This looks like a fun contest. Is there a natural limit to how much some data could be compressed?

Edit: Seems like no https://en.wikipedia.org/wiki/Kolmogorov_complexity

Statistically without knowledge of the underlying data, yes: bit entropy.[0]

But in actuality, if you can discover, elucidate or approximate (in lossy compression) a better generator, then you can compress data far beyond simple repetitions and/or patterns.

0. https://en.wikipedia.org/wiki/Entropy_(information_theory)