Let us consider a Penrose tiling of $\mathbb R^2$. Starting with an arbitrary point on the tiling, draw an arbitrary straight line. Assume that this straight line never overlaps perfectly with a boundary edge of a tile.

Create a sequence by recording what tiles the straight line intersects as it proceeds from its starting point to infinity. As an example, for the above picture the first few terms of the sequence will be $$GBGGBBBGBGGBGBGG...$$ Where $G$ represents the Green skinny rhombus tile, and $B$ represents the fat blue rhombus tile

Is there an algorithm to generate sequences of this type? So far I have been drawing a line and marking the tiles the line intersects by sight, and I am hoping there is an easier way.