Can fractal dimension distinguish between grand-design and flocculent spiral arms?

About two-thirds of disk galaxies host spiral arms, ranging from well-delineated grand-design spirals to fragmented flocculent spiral galaxies. We introduce fractal dimension $D_B$ as a non-parametric measure to distinguish between grand-designs and flocculents. We calculate the $D_B$ of 197 grand-designs and 322 flocculents from SDSS DR18, using the samples of \citet{Buta..2015} and \citet{Sarkar..2023}. Our calculated median values of $D_B$ are $1.29^{+0.06}_{-0.04}$ and $1.38^{+0.05}_{-0.06}$ for the grand-designs and flocculents, respectively. In addition, a Kolmogorov-Smirnov (K-S) test rejects null hypothesis that these distributions are drawn from the same population. Finally, using a Random Forest (RF) model, we compare the effectiveness of $D_B$ in classifying spiral arm morphology, as compared to five other parameters viz. total atomic hydrogen HI mass $M_{HI}$, ratio of atomic hydrogen mass-to-blue luminosity $M_{HI} /L_B$, concentration index $C_i$, clumpiness $S$ and arm-contrast $C$. Our results indicate that $D_B$ has the highest feature index (30.8\%), followed by $C_i$ (26.0\%) and $M_{HI}$ (21.0\%). In fact, C, the metric routinely used to distinguish between the spiral morphologies has a feature importance of 8.3\%. Further, $D_B$ for grand-designs is found to anti-correlate with the central velocity dispersion with a correlation coefficient of -0.3 and $p \ll 0.05$. A high value of central velocity dispersion indicates a central Q-barrier, which favors the formation of grand designs according to the density wave theory. Thus, fractal dimension serves as a robust metric to distinguish between spiral morphologies and also links to the formation mechanism of spiral features.