Abstract
The intermediate dimensions of a set $\Lambda$, elsewhere denoted by $\dim_{\theta} \Lambda$, interpolate between its Hausdorff and box dimensions using the parameter $\theta\in[0,1]$. For a Bedford–McMullen carpet $\Lambda$ with distinct Hausdorff and box dimensions, we show that $\dim_{\theta} \Lambda$ is strictly less than the box dimension of $\Lambda$ for every $\theta<1$. Moreover, the derivative of the upper bound is strictly positive at $\theta=1$. This answers a question of Fraser; however, determining a precise formula for $\dim_{\theta}\Lambda$ still remains a challenging problem.
Type
Publication
J. Fractal Geom. 9(1), 151-169
