Parquet deformations animated
Cairo tiling deformation
Parquet deformation
I later discovered this was called a "parquet deformation". It happens to be the #9 on this page by David Bailey:
http://www.tess-elation.co.uk/parquet-deformations
GIF (Cairo wave) - optimized
![GIF (Cairo wave) - optimized](https://www.geogebra.org/resource/afhkbh7g/uYegj4zO2a7lC73V/material-afhkbh7g.gif)
Parquet deformation #4
Parquet deformation #4 (GIF)
![Parquet deformation #4 (GIF)](https://www.geogebra.org/resource/prd4p9cy/PMt5E28GI80TQmjq/material-prd4p9cy.png)