Mechanics Sequence - Colegiul Ortodox "Mitropolitul Nicolae Colan" (Cluj-Roumanie) Lycée Marseilleveyre (Marseille), Lycée Victor Hugo (Marseille)

One draws a grid on a plane formed by regular intervals of horizontal and vertical lines. Then, a half-line is drawn in any direction. As one travels along this half-line, observe the lines it intersects. Assign 1 to each vertical line and 2 to each horizontal line. If the line passes through an intersection point between horizontal and vertical lines, arbitrarily choose to write 1 and then 2.
What is obtained for half-lines [OA) for points A with simple coordinates, for example, (3; 2)? Can one predict, based on the coordinates of A, the length of the repeating block (if it exists) or the proportion of 2 in the sequence?
Can such a sequence contain 1122? Are there other forbidden blocks?