Nature's statistical symmetries and asymmetries, a characterization by wavelets and an illustration with clouds
Anthony B. Davis · University of North Texas Digital Library (University of North Texas) · 2001
Wavelets are the mathematical equivalent of a microscope, a means of looking at more or less detail in data. By applying wavelet transforms to remote sensing data (satellite images, atmospheric profiles, etc.), we can discover symmetries in Nature's ways of changing in time and displaying a highly variable environment at any given time. These symmetries are not exact but statistical. The most intriguing one is 'scale-invariance' which describes how spatial statistics collected over a wide range of scales (using wavelets) follow simple power laws with respect to the scale parameter. The geometrical counterparts of statistical scale-invariance are the random fractals so often observed in Nature. This wavelet-based exploration of natural symmetry will be illustrated with clouds where asymmetries and broken symmetries are also uncovered Both symmetry and symmetry-breaking have deep physical meanings.