A Multi-Fractal Spectrum Analysis of Turbulence Data and the DNA of Worms

This paper discusses the physical meanings of various parameters in multi-fractal spectrum and offers the thermo-mechanical formula in calculating the multi-fractal spectrum. Besides it works out the sets of multi-fractal Cantor, the multi-fractal spectrum of turbulence data of Rayleigh-Benard convection and DNA series by means of wavelet transform maximum modulus (WTMM). In the end, it arrives at the conclusions that the means of WTMM is plausible on the application of multi-fractal research, multi-fractal spectrum offers function alpha similar to f (alpha), which describes all the sub-collections' characters. So it gives specific information of a system. Turbulence is similar to DNA's multi-fractal character. The latter is more uneven and complex. Multi-fractal spectrum analysis can reveal the uneven overall distribution information of the series (or sets). But it has a limited description of the local position information of signal singularity and concrete local structure.