In 1879, Fritz Muller formulated the first mathematical evolutionary model to explain mutualistic mimicry between coexisting defended prey. Yet, whether local mimicry drives the structure of aposematic prey signals across their entire geographic distribution remains untested because the perception of pattern similarity has never been assessed at large spatial scale. Here, we implement a citizen science survey to map, throughout the Neotropics, variation in the wing patterns of heliconiine butterflies (Nymphalidae) as perceived by vertebrate cognitive systems. We show that despite a continuum of perceived similarity in wing patterns at the continental scale, the convergence of sympatric species into discrete mimicry rings is ubiquitous among local communities. These results expand Muller\'s historical predictions by quantifying the rampant convergence of prey signals across an entire continent.