Abstract

Entwined circular rings ("In elkaar gevlochten cirkelvormige ringen") was the title that M.C. Escher gave to a little research project he started around 1945. Although the start of this project was very well set up he didn't come further than the first page on which he shows us how you can make patterns of entwined circular rings based upon a square grid. Because I often make use of these kinds of patterns in my own work I decided to pick up this research project and try to find out how Escher would have continued this project.

1. Introduction

1.1. Escher's drawings. In 1979 I had the opportunity to go through Escher's notebooks in the Haags Gemeentemuseum in the Hague, Holland. In one of the notebooks we can find several drawings of patterns of entwined circular rings. And one of the pages is set up as a start of research project, probably with the goal to find out the different possibilities of these kinds of patterns. The first page represents a list of four such patterns based on a square grid. The title on the page with these drawings (see Figure 1) says: "A: four-fold axes at each center point.". On other pages in this notebook we can find some more drawings of patterns with entwined circular rings based upon a triangular grid (Figure 2). All these drawings are published in Doris Schattschneider's book M.C. Escher: Visions of Symmetry (ref. [1]).