Multifractal Spectrum Analysis on Microscope Image of Eutectic Carbides by a Quadratic Function Fitting

Multifractal is employed to analyze standard atlas of the distribution of degree 1~8 eutectic carbides in alloy. We do a research on relationship between partition function & forming element, and multifractal spectrum & singularity. Graph of partition function & forming element presents a favorable linear in the condition of weighting factor q>0 or q<0, which proves that the distribution of eutectic carbides has character of scaling invariability in the range of 0 and 50 as ideal fractal; Graph of multifractal spectrum & singularity presents bell-shaped or hooked, and the narrower the shape is, the more symmetrical the distribution of eutectic carbides is; and vice versa. We also finds the coefficients of a polynomial multifractal spectrum of degree 2 that fits singularity, which provides eigenvalues to make advanced research on pattern recognition of degree 1~8 eutectic carbides.