The automata interpretation of integer sequences

Transformation of phase pictures to geometrical images of laws of functioning of state machines, offered and developed by V. A. Tverdokhlebov, has allowed to represent phase pictures by uniform mathematical structures – broken lines with numerical coordinates of points. V. A. Tverdokhlebov shows, that sequence of elements from the finite set, combined with linear order on set of input words, defines laws of functioning of the discrete determined dynamic system (state machine). It allows carry out the analysis of laws of functioning of state machines on the basis of research of properties of numerical sequences, and also it allows to research properties of numerical sequences by the analysis of properties of state machines.