Seeking woman endowed also with brain cells

Once a software engineer in US, now building toward inventor/entrepreneur life in Crete. I’m working on something that blends analog + digital with software and hardware. 10 points for attempting the following puzzle in good faith and without searching or plugging into an AI: Give a "directional" sequence of 0 and 1 symbols. That is, when repeated infinitely, it is distinct from infinite repetition of its reverse. For example, 011 doesn’t work as repeating it yields …011011011… and repeating the reverse yields …110110110… which are the same pattern (when expanded infinitely in both directions, the shift of 1 position loses significance). [Motivation: As we know, Theseus left a trail of thread to be able to retrace his steps. This is the upgrade where the trail also encodes the direction of travel along the path rather than just the path itself.] [Also there is the biology connection to ants, which are able to determine the direction of their trails. However, ants cheat by using 3 symbols rather than 2.] (The reason for this puzzle is that I don't see myself being able to spend any significant amount of time with anyone who can't appreciate hearing about an interesting engineering solution, provided it's explained at an appropriate level that doesn't assume too much existing knowledge of the subject. Accordingly, the puzzle is designed not to require any particular background knowledge.)