New characters can be invented on the fly, but not every random scribble would be considered a character. In practice, only a handful of different stroke types are used, which gives even newly invented nonsense characters a recognizable visual style. For any finite stroke count, there's only a finite number of combinations, so the infinte set of characters with unbounded stroke count can be enumerated.

It can also be sorted using the radical and stroke count, although then you can't enumerate it in order because there's an infinite number of possible characters for each radical.