Noam Chomsky has suggested that the human language capacity may be “something like a snowflake, taking the form it does by virtue of natural law”(Chomsky 2011: 26). Inspired by his suggestion, this chapter considers syntactic patterns themselves as something like crystal lattices. We formalize different iterable syntactic configurations (self-similar patterns of Merge) as matrices, and examine their spectrum of eigenvalues. We identify three desirable eigenspectrum properties, motivated by comparisons with physics, as well as theory-internal considerations, that seem likely to be significant for syntactic forms. We observe that the format corresponding to the familiar X-bar schema, intimately related to the Fibonacci numbers, is uniquely special: Among all possible organizations, it is the only one with all three desirable properties.We speculate that this convergence of appealing mathematics might make X-bar-like phrase structure an attractor for linguistic expressions, even if Merge (the basic combinatory operation) is, in principle, free. Elsewhere in nature, in-principle-free growth processes frequently fall into self-similar patterns, with a special role for Fibonacci-related forms. We suggest that the recursive nature of syntax, whereby intermediate stages of growth set the conditions for subsequent growth, makes self-organization along these lines plausible.