You might find
iOrnament of interest for your problem. Prof. Dr. Dr. Richter-Gebert from TU Munich has designed the app. With it you can apply group-theoretic symmetries and permutations to a drawn picture. They also tried to recreate the Escher-pictures with their app and connect it to Group Theory.
A gallery of some pictures can be found here:
One of the example-pictures created with the app that goes into the "Escher-direction" is the following:
Prof. Richter-Gebert has also given several talks about the mathematics behind the app and the pictures. One of the talks has been uploaded by the National Museum of Mathematics under the following link:
Some information about the mathematics involved is also given in the app itself. There are also some papers by Richter-Gebert (in German), for example this one
Richter-Gebert, Jürgen. "iOrnament–Die Kunst der glatten Linie." Mitteilungen der Deutschen Mathematiker-Vereinigung 25.2 (2017): 71-74.
but also English ones such as this one
von Gagern, Martin, and Jürgen Richter-Gebert. "Hyperbolization of Euclidean ornaments." Electronic Journal of Combinatorics 16.2 (2009): R12.
or this one (not by Richter-Gebert):
Adanova, Venera, and Sibel Tari. "Analysis of planar ornament patterns via motif asymmetry assumption and local connections." Journal of Mathematical Imaging and Vision 61.3 (2019): 269-291.