Application of the laws to compose fractal computation algorithms when modeling and analyzing their growth

Generalized analysis of the methods to construct fractals let to find algebraic patterns of fractal algorithm, fractal operators fi formalizing basic operations to construct the fractal structures of a specific type being the major concept. The fi are introduced with multiplication and addition operations together with the concepts of singular, zero and inverse operator that allow defining periodic and quasi-periodic fractal structures. An endless fractal length - basic operator which can give a possibility to obtain a limit fractal synthesis idea as a structure without self-similarity but with a regularly decreasing scale. The connection between fractal growth computations and widely examples of application in the nature is considered. Methods to analyze growth processes are offered, their basic characteristics are shown. The mathematical description of the fractal growth characteristics and their dependence on specifically defined parameters of algorithm are given. The analysis of fractal point growth trajectory is made. The algorithms applied and the methods to analyze growth processes are shown to be modernized and adapted for wide spectrum of tasks.