Period-Doubled Wave
What It Is
Oversampled period-2 oscillation --- a sinusoid whose alternate base cycles carry different amplitude, the canonical orbit just past a period-doubling bifurcation. Carries a subharmonic at f/2 (full period = two base cycles). The oversampled continuous analog of the critically-sampled period-2/4 maps, which the atlas otherwise lacks.
Interpretation
Standard analysis sees: smooth / autocorrelated; long-range memory (persistent); strongly periodic; low-complexity (predictable, not noise-like); volatility-clustering (bursty). The atlas finds no named structure, but the source is distinctively extreme on Bispectrum:off_diagonal_ratio (+3.7z) — beyond what the standard bank predicts for it. It sits beside Sine Wave in the atlas (standard-bank rank 27) — a neighbor conventional features miss.
Bispectrum:off_diagonal_ratio | +3.6z | bank-miss 2.5σ |
Bispectrum:coupling_frequency_centroid | -2.5z | bank-miss 1.9σ |
Composition
Render Gallery
_(centered)/signed_log_z/Period-Doubled_Wave.png)
_(centered)/xy_path/Period-Doubled_Wave.png)
/barcode/Period-Doubled_Wave.png)
/d_curve/Period-Doubled_Wave.png)
/phi_spectrum/Period-Doubled_Wave.png)
/default/Period-Doubled_Wave.png)
/default/Period-Doubled_Wave.png)
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Sine Wave | 2.74 | |
| Duffing Oscillator | 2.96 | cross-origin |
| Hénon-Heiles | 3.19 | cross-origin |
Which Geometries Light Up
Bispectrum › Bispectrum:off_diagonal_ratio | rank 4/306 | 0.8841 |
Hodge–Laplacian › Hodge–Laplacian:solenoidal_fraction | rank 2/306 | 0.9970 |
Hodge–Laplacian › Hodge–Laplacian:curl_div_ratio | rank 4/306 | 5.8377 |
p-Variation › p-Variation:variation_index | rank 302/306 | 1.0008 |