The purpose of this repository is to disseminate the numerical experiments reported in the following paper:

• Samuel A. Ballas, Tom Needham, and Clayton Shonkwiler. On the existence of Parseval frames for vector bundles. Transactions of the American Mathematical Society, Series B 12 (2025), 395–416. arXiv:2312.13488 [math.DG].

The numerical experiments are performed in the Mathematica notebook vf.nb. If you do not have Mathematica installed, this can be opened (but not evaluated) with the free Wolfram Player.

Note that the notebook evaluates simplex noise using lmas’s Python port of Kurt Spencer’s original code. To use this functionality, you’ll need to run pip install opensimplex.

This work was supported by the National Science Foundation (DMS–2107808 and DMS–2107700).