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The paper is devoted to the study of combinatorial determinacy properties ofa family of substitution complexes consisting of quadrilaterals gluedside-to-side with each other. These properties are useful in constructingalgebraic structures with a finite number of defining relations. In particular,this method was used when constructing a finitely presented infinitenisemigroup satisfying the identity x^9 =0. This construction responds to theproblem of L. N. Shevrin and M. V. Sapir. In this paper, we investigate thepossibility of coloring the entire sequence of complexes into a finite numberof colors, in which the property of weak determinism is fulfilled: if thecolors of the three vertices of a certain quadrilateral are known, then thecolor of the fourth side is uniquely determined, except in some cases of aspecial arrangement of the quadrilateral.

On the determinicity of paths on substitution complexes