Escher Strange Loops

Ascending and descending, M.C. Escher 1960

39 years from the death of Maurits Cornelis Escher (17 June 1898 – 27 March 1972)
The “Strange Loop” phenomenon occurs whenever, by moving upwards (or downwards) through the levels of some hierarchical system, we unexpectedly find ourselves right back where we started… Sometimes I use the term Tangled Hierarchy to describe a system in which a Strange Loop occurs…
To my mind, the most beautiful and powerful visual realizations of this notion of Strange Loops exist in the work of the Dutch graphic artist M.C. Escher, who lived from 1902 to 1972. Escher was the creator of some of the most intellectually stimulating drawings of all time. Many of them have their origin in paradox, illusion, or double-meaning. Mathematicians were among the first admirers of Escher’s drawings, and this is understandable because they often are based on mathematical principles of symmetry or patterns …
But there is much more to a typical Escher drawing than just symmetry or pattern: there is often an underlying idea, realized in artistic form. And in particular, the Strange Loop is one of the most recurrent themes in Escher’s work …
Escher realized Strange Loops in several different ways, and they can be arranged according to the tightness of the loop. The lithograph Ascending and Descending, in which monks trudge forever in loops, is the loosest version, since it involves so many steps before the starting point is regained. A tighter loop is contained in Waterfall, which involves only six discrete steps...

Douglas R. Hofstadter [Gödel, Escher, Bach: An eternal golden braid. A metaphorical fugue on minds and machines in the spirit of Lewis Carroll, 1979]

Waterfall, M.C. Escher 1961