Dynamo is a suite of easy-to-use Mathematica notebooks for generating phase diagrams, vector fields, and other graphics related to evolutionary game dynamics.
The four phase diagrams above were generated using the four Dynamo workbooks. (In the first two figures, colors reflect speed of motion: blue is slowest, red is fastest.)
For more pictures and animations, visit the project gallery.
Dynamo now takes advantage of Mathematica's ability to perform live rotation of three-dimensional graphics.
Francisco Franchetti and I have written an introduction to Dynamo. We describe how to use the software's default settings to generate phase diagrams quickly and easily. We then explain how to take advantage of the software's intermediate and advanced features to create diagrams that highlight the key properties of the dynamical system under study. Sample code and output are provided to help demonstrate the software's capabilities.
Dynamo v1.1 and v0.2.5 run in Mathematica 6, 7, and 8. They do not run in Mathematica 4 or 5. For the legacy version (0.1.5) that does, visit here.
Dynamo is free, open source software.
If you use Dynamo in your work (e.g., to create figures for articles or books), we would be grateful for your citation.
W. H. Sandholm, E. Dokumaci, and F. Franchetti (2012). Dynamo: Diagrams for Evolutionary Game Dynamics. http://www.ssc.wisc.edu/~whs/dynamo.
I am maintaing a list of papers and books containing figures created in Dynamo - and here it is.
Please e-mail me with any feedback you have about the program, or to have your publication added to our list.
In 2003, I began working on Dynamo when I realized I would need to create many illustrations of game dynamics for my book on evolutionary game theory. Emin Dokumaci was the lead programmer of Dynamo from 2003-2007, and did most of the coding of the Mathematica 4/5 version of the software.
In 2007, Wolfram released Mathematica 6, which included some impressive new features (like rotatable 3D graphics), but also many small changes in the programming language that made code written for older versions of Mathematica behave badly. Grrrr. So the code was frozen, until...
In 2010, Francisco Franchetti became the new lead programmer of Dynamo, and he gamely updated the Dynamo code to run Mathematica 6/7.
In April 2011, Francisco and I completed a polished version of Dynamo 3S, which we have (after only eight years!) dubbed version 1.0. The corresponding updates of the other notebooks are underway.
In March 2012, Francisco and I finished a paper explaining how to use Dynamo, and posted a polished version of Dynamo 4S.
The Gambit library, by Richard McKelvey, Andy McLennan, and Ted Turocy, provides a variety of tools for drawing and (especially) solving normal and extensive form games.
Christoph Hauert's VirtualLabs in evolutionary game theory provides tools for studying evolutionary dynamics in spatial games - that is, games played by agents located at points on lattices or other graphs. The animations are amazing - see for yourself!
Julián García and Matthijs van Veelen maintain an Evolution and Games wiki. It provides Java applets for running simulations of evolutionary game models, as well as tutorials on various topics in evolutionary game theory.
I am grateful for financial support from the National Science Foundation under Grants SES-0092145, SES-0617753, and SES-0851580.