One class of continuous locally complicated functions related to infinite-symbol Φ-representation of numbers

In the paper, we introduce and study a massive class of continuous functions defined on the interval (0;1) using a special encoding (representation) of the argument with an alphabet Z={0,±1,±2,...}
This class of functions contains monotonic, non-monotonic, nowhere monotonic functions and functions without monotonicity intervals except for constancy intervals, Cantor-type and quasi-Cantor-type functions as well as functions of bounded and unbounded variation. The criteria for the function f to be monotonic and to be a function of the Cantor type as well as the criterion of nowhere monotonicity are proved. Expressions for the Lebesgue measure of the set of non-constancy of the function and for the variation of the function are found. Necessary and sufficient conditions for the function to be of unbounded variation are established.