Rotorrelated

Rotorrelated is an informal term used to describe systems, processes, or datasets whose correlation structure is organized by rotational symmetry or rotor-like transformations. The expression is not a standard technical term, but it is used in discussions of circular data, rotating frames, and symmetry-driven models to convey that correlations depend on orientation rather than absolute position.

In mathematical terms, a rotorrelated process can be described on the circle S^1 or in a rotating frame by a covariances that are invariant under the rotation group SO(2). Concretely, the autocovariance Cov(X(θ), X(φ)) often depends only on the angular difference θ − φ (taken modulo 2π) rather than on θ and φ separately. This leads to covariance functions C(Δ) that are periodic with period 2π and capture how similarity decays with angular separation.

Rotorrelated models encompass circular processes such as those driven by wrapped distributions (e.g., von Mises, wrapped normal) and random fields where interaction depends on angular distance rather than absolute orientation. They are relevant in applications involving directional data, such as meteorology (wind direction), animal orientation studies, and signal processing of angular measurements, as well as in physics where rotating frames or spin-like variables show rotationally symmetric correlations.

Because rotorrelated is not a formal designation, definitions and emphasis can vary by context. Related concepts include rotational invariance, circular statistics, and symmetry-based covariance modeling.