Symmetry, Periodicity, and M. C. Escher

Updated 8/15/02

... I wander totally alone around the garden of periodic drawings. However satisfying it may be to possess one's own domain, yet loneliness is not as enjoyable as one might expect; and in this case I really find incomprehensible...But periodic drawings are not merely a nervous tic, a habit, or a hobby. They are not subjective; they are objective. And I cannot accept, with the best will in the world, that something so obvious and ready to hand as the giving of recognizable form, meaning, function, and purpose to figures that fill each other out, should never have come into the head of any other man but me. For once one has crossed over the threshold of the early stages this activity takes on a more worth than any other form of decorative art.

-M. C. Escher, Regelmatige Vlakverdeling Utrecht, (Periodic Space-Filling) 1958

In 1993, I began exploring the periodic nature of Escher's work, and I saw how naturally it would apply to the intertwined bodies I was working with. By using certain symmetries, I was able to create from one cell an ever expanding picture that revealed lovely patterns. The two paintings on the following pages illustrate what I mean.

Escher was quite right that once an artist "crossed over the threshold of the early stages this activity takes on more worth than any other form of decorative art." I too find the results compelling, but I think there is a simple reason why other artists have avoided exploring it for themselves. Escher goes on to say, from this same quote, "I knew no rules of the game and I tried, almost without knowing what I was about, to fit together congruent surfaces to which I tried to give animal shapes ... later the designing of new motifs gradually came with rather less struggle than in the early days, and yet this has remained a very strenuous occupation, a real mania to which I became enslaved and from which I can only with great difficulty free myself."

Even when my floating bodies were self-contained, getting everyone to fit was difficult. But the process of implementing periodicity provides such an intriguing puzzle with such possibility, it is indeed hard to free oneself.

You are visitor number since 2/21/97