How children perceive fractals: Hierarchical self-similarity and cognitive development

摘要: The ability to understand and generate hierarchical structures is a crucial component of human cognition, available in language, music, mathematics problem solving. Recursion particularly useful mechanism for generating complex hierarchies by means self-embedding rules. In the visual domain, fractals are recursive which simple transformation rules infinite depth. Research on how children acquire these can provide valuable insight into cognitive requirements learning constraints recursion. Here, we used investigate acquisition recursion probed correlations with grammar comprehension general intelligence. We compared second (n = 26) fourth graders their represent two types structures: Recursive rules, one hand, new levels; iterative other merely insert items within without levels. found that majority graders, but not were able both This difference was partially accounted graders’ impairment detecting mistakes, correlated between-grade differences tasks. Empirically, iteration also differed at least aspect: While learn seemed depend previous representations, opposite true, i.e., before they acquired representations. These results suggest vision follows similar domains share resources involved processing.