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Abstract The Arctic marginal ice zone (MIZ) is the transitional region between dense pack ice and open ocean. As an increasingly important component of the polar marine environment, recent investigations have focused on changes in MIZ size and location as the climate has warmed. Fractal geometry offers a universal measure of complexity, shape, and self-similarity across scales, and a powerful tool for characterizing MIZ evolution. Here we analyze the fractal dimension of the Arctic MIZ boundary and find a pronounced seasonal cycle that is repeated almost exactly each year, with a sharp maximum in late summer. The long-term trend is slight, with a decrease of less than 2% over the satellite era, while MIZ width has increased over the same period by almost 40%. Our results have important implications for climatic and ecological processes which depend critically on MIZ geometry. We demonstrate thermodynamic feedbacks through statistical analysis and provide context for future applications.