This image from the open3D docs is mapped onto a torus.

A Dehn Twist, specically the one defined by the matrix $$\begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}$$ is applied to the same image as before, which is a UV checkerboard texture commonly used for testing in 3D graphics. It is then mapped onto the torus.

The Dehn Twist $$\begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}$$ is applied again to the transformed image