Arnold weak resonance equation as the model of Greek ornamental design

TL;DR

This paper introduces a mathematical model based on weak resonance differential equations to replicate and analyze ancient Greek ornamental designs, revealing how parameter variations influence design features and enabling the creation of new patterns.

Contribution

The study applies Arnold's weak resonance equation to model Greek ornamental designs, providing insights into their structure and variability, and offering a method to generate new designs.

Findings

Model reproduces ancient Greek ornamental patterns.

Parameter changes affect design features and indeterminacy.

Enables creation of new ornamental designs.

Abstract

We propose and study a mathematical model that qualitatively reproduces several ancient ornamental designs than one can see in historical museums of Crete and Athens. The designs contain several rings that circumscribe a fixed number of centers or spirals, specific to each design. The model 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.