# Arnold’s Weak Resonance Equation as the Model of Greek Ornamental Design

## Abstract

We propose and study a mathematical model that reproduces qualitatively several ancient ornamental designs that one can see in archeological and historical museums of Crete and Athens. The spiraling wave pattern can be seen throughout the full spectrum Classical tradition. The designs contain several rings that circumscribe a fixed number of “flowers” (centers or spirals), specific to each design.

The model proposed is based on a complex differential equation of “weak resonance” (Arnold 1977). We analyze the role of the model parameters in giving rise to different peculiarities of the repeated designs, in particular, the “dynamical indeterminacy.” The model allows tracing design changes under parameter variation, as well as to construct some new ornamental designs. We discuss how observed ornamental design may reflect some philosophical ideas of ancient inhabitants of Greece.

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