# Fractal plate reconstructions with spreading asymmetry

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## Abstract

Information theory and fractal analysis are the basis of a novel fitting criterion for simultaneous plate tectonic reconstructions of magnetic isochrons and fracture zone crossings of a range of ages, rather than a single isochron age. Accretionary boundaries are modeled as two-dimensional fractal structures including both contemporary spreading boundaries and reconstructed magnetic isochron and fracture zone crossings. Each model incorporates reconstruction parameters which describe the full accretionary history, including asymmetry. The reconstruction parameters are derived by spline interpolation in time of trial rotation pseudovectors, including variable asymmetric spreading between ridge segments. Iterative algorithms, without partial derivative constraints, converge on a nominally optimal model by minimizing the sum of two-dimensional fractal bins, over the range of bin-spacings, and produce thereby progressively refined fractal spectra. The new method can incorporate all isochron identifications from the selected plates and age range in the iterative calculation set. The solution set also provides continuous instantaneous rotation parameters, including asymmetries. An example data set illustrates the methodology and model results.

The rationale for an optimal fractal criterion is rooted in recent developments in information theory: fractal structures maximize Shannon information entropy distributed over a range of scales. The fractal measure is the sum of bins occupied by reconstructed data points for each bin spacing. The fitting criterion utilized in this work is, in turn, the grand sum of the fractal measures over all calculated bin spacings. The optimal fractal measure for the grand sum has *minimal* integrated “fractality” relative to non-optimal sets while maximizing entropy for the optimal parameters for each bin spacing.

### Keywords

Plate tectonics Plate reconstructions Seafloor spreading Asymmetric spreading Fractals Information theory Maximum entropy## Supplementary material

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