On the fractal dimension of the Duffing attractor

TL;DR

This paper investigates the fractal dimensions of the Duffing attractor, demonstrating that both box counting and correlation dimensions converge to finite values with increasing data points, specifically around 1.43 and 1.38.

Contribution

It provides numerical estimates of the fractal dimensions of the Duffing attractor and shows their convergence behavior as data points increase.

Findings

Fractal dimensions tend to finite values with more points

Estimated box counting dimension is approximately 1.43

Estimated correlation dimension is approximately 1.38

Abstract

The box counting dimension $d_C$ and the correlation dimension $d_G$ change with the number of numerically generated points forming the attractor. At a sufficiently large number of points the fractal dimension tends to a finite value. The obtained values are $d_C\approx 1.43$ and $d_G\approx 1.38$.