I think each "line" is a stack expression, where one direction marks what value the stack pushes at that point, and the other direction (or index on the canvas? it's really unclear) marks the operation? So, maybe going down two lines is the number "two", then going right "one" pushes; now if we continue "right" three steps that means "add"?

There's no conditional operator on a single line. Instead, if two lines come "near" each other there's an alternate denotation that compares the values and either terminates (or rolls back?) the line's behavior to some earlier point (perhaps dependent on the value in the stack?)

It needs some fully commented programs as examples.