# Python scripts

Here are some of the python scripts we've been using during the course (2012-2013).

## forcedVanDerPol_Animation.py

(requires parallel python, see below) \\ This script is more complex than the rest of our scripts. The output is a movie. \\ The state space of the Van der Pol oscillator is the plane (the forced vanderpol requires an additional state variable, the phase). We start our simulation with initial conditions that are evenly distributed in a given range. As time evolves, many solutions will converge to the same attractors. As different solutions accumulate in state space, the density of solutions increases. This density is color coded in our movie. \\ For example; \\ If the system had a stable fixed point in (0,0), we would visualize a blue stain (low density in the starting range) that shrinks into a red dot in (0,0) (high density close to the fixed point). This means that all the solutions get closer and closer as they approach the fixed point. \\ The simulation runs in parallell and requires the package 'parallel python' (import pp). You can download this package here, \\ http://www.parallelpython.com/ \\ Beware of the computational cost of generating this movie. You don't want to have too many initial conditions and/or integrate them for a long time. \\

## Zipf's law

This script takes a file with text and ranks the ocurrence of words. You can test this script with testText.txt (a wikipedia article on mate) An empirical law formulated using mathematical statistics, refers to the fact that many types of data studied in the physical and social sciences can be approximated with a Zipfian distribution, one of a family of related discrete power law probability distributions \cite{wikipedia}.