In this paper we investigate a hypothesized cognitive bias for isomorphic mappings between conceptual structure and linear order in the noun phrase. This bias has been proposed as a possible explanation for a striking asymmetry in the typology of the noun phrase–linear orders which place the adjective closest to the noun, then the numeral, then the demonstrative, are over-represented in the world’s languages. Previous experimental work has provided evidence that an isomorphism bias affects English-speaking learners’ inferences about the relative order of modifiers in an artificial language. Here, we use the silent gesture paradigm to explore whether the isomorphism bias influences spontaneous gestures innovated by participants in a modality with which they have relatively little prior experience. We find that gesture order largely conforms to the same striking pattern found in noun phrase typology, supporting the role of the isomorphism bias in shaping the emergence of language (and language-like) systems.