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Using the $Q_s$-representation of real numbers (generalization of classic $s$-adic representation) we construct an infinite-parameter family of continuous functions with heterogeneous properties. We prove that these functions are well defined, continuous and have not monotonicity intervals except for intervals where they are constant. Criterion for variation of the function to be bounded is also found. We are particularly interested in questions about level sets and self-similarity of graph of function.