Wolfram Library Archive

All Collections Articles Books Conference Proceedings
Courseware Demos MathSource Technical Notes
Title Downloads

Pi from agent border crossings by NetLogo package

Ervin Wirth
Organization: Budapest University of Technology and Economics
Department: Photogrammetry and Geoinformatics
Revision date


In this tutorial I will guide you through a novel way of calculating the perimeter (or even the surface) of formations by an integrated model with logical agents. The logical agents are wandering (as random walking) around the world, which their movements follows a uniform distribution of rotations. They registrate the land cover changes under their feet to a common sum, that I consider as a Monte Carlo integral. By simulating the walking for a longer period, I can discover that the model converges from stochastic to a deterministic one. This can be proven by the rerunning of algorithm more times, and plot the results. The plots and test are convince us about the normal distribution of the results. Finally with high parameter setups I can approximate well the value of Pi.

*Applied Mathematics > Numerical Methods
*Applied Mathematics > Numerical Methods > Approximation Theory
*Mathematics > Discrete Mathematics
*Wolfram Technology > Linking Technology > J/Link

logical agents, perimeter, pi, monte carlo method, netlogo, agent-based modelling, random walking, uniform distribution, normal distribution, torus, simulation, stochastic, deterministic
Downloads Download Wolfram CDF Player

1.asc (469.6 KB) - ASCII file
2.asc (469.6 KB) - ASCII file
ABM.pdf (203.8 KB) - PDF Document
1.prj (372 B) - Unknown MIME type
2.prj (372 B) - Unknown MIME type
ABM.nb (970.5 KB) - Mathematica Notebook
Introduction.nlogo (12.4 KB) - Unknown MIME type