The branching patterns of retinal arterial and venous systems have characteristics of a fractal, a geometrical pattern whose parts resemble the whole. Fluorescein angiogram collages were digitised and analysed, demonstrating that retinal arterial and venous patterns have fractal dimensions of 1.63 +/- 0.05 and 1.71 +/- 0.07, respectively, consistent with the 1.68 +/- 0.05 dimension of diffusion limited aggregation. This finding prompts speculation that factors controlling retinal angiogenesis may obey Laplace's equation, with fluctuations in the distribution of embryonic cell-free spaces providing the randomness needed for fractal behaviour and for the uniqueness of each individual's retinal vascular pattern. Since fractal dimensions characterise how completely vascular patterns span the retina, they can provide insight into the relationship between vascular patterns and retinal disease. Fractal geometry offers a more accurate description of ocular anatomy and pathology than classical geometry, and provides a new language for posing questions about the complex geometrical patterns that are seen in ophthalmic practice.