The construction methods analysis of known geometric fractals allows us to reveal algebraic features of fractal algorithms composition. The main concept of the analysis results is fractal operators which are basic operations for constructing fractals of a certain type. The result of using operators for geometric fractals is a structure with fractures of triangular, square, trapezoidal and similar forms. Multiplication and addition operations are introduced for operators, as well as the concept of the unit, null and inverse operator, which allows us to define periodic and quasiperiodic fractal structures. An algorithm for the formation of periodic and stochastic fractal structures is proposed, a distinctive feature of which is the implementation of the probabilistic choice of the basic geometric primitive on the current iterative cycle. The software implementation of the proposed algorithm confirmed the validity of the algebraic approach in studying and modeling fractal with a complex structure.
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