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Research Environments


Automata is a control program for a collection of programs for working with automatic groups. The aim of the package is to construct the word acceptor and multiplier automata associated with a shortest word automatic group.

The individual programs, as well as the C source code are publicly available by ftp from the Geometry Center. The automata package was written by David Epstein, Derek Holt and Sarah Rees of the University of Warwick (in part at the Center). For more information, consult the man pages, or contact Derek Holt (dfh@maths.warwick.ac.uk) or David Epstein (dbae@maths.warwick.ac.uk).


DsTool (pronounced dee-ess-tool) is an X11 implementation of an environment for investigating dynamical systems It is an efficient research tool that integrates a friendly graphical user interface, data management capabilities, a rich set of numerical algorithms together with the flexibility to add more algorithms and communicate data with other programs. DsTool has been implemented for use with the X Window system from MIT with the XView toolkit and is based upon the program kaos, written by S. Kim and J. Guckenheimer.

DsTool is available by anonymous ftp from the Center for Applied Mathematics at Cornell University, cam.cornell.edu, in the pub/dstool subdirectory. It is also installed locally at the Geometry Center.

A on-line tour of DsTool is also available.


The Surface Evolver is an interactive program for the study of surfaces shaped by surface tension. Given an initial surface, the Evolver can evolve it toward minimal energy. The energy can be surface tension, gravitational energy, squared mean curvature, or user-defined surface integrals. The Evolver can handle arbitrary topology (as seen in real soap bubble clusters), volume constraints, boundary constraints, boundary contact angles, prescribed mean curvature, crystalline integrands, gravity, and constraints expressed as surface integrals. The surface can be in an arbitrary dimensional Riemannian space with a metric, and the space can be a quotient space under a group action. The Evolver was written for one and two dimensional surfaces, but it can do higher dimensional surfaces with some restrictions on the features available.

The Evolver was written as part of the Geometry Supercomputing Project (now the Geometry Center) by Ken Brakke (brakke@geom.umn.edu). For further information about Evolver, consult the Evolver home page.


KnotPlot is a fairly elaborate program to visualize and manipulate knots in three and four dimensions. Knots can be loaded from a database of several hundred knots and links (the complete appendix C of Rolfsen's book `Knots and Links') or sketched by hand in three dimensions. Also, knots may be constructed via the Conway notation or using a tangle calculator. A number of special knot types (torus knots, knot chains, Lissajous knots) may be created on the fly. New knots can be created from old knots using a number of transformations, by relaxing the knot under several types of dynamics, or by direct manipulation with the mouse. KnotPlot exports data to numerous file formats, including picture formats, 3D surface models, and various others. Encapsulated Postscript files suitable for inclusion into research papers are easily generated in many flavours. Finally, several excursions into 4D may be made (twist-spun knots and other things).

KnotPlot is installed at the Center and runs on the Silicon Graphics machines. An extensive on-line manual is available.

More information, MPEG animations, hundreds of images, and downloadable goodies may be found at the KnotPlot Site at the University of British Columbia.


Pisces is a Platform for Implicit Surfaces and Curves and the Exploration of Singularities. In a nutshell, Pisces is a project that attempts to supply the mathematical and scientific communities with numerical tools to compute and visualize curves and surfaces that are defined implicitly. For a simple example, note that the equation to x^2+y^2=1 is satisfied by the set of points on in the plane that lie on the unit circle, so that the equation implicitly defines the unit circle. One product of the Pisces project is a software package that provides a variety of state-of-the-art algorithms for computing implicitly-defined curves and surfaces. This software is under development. Release is scheduled for mid-October.

For a more in depth overview, consult the Pisces home page (also under development).


Snappea is a collection of interconnected programs for analyzing hyperbolic manifolds. In particular, it analyzes the hyperbolic structure of knot compliments. The user can interactively edit a link, compactify the complement via Dehn fillings, and display Dirichlet domains for the resulting uniformized hyperbolic manifold. Once can also compute many related mathematical quantities, such as Chern-Simons invariants , volumes, fundamental groups presentations complete with generators in PSL(2,C), length spectra, and homology groups. Besides working with knot complements, users can explore manifolds from a large and growing "manifold census" or investigate hyperbolic structures on punctured torus bundles.

More information can be found on the Snappea download page and in the documentation which accompanies the software distribution available there.

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Created: Fri Sep 8 11:39:00 1995 --- Last modified: Jun 18 1996