M.C. Escher occupies a unique spot among the most popular artists of the past century. While his contemporaries focused on breaking from traditional art and its emphasis on realism and beauty, Escher found his muse in symmetry and infinity. His attachment to geometric forms made him one of modernism’s most recognizable artists and his work remains as relevant as ever.
Escher’s early works are an odd mix of cubism and traditional woodcut. From these beginnings, one could already note Escher’s fondness for repetition and clean shapes. While simple and exploratory, these works were the signs of a nascent art career.
Beginning in the mid-1930s, Escher’s work turned very pointedly to the style we associate with him today. Some of his most iconic works were completed in this period and his fascination with spherical distortion, recursion, and optical illusions took full force. Recursion figured very prominently in this and later periods, so it’s worth understanding what it is and how Escher was led to it.
Few people have heard of Roger Penrose, H.S.M. Coxeter, or George Polya, but all of these mathematicians influenced Escher’s approach to art. Penrose and Coxeter especially had a lasting impact on Escher and his own mathematical research, as both were interested in geometry and repetition. Penrose was interested in repetition and had, later in life, discovered a specific set of tiles called Penrose tilings which are recognizable in floor designs in various buildings. Coxeter was an expert geometer who introduced Escher to many higher-level geometrical concepts. Escher himself was interested in topology, the study of surfaces, and tessellations, non-overlapping patterns. It’s unclear if Escher was aware of the study of recursion in mathematics, but his work shows some of the most interesting examples of it in the arts.
Recursion is a fairly simple concept. Something that recurs references itself. The reflection in a mirror of a mirror is recursive: the reflected mirror is reflecting its own image and doing so indefinitely. You’ve also likely seen the Droste effect when using camcorders hooked up to a TV or a computer: when the camcorder is looking at the screen, you can see an infinite series of screens generate themselves, since the camcorder is recording the same image that it’s sending to the screen. The game Portal is a great example of recursion, when two portals could be opened side by side in a narrow space and looking in either one produced an infinite series of the same image.
Escher combined recursion and pattern repetition in a unique way. Some of the works featuring this combination exhibits some complex mathematical and physical ideas, but to the casual viewer the works are sublime. The swans image above features this sort of combination. Note that the swans are tiled very precisely, with the same distance from adjacent swans and swans in the next row. Note also that they are in a closed loop, which is one construct made...