Recurrence Plot
Explore when a time series returns near an earlier state, with explicit delay coordinates and distance thresholds.
About this tool
Choose a logistic or pasted uniformly sampled scalar series. Calculate builds vectors (x[i], x[i+τ], …, x[i+(m−1)τ]); m=1 uses the scalar directly. Insufficient data is an error, never an automatic change of dimension. Samples start after discarded map iterations; vector indices start at 1. The selected consecutive window contains at most 800 vectors; earlier/later windows are selectable.
Normalize range maps the entire input series to 0–1 before embedding. ε then uses this dimensionless scale, with Euclidean distance over all m coordinates (maximum √m). Original values retains input units. Normalization handles extreme spans but cannot recover lost floating-point precision. Threshold comparison is inclusive: distance ≤ ε; at ε=0 only exactly identical vectors match.
Blue cells are recurrent, light cells are not. Gray cells have |i−j|≤W and are excluded from both the plot and rate. Default W=0 excludes self-pairs. Recurrence rate divides eligible recurrent unordered pairs by all eligible unordered pairs; the symmetric ordered-pair fraction is identical. No hidden denominator including the identity diagonal.
Click a cell or enter i/j in Inspect a pair to see the actual distance and decision. Resizing redraws cached data; calculation is cancellable. PNG retains axes and actual parameters. Pasted series stays in memory and is never saved with preferences.
Patterns depend on sampling, threshold, normalization, embedding and window; periodic or constant series also recur. This is a descriptive recurrence plot, not a proof of Poincaré recurrence, determinism or chaos, and not full recurrence quantification analysis.