Self-Driven Particle Model,
an Interactive Tutorial by Sam and
Designed for SIAM's DSWeb Tutorials, Fall 2005
The Self-Driven Particle Model is a toy dynamical
system in which particles move in 2-dimensions, and interact with each
other according to a simple rule. Particles
move at a constant speed, and their orientation is set to be the
average orientation of all particles (including themselves) within an
interaction radius, plus a random term. This model has been shown
to exhibit complex dynamical behavior, including a 2nd order phase
transition, criticality and clustering. This tutorial introduces
the model incrementally, and depicts the computation of the order
parameter, critical parameter and critical exponent.
The Self-Driven Particle Model was proposed as a
minimal description of swarming behavior in 2-dimensions, and has been
compared to transport of groups of quadrupeds, bacterial migration and
bird flocking. The system was first studied by
, a special case of the model introduced by . Although more
realistic models have been developed
for direct study of such systems , the Self-Driven Particle Model
remains important because of the model simplicity richness of the
emergent phenomena. The model is analagous to the Ising model,
with particle randomness analagous to temperature, and particle
clusters analogous to spin clusters .
This system is highly visual, and the emergent
properties are easy to visualize. We hope that this introductory
tutorial will facilitate visualization and understanding of emergent
The Tutorial is organized into three main
I. Introduction to the Model
II. Emergent Properties
A. Order Parameter
B. Criticial Values
C. Critical Exponent.
III. Open-Ended platform for experimentation.
This Interactive Tutorial requires
Java 1.4.2 and up:
Once you have verified your Java 1.4.2+ installation:
Launch the Interactive Tutorial via Java Web
Click here to View Screenshots
Errata (Known Bugs)
T. Vicsek, A. Cziro´k, E. Ben-Jacob, I. Cohen, and O. Shochet,
Novel type of Phase Transition in a System of Self-Driven Particles,
Phys. Rev. Lett. 75, 1226 (1995).
 C. Reynolds. Flocks, birds, and schools: a distributed behavioral
model. Computer Graphics, 21:25–34, 1987.
 D. Helbing, Traffic and Related Self-Driven Many Particle Systems,
Reviews of Modern Physics, 2001
C. Huepe, M. Aldana, Intermittency and Clustering in a System of
Particles, Physical Review Letters, Vol. 92, #16, 2004.
 A. Jadbabaie, J. Lin, and A. S. Morse, Coordination of
Groups of Mobile Autonomous Agents Using Nearest Neighbor Rules, IEEE Transactions
on Automatic Control, Volume 48, Issue
6, June 2003, pages 988-1001.