Animals' sensory systems evolved to efficiently process information from their environmental niches. Niches often include irregular shapes and rough textures (e.g., jagged terrain, canopy outlines) that must be navigated to find food, escape predators, and master other fitness-related challenges. For most primates, vision is the dominant sensory modality and thus, primates have evolved systems for processing complicated visual stimuli. One way to quantify information present in visual stimuli in natural scenes is evaluating their fractal dimension. We hypothesized that sensitivity to complicated geometric forms, indexed by fractal dimension, is an evolutionarily conserved capacity, and tested this capacity in rhesus macaques (Macaca mulatta). Monkeys viewed paired black and white images of simulated self-similar contours that systematically varied in fractal dimension while their attention to the stimuli was measured using noninvasive infrared eye tracking. They fixated more frequently on, dwelled for longer durations on, and had attentional biases towards images that contain boundary contours with higher fractal dimensions. This indicates that, like humans, they discriminate between visual stimuli on the basis of fractal dimension and may prefer viewing informationally rich visual stimuli. Our findings suggest that sensitivity to fractal dimension may be a wider ability of the vertebrate vision system.