Attraction and Repulsion in Dynamical Systems

This Demonstration simulates attraction and repulsion in dynamical systems, described by a potential function , with being the relevant distance parameter. When applied to -body systems, this simple formula can lead to rich and diverse dynamics for different values of , , , and .


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


Typically, the attraction term dominates at larger distances, while the repulsion is dominant at smaller distances. For and this formula refers to the Lennard–Jones 6-12 potential, used in molecular dynamics models. For it could be viewed as gravitational potential plus an added repulsive component at close distances. In general, this kind of function could be used in simulations related to a variety of problem domains. In [1] such potential functions are applied to model swarming behavior or variations of chase-and-evade algorithms.
[1] D. M. Bourg and G. Seemann, AI for Game Developers, Sebastopol, CA: O'Reilly Media, 2004 pp. 80–89.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+