Marcel F. Corchado Albelo, Maria D. Kazachenko, Ryan J. French, Vadim M. Uritsky, Emily Mason, Cole A. Tamburri, Rahul Yadav, Benjamin J. Lynch

Recent three-dimensional flare models suggest that flare-ribbon substructure is linked to the fragmentation of the reconnecting current sheet in the corona. Flare-ribbon substructure can therefore potentially serve as a unique diagnostic tool for physical processes in the flare current sheet. In this paper, we describe a new method to quantify the evolution of ribbon substructure, which first extract the ribbon's leading bright front and the quantifies its morphology using the box-counting dimension and Correlation Dimension Mapping (CDM). We first test our method using synthetic observations. We then find that when the flare ribbon boundary has more multi-spatial-scale features (higher box-counting dimension), hard X-ray (HXR) emission and magnetic reconnection rates are the strongest. We also find that the flare-ribbon complexity characterized by CDM has moderate correlation with the IRIS Si IV 1402.77 Å non-thermal velocity (in the negative-polarity ribbon) and reconnection flux rates (in ribbons of both magnetic polarities). We conclude that the build-up of the spatial complexity of the ribbons at multiple spatial scales can serve as an observational proxy for current-sheet fragmentation in the corona.