Trying to find a young adult book from the 80s or 90s, it may have actually been part of a series. Seem to remember it involved chaos theory and, towards the end of one book, the protagonist encounters himself from another dimension (?) Can't remember much more except possibly a love interest that both the protagonist and his other self pursued (?) Thank you!
This sounds to me like 0X (1975), the final book from Piers Anthony's "Of Men and Manta" series. I read it when I was quite young (early 80s), but exactly the same plot elements have stuck with me: the references to chaos theory --here revolving around a sentient cellular automaton --and the alternate universe antagonist versions of the main characters. The Wikipedia entry doesn't have much about those portions of the book, but there is more detail confirming my memories here. One of the details that stuck out to me is that some of the characters that met their alternate selves ended up diverging greatly from them just from the experience of having met them.
Anthony would go on to revisit parallel universes and chaos theory (a bit incoherently) in his Mode series.