Not in atlas — all metrics redundant with existing geometries at |r| > 0.9.
What it measures: Does the signal ever return to places it's been before — and when it does, does it follow the same path?
Embeds the signal in 3D via delay coordinates, then asks: for every pair of points in the trajectory, are they close? The answers form a binary recurrence matrix whose texture reveals the dynamics.
Of the recurrent points, what fraction form diagonal lines in the recurrence matrix? Diagonal lines mean: when the signal returns to a previous state, it follows the same trajectory it followed last time. All logistic periodic orbits score 1.0 (perfectly deterministic — they retrace their paths exactly). White noise scores 0.71 (some diagonal structure by chance). Constants score 0.0 (everything is recurrent, but there's no trajectory to follow).
What fraction form vertical lines? Vertical lines mean: the signal gets stuck near one state for extended periods. Thue-Morse, Rule 30, and Symbolic Henon all score 1.0. Logistic period-4 scores 0.0 — it recurs but never lingers.
When the signal gets stuck, how long does it stay? Thue-Morse and Rule 30 score 249.5 (maximal trapping — the symbolic dynamics creates long laminar stretches). Exponential chirp scores 0 (never stays anywhere).
How varied are the diagonal line lengths? Thue-Morse and Rule 30 maximize this at 6.2 bits: they revisit their trajectory at many different timescales. Simple periodic orbits have low entropy (one dominant recurrence period).
Fraction of all point pairs that are within the recurrence threshold. Quantum Walk, Morse Code, and Thue-Morse all score 1.0 (every pair is recurrent — the point cloud is maximally dense). Dice Rolls (0.03) and PRNGs score near zero (space-filling trajectories with few recurrences). This is the most basic RQA measure: how "self-overlapping" is the trajectory?
Average length of diagonal lines in the recurrence matrix. Logistic period-5 and period-4 hit 250 (maximum — every recurrence extends for the full analysis window). Van der Pol and SIR score 0.0 (no diagonal structure). Long diagonals mean the signal retraces extended trajectory segments, not just individual states.
Length of the longest diagonal line. Rule 30, Symbolic Henon, and Thue-Morse all score 497 (maximum). This is the longest interval over which the signal perfectly retraces a previous trajectory — a direct measure of the maximum Lyapunov time.
Fraction of recurrence-connected triples that form triangles (clustering coefficient of the recurrence network). Logistic period-4 and period-3 score 1.0 (all recurrent neighbors are also mutually recurrent — the recurrence structure is clique-like). Rössler and Sine score 0.0 (recurrence neighborhoods are chain-like, not clustered).
Recurrence Quantification drives the gap between the ordinal view's C3 (symbolic dynamics: high recurrence, high laminarity) and C2 (smooth correlated noise: low recurrence). In the solar eclipse VLF investigation, laminarity and determinism were significant only during the eclipse-active interval — the D-layer collapse changed the signal's recurrence structure in real time.