关键词: 对称, 标度律, 自相似, 对称, 标度律, 自相似

Abstract: The scaling symmetry is elementary characteristic of characterless scale phenomena such as length of the coast, tubulence, critical phase transitions. The scaling Symmetry is to seek after invariance under scale transformation for dynamical system. The Fiegenbaum constant is a famous invariance via period doubling scaling transformation for chaotic system. The climatic colding and warming change with time scale, but there is also invariance. In mathematically the scaling symmetry may be considered as a interated map, in biologically as a self-reproduction. The self-simitarity of scale transformation is related to spiral structure in nature.

Key words: symmetry, scaling law, self-similar, symmetry, scaling law, self-similar