Classical sorting algorithms as a model of morphogenesis: Self-sorting arrays reveal unexpected competencies in a minimal model of basal intelligence

Abstract

The Diverse Intelligence research seeks to understand commonalities in behavioral competencies across a wide range of implementations. Especially interesting are simple systems that provide unexpected examples of memory, decision-making, or problem-solving in substrates that at first glance do not appear to be complex enough to implement such capabilities. We seek to develop tools to determine minimal requirements for such capabilities, and to learn to recognize and predict basal forms of intelligence in unconventional substrates. Here, we apply novel analyses to the behavior of classical sorting algorithms—short pieces of code studied for many decades. To study these sorting algorithms as a model of biological morphogenesis and its competencies, we break two formerly ubiquitous assumptions: top-down control (instead, each element within an array of numbers can exert minimal agency and implement sorting policies from the bottom up), and fully reliable hardware (instead, allowing elements to be “damaged” and fail to execute the algorithm). We quantitatively characterize sorting activity as traversal of a problem space, showing that arrays of autonomous elements sort themselves more reliably and robustly than traditional implementations in the presence of errors. Moreover, we find the ability to temporarily reduce progress in order to navigate around a defect, and unexpected clustering behavior among elements in chimeric arrays consisting of two different algorithms. The discovery of emergent problem-solving capacities in simple, familiar algorithms contributes a new perspective showing how basal forms of intelligence can emerge in simple systems without being explicitly encoded in their underlying mechanics.