Recurrence Plot of Mathematical Functions and Constants

A recurrence plot illustrates the recurrence of states in a phase space where all the possible states of a system can be seen. Recurrence plots can be used to view and study mathematical functions such as sine and sinc or constants like , and so on. In the case of a function , the values used are the finite sequence , where is the size. In the case of a number, the values used are the digits of its decimal expansion taken to places.

The expression plotted is , where is the Heaviside step function, is the sequence, and is a kind of tolerance.

The point view is a graphical representation of the matrix , which is binary because of the unit step function. In the density view, the points are grouped in clusters to give a smoother representation of the matrix, and the matrix rows are rotated (vertical shift).

The mesh draws lines that highlight the white spaces for the point view and gives reference rulers for the density view.