Humans learn and generate languages, music, games, and seemingly limitless varieties of other structures across domains. Unlike many AI systems, we often do so from little data. How do we learn such large varieties of richly structured representations so efficiently? One possibility is that people ``learn by programming,'' synthesizing data-generating algorithms to explain what we observe. We examine the nature and origins of this learning mechanism in adults, children, and nonhuman primates (macaque monkeys), using a highly unconstrained sequence prediction task. Although adults and children quickly learn many richly structured sequences, monkeys learn only the simplest sequences (e.g. lines). We test multiple learning models, finding that adults are best explained by a ``Language of Thought''-like program-learning model and monkeys by a simpler extrapolation strategy. Children exhibit varied learning strategies but are best fit in aggregate by an intermediately expressive model. Paper available at https://sites.google.com/view/patternlearning.

Orthogonal to guided growth of nanoparticle (NP) crystals using DNA or supramolecules, a trace amount of polymeric impurities (<0.1 wt.%) leads to reproducible, rapid growth of 3D NP crystals in solution and on patterned substrates with high yield. When polymers preferentially precipitate on the NP surfaces, small NP clusters form and serve as nuclei for NP crystal growth in dilute solutions. This precipitation-induced NP crystallization process is applicable for a range of polymers, and the resultant 3-D NP crystals are tunable by varying polymeric additives loading, solvent evaporation rate, and NP size. The present study elucidates how to balance cohesive energy density and NP diffusivity to simultaneously favor nuclei formation energetically and kinetic growth in dilute solutions to rapidly crystalize NPs over multiple length scales. Furthermore, the amount of impurities needed to grow NP crystals (<0.1%) reminds us the importance of fine details to interpret experimental observations in nanoscience.

Despite persistent and extensive observations of crystals with chiral shapes, the mechanisms underlying their formation are not well understood. Although past studies suggest that chiral shapes can form because of crystallization in the presence of chiral additives, or because of an intrinsic tendency that stems from the crystal structure, there are many cases in which these explanations are not suitable or have not been tested. Here, an investigation of model tellurium nanocrystals provides insights into the chain of chirality transfer between crystal structure and shape. We show that this transfer is mediated by screw dislocations, and shape chirality is not an outcome of the chiral crystal structure or ligands.