Torus under the Identity Map

This image (from open3D docs) is mapped onto a torus.

UV Checkerboard Texture

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.

UV Checkerboard Texture UV Checkerboard Texture

Torus after the First Iteration

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

UV Checkerboard Texture UV Checkerboard Texture UV Checkerboard Texture

Torus after the Second Iteration

Torus under the Third Iteration

Torus under the Fourth Iteration

Torus under the Fifth Iteration

Torus under the Sixth Iteration

Torus under the Seventh Iteration

Torus under the Eighth Iteration

Torus under the Ninth Iteration

Torus under the Tenth Iteration