Johan Hjelm. Naturally the conversation turned to the awesomeness of Python, and whether there was any way to create animated FiPy simulations directly in the IPython Notebook.
FiPy is "an object oriented, partial differential equation (PDE) solver, written in Python, based on a standard finite volume (FV) approach." Fair enough. More usefully, there are a couple of examples on the website that model diffusion, electrodeposition and convection. I focussed on the mesh20x20 diffusion example.
If you run the example at the command-line it pops up a matplotlib window showing the progress of the simulation. However, direct entry of the example into an IPython Notebook just results in a single graph for the simulation. To adapt it, I added a call to clear_output(), and used IPython's display() command to directly display the matplotlib figure associated with the simulation.
In short, here are the results as an IPython notebook, a Python script, and as an HTML page (and another HTML page, created on-the-fly from the notebook URL by http://nbviewer.ipython.org).
Notes: I used IPython 0.13.1 on Windows. To downgrade the notebook to earlier versions, see this discussion. Also, the statement "from IPython.display import clear_output" may need to be changed to "from IPython.core.display import clear_output".