Dragon Curves Revisited

Abstract

It has happened several times in recent history that a mathematical discovery of great beauty and importance was originally published in a journal that would not likely to be read by many a working mathematician. One famous example is the Penrose tilings [15]. Surely, Penrose tilings and the theory of quasicrystals is now a major area of research (see, e.g., [17]), and not only in mathematics but also in physics and chemistry, as witnessed by the 2011 Nobel Prize awarded to D. Shechtman for “the discovery of quasicrystals” in 1982. It is a pleasure to mention that this magazine played a role in popularizing Penrose tilings [16]. The topic of this column is another mathematical object of comparable beauty, the Dragon curves, whose theory was created by Chandler Davis and Donald Knuth [4]. The original articles are not easily available (they are reprinted in [10], along with previously unpublished addendum). Mathematical Intelligencer wrote about Dragon curves more than 30 years ago [5, 6, 7]. In spite of the existence of a Wikipedia article on the subject and in spite of their appearance in M. Crichton’s popular novel “Jurassic Park”, Dragon curves are not sufficiently well known to contemporary mathematicians, especially the younger ones who missed the original excitement of 40+ years ago. The goal of this article is to bring Dragon curves to spotlight again and to pay tribute to Chandler Davis, a co-author of an elegant theory that explains the striking features of these curves. This article is merely an invitation to the subject; the reader should not expect a thorough survey of the results or proofs.