Introducing CUSTOM: A customized, ultraprecise, standardization-oriented, multipurpose algorithm for generating nonsymbolic number stimuli

When evaluating the properties of a set of elements in a natural environment, an increase in numerosity unavoidably corresponds to an increase in the physical properties of the set: Five apples differ from ten apples not only in numerosity, but also in their visual features, such as volume, density, and surface. Since nonsymbolic number processing is typically investigated through the presentation of arrays of elements, it is mandatory to keep track of the visual features characterizing the stimuli. A plethora of solutions have been proposed to address this complex methodological issue; yet, there is no agreed-upon standard for how to measure and control for visual features. Here we present the “customized ultraprecise standardization-oriented multipurpose” (CUSTOM) algorithm for generating nonsymbolic number stimuli. It is characterized by several core features: The absence of fixed parameters or rules—apart from geometrical constraints—lets the user freely manipulate the visual features of the stimuli; control over the visual features of the stimuli is extremely accurate; no modification is required in order to perform different types of manipulation; and users can re-create any set of stimuli described so far in previous experiments on numerical cognition, for a wide variety of tasks, including comparison, estimation, habituation, and match-to-sample. The CUSTOM algorithm could represent an asset in the field of numerical cognition, as a versatile instrument for effectively generating high-precision visual stimuli within an unbiased theoretical framework.