We have two purposes here:
First thing is to have a Monte Carlo simulation example in Python. We implement Buffon's experiment where one estimates number π by trowing a needle on a pattern made of parallel lines. Monte Carlo simulation evaluates an integral that appears in the process, by a numerical experiment.
The other thing we want to show is how to manipulate Postscript trough python programs, and create PS documents interactively. A Post Script document made here is tailored specifically to plot results of Buffon needle experiment.
More specifically, we are merging Monte Carlo simulation example and the postscript functionality to produce a wonderful image found in a book by Werner Krauth - Statistical Mechanics - Algorithms and Computation. The figure we make is a reconstruction of Fig. 1.10 in the book.
To run the example just type in shell (or just run the script):
python buffon.py
You will be prompted to enter the number of needles. To reproduce the image from the book I enter 2000:
Number of needles: 2000
Simulation over!
The result is a Postscript document 'buffon-experiment-fig'. You may convert it to PDF:
ps2pdf buffon-experiment-fig.ps
