Period-Tripling and Fractal Features in Multi-Billion Year Geological Records

Period-tripling is a common but rarely studied feature of natural processes. Its detection in long-term geological events is often restricted by poor preservation, inadequate time-resolution, and insufficient record lengths. This work includes an analysis of the highest-resolution and most complete multi-billion year sequence of geological and paleobiological records to determine the hierarchy of nonlinear (fractal) and periodic components. Using wavelet, spectral, and nonlinear analysis methods, a similar set of cycles emerged from these different records. The analyses indicate that the period-tripling pattern persists in geological and paleobiological events on time-scales of 30 to 1600 million years. The observed quasi-periodic tripling pattern could theoretically arise similar to bifurcations in a logistic map with a growth potential parameter of . Many of the period-tripled cycles exhibit half-cycle counter-parts. Most likely, the half-cycles developed from oscillations involving low-dynamic states versus the high-dynamic states of the full-cycles. Moreover, the period-tripling process contributes to fractal clustering of geological and biological events such as the eruptions of large igneous provinces. This is verified with the box-counting method for a model with a single dominant variable (a one-dimensional vector of ), for observational spans of less than 180 million years, and for a Cantor set model with a box dimension of ln(6)/ln(9).