**Up:** *mathematical computation*

# Research Environments

## Automata

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

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.

## Evolver

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

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

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

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.

**Up:** *mathematical computation*

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