Dementia is believed to be associated with changes in the physical structure of brain tissue, particularly in the pattern of small blood vessels. This study investigates one of the current research questions in the understanding of dementia, that is, whether there are differentiating factors in the structure of blood vessels of the cortex associated with different dementia subtypes and controls. Our approach is to use automated classification techniques to build predictive models based on fractal and non-fractal morphological descriptors, in order to label images of post mortem brain tissue with the appropriate pathology. Our goal is not to provide automated diagnosis, but to confirm or deny the presence of a relationship between morphological features and disease. The use of a variety of machine learning methods allows the exploration of the complex relationships that may exist. This study also addresses the choice of suitable features and the role of fractal analysis in medical image processing. The results suggest that there are differentiating factors, but these are difficult to detect, and vary between different areas of the cortex. Features derived from multi-fractal analysis showed more promise in this application than the non-fractal features we studied.