*Multimodal mathematical visualization* expands the notion of "image"
to include 3D, motion, sound, and (eventually) haptics. It is an
inherently time-based form and, as such, shares many of the immersive,
tele-immersive, and large-scale visualization research questions of
data visualization and tangible/intangible computing. Methodologies
and classification systems developed for the dynamic perception of
complex, yet deterministic, mathematical structures can contribute
much to these fields.

**1.**
**A visual study for a
sound map**. In the Viz-server object shown, multiple
integer lattices in the plane have been rescaled to
lattices. The resultant rational lattice in the plane is then rescaled
by horizontal and vertical frequencies and multiplied by a flow time
parameter that starts at zero. Under the quotient
one obtains a rational lattice whose "endpoint" flows along the torus
knot defined by the (now) longitudinal and meridian frequencies of the
scaling. The dominant visual structure observed is the local proximity
(in time) of simple rational alignments in the flow. Lattice points
converge to, and diverge from, flow time events. This visual structure
is further accentuated by staggering the longitudinal and meridian
radii of the torus as a function of the flow time, giving a visual
study for a sound map.

**2.**
**MVS
(Mathematics Visualization System)**. This work is being
done in the MVS environment. MVS is a visualization tool tailored to
multimodal mathematical visualization; optimized for perceiving
abstract structure mapped flexibly to multimodal parameters; a time
based form rather than static viewer; dynamic loading of mathematical
concept to be visualized. It has an emphasis on abstract rather than
realistic displays, the capability to render even computationally
demanding visualizations, and has been designed from the beginning for
use with immersive or virtual reality displays. MVS shares some
similarities with Visual Python, in particular allowing mathematicians
with programming skills but not detailed knowledge of 3D graphics to be
able to create visualizations

The core of MVS is written in C++ and uses the SGI Performer 3D graphical toolkit for rendering. The mathematical algorithms that generate the visualizations are written in Python and C. The current version of MVS runs on SGI IRIX, with a Linux version in the works. Development is being done by Robin Johnson, Julie Tolmie and Hugh Fisher presently. Further information can be found at http://mvs.sourceforge.net/

**3.**
**Collaborative Environments: low end/high end, 2D vs. 3D,
immersive vs. remote**. MVS objects currently run in
numerous remote environments using Viz-Server: Julie Tolmie and Robin
Johnson (below left) are working in Vancouver in the Fakespace at SFU
Surrey; the Cave at NewMIC; and SFU Colab. The object demonstrated
today is running remotely from the Viz-server at NewMIC. Meredith
Walsh, Stephen Barass, and Hugh Fisher (below right) in the Wedge,
VELab (Virtual Environments Laboratory), CSIRO, Canberra, earlier this
year. Presently work is also being done to provide MVS with it's own
collaboration system for use with low bandwidth networks.

Other remote and local collaborators interested in the data visualization and tangible/intangible computing aspects of this work include the V2 Institute for the Unstable Media, (Rotterdam, The Netherlands), Interactive Arts (SFU Surrey), School of Contemporary Arts (SFU).

Julie Tolmie - julie_tolmie@sfu.ca
- CoLab Member and SFU Surrey Faculty