Why quasicrystals shouldn't exist but are turning up in strange places Matter with "forbidden" symmetries was once thought to be confined to lab experiments, but is now being found in some of the world's most extreme environments In autumn 1945, Lincoln LaPaz crouched over a patch of scorched ground in the Jornada del Muerto desert of New Mexico. LaPaz, an astronomer, was out hunting for meteorites. He had spotted something in the dust: a strange, glittering crust of blood-red glass. This was no meteorite, but it was striking enough that he held onto it. It wasn't until decades later that anyone would realise quite how special LaPaz's chance find was.

In addition, since only the binary failure can be obtained, the number of latent constraints is also unknown.

In addition, since only the binary failure can be obtained, the number of latent constraints is also unknown.

New studies of the "platypus of materials" help explain how their atoms arrange themselves into orderly, but nonrepeating, patterns. Since their discovery in 1982, exotic materials known as quasicrystals have bedeviled physicists and chemists. Their atoms arrange themselves into chains of pentagons, decagons, and other shapes to form patterns that never quite repeat. These patterns seem to defy physical laws and intuition. How can atoms possibly "know" how to form elaborate nonrepeating arrangements without an advanced understanding of mathematics?

This essay proposes an interpretive analogy between large language models (LLMs) and quasicrystals, systems that exhibit global coherence without periodic repetition, generated through local constraints. While LLMs are typically evaluated in terms of predictive accuracy, factuality, or alignment, this structural perspective suggests that one of their most characteristic behaviors is the production of internally resonant linguistic patterns. Drawing on the history of quasicrystals, which forced a redefinition of structural order in physical systems, the analogy highlights an alternative mode of coherence in generative language: constraint-based organization without repetition or symbolic intent. Rather than viewing LLMs as imperfect agents or stochastic approximators, we suggest understanding them as generators of quasi-structured outputs. This framing complements existing evaluation paradigms by foregrounding formal coherence and pattern as interpretable features of model behavior. While the analogy has limits, it offers a conceptual tool for exploring how coherence might arise and be assessed in systems where meaning is emergent, partial, or inaccessible. In support of this perspective, we draw on philosophy of science and language, including model-based accounts of scientific representation, structural realism, and inferentialist views of meaning. We further propose the notion of structural evaluation: a mode of assessment that examines how well outputs propagate constraint, variation, and order across spans of generated text. This essay aims to reframe the current discussion around large language models, not by rejecting existing methods, but by suggesting an additional axis of interpretation grounded in structure rather than semantics.

Recent work on GPT [1], BERT [2], and related models has proven immensely successful, not only in direct language modeling tasks but also other domains including translation, question answering, and even code [3] and music [4] generation. In addition to directly performing transfer learning, prompt engineering has emerged as a promising method to leverage the power of large language models trained on diverse types of texts [5, 6]. The general strategy of pretraining large models on easily-gathered unlabeled data using self-supervised tasks and then fine-tuning on more relevant labeled data is especially appealing for many scientific domains where labeled data may be difficult to come by. In materials physics, it is well understood how structure plays a significant role in electrical, thermal, or mechanical properties of a material, and scientists target particular structures as they design new materials for desired applications. For crystals, "structure" typically refers to the basic building unit which is repeated along a periodic lattice to create a bulk crystal, but--particularly for aperiodic or non-crystalline materials--it can also refer to any symmetry or non-random ordering present in the arrangements of particles or atoms. Assessing order and its evolution in three-dimensional structures is a challenging, but critical method for understanding the self-assembly and growth of complex materials; particularly as the scope and magnitude of experiment and simulation data analysis continues to expand, machine learning techniques that are able to leverage large amounts of unlabeled data will become ever more crucial. In this work, we use self-supervised learning (SSL) tasks that can broadly be used to train models for quantifying order and distinguishing assemblies in non-idealized material structures. The choice of SSL for this application was inspired by previous work that has developed SSL tasks for three-dimensional point clouds, which are a natural choice for representing three-dimensional positional data. Thabet et al. [7] formulated self-supervised tasks in terms of a space-filling curve; Sharma and Kaul [8] trained deep networks to model data based on a three-dimensional cover tree; the method proposed in Eckart et al. [9] models simple, soft "patches" of 3D point clouds in order to reconstruct its inputs; and Pang et al. [10] spatially mask

Sharon Glotzer has made a number of career-shifting discoveries, each one the kind "that completely changes the way you look at the world," she said, "and causes you to say, 'Wow, I need to follow this.'" A theoretical soft condensed matter physicist by training who now heads a thriving 33-person research group spanning three departments at the University of Michigan in Ann Arbor, Glotzer uses computer simulations to study emergence--the phenomenon whereby simple objects give rise to surprising collective behaviors. "When flocks of starlings make these incredible patterns in the sky that look like they're not even real, the way they're changing constantly--people have been seeing those patterns since people were on the planet," she said. "But only recently have scientists started to ask the question, how do they do that? How are the birds communicating so that it seems like they're all following a blueprint?"