is still extremely slow and it also looks messy.

So how would I plot this in a sensible way? Even a link to something like "learn to do plotting in Python properly" is welcome as an answer. Thanks!