This study aimed to quantify and investigate differences in the geometric and algorithmic complexity of the microvasculature in nailfold capillaroscopy (NFC) images displaying a scleroderma pattern and those displaying a 'normal' pattern. 11 NFC images were qualitatively classified by a capillary specialist as indicative of 'clear microangiopathy' (CM), i.e. a scleroderma pattern, and 11 as 'not clear microangiopathy' (NCM), i.e. a 'normal' pattern. Pre-processing was performed, and fractal dimension (FD) and Kolmogorov complexity (KC) were calculated following image binarisation. FD and KC were compared between groups, and a k-means cluster analysis (n = 2) on all images was performed, without prior knowledge of the group assigned to them (i.e. CM or NCM), using FD and KC as inputs. CM images had significantly reduced FD and KC compared to NCM images, and the cluster analysis displayed promising results that the quantitative classification of images into CM and NCM groups is possible using the mathematical measures of FD and KC. The analysis techniques used show promise for quantitative microvascular investigation in patients with systemic sclerosis.