This page shows a splash in a pond. The animations produced by DPGraph and Mathematica are compared.

A solution to the wave equation, utt = uxx + uyy, which is periodic in time, radially symmetric, and has outgoing waves is

u =J0(r)cos(t) + Y0(r)sin(t) ,
where J0 and Y0 the Bessel functions of the first and second kind (both of order 0). The second function, Y0, is unbounded as r approaches 0.

The Bessel functions are defined in Mathematica, but not in DPGraph, where I used approximations involving sines and cosines.

Click on the thumbnail to run the animation. To stop the DPGraph animation, close the program. To stop the Mathematica animation, which is an animated GIF displayed by your browser, click "back."

[DPGraph splash]
DPGraph (654 Bytes, < 1 KB)
[Mathematica splash]
Mathematica v.5 (594 KB)
The Mathematica source code that produced the animated GIF is here (6 KB). You may download it and use it as a template for your own animations.

Here is an updated splash file using Mathematica version 8.

Here is an example of a demonstration in Mathematica, for a quantum barrier.

As an experiment to see if we can get 3D graphics that most people can see, I made it by exporting a CDF file from within Mathematica v. 8. If you cannot view it, try installing Mathematica's CDF viewer. Reloading the page restores the original viewpoint.

Jim Swift's DPGraph page     Jim Swift's home page     Department of Mathematics     NAU
e-mail: Jim.Swift@nau.edu