As a first step towards understanding the geometric structure of the attractor shown in the Poincaré plot using a recurrence plot, we focused on the structure of a single vertical or horizontal line of the recurrence plot. Because each column of a recurrence plot is a binary sequence of the same length, we randomly choice some columns (or rows) of a recurrence plot and connect them with AND, OR, and NOT operators to see if we can represent other columns. We use a greedy algorithm to obtain the arithmetic representation at a practical calculation. In this report, we evaluate the amount of arithmetic representations obtained for the Logistic map, random sequences, AR models with dynamical noise, and simple sinusoids, in terms of the amount of NAND operators required. Recurrence rates were fix to 0.03, and the length of the time series ranged from 100 to 43,128 points. The value of each point in the time series was normalized from 0 to 1. Surprisingly, the AR model with dynamical noise required the most operators other than random sequences. Furthermore, we found that the AR model was sensitive to even small amounts of dynamical noise. The reason for this behavior may caused by a balance between the complexity of the base and the target.