There is a whole scientific field on this, called Information Theory. Compressing entropy is limited by its randomness.
For instance see: https://en.wikipedia.org/wiki/Entropy_%28information_theory%...
and
For instance see: https://en.wikipedia.org/wiki/Entropy_%28information_theory%...
and
For example to recover the state of an entire simulated universe you just need the value of the initial seed and the generator.
For complex reason, human language (spoken and written) is about 50% redundant, across a wide range of independent languages.
Tabular data can be vastly more compressible, and I'd routinely see 90% or better compression across a range of datasets (mostly business, financial, and healthcare data). Data of highly random events might be somewhat less so.
Image, audio, and video data, when in codecs is already highly compressed. When you're working with raw (WAV, TIFF, BMP, RAW) datatypes, there's a huge opportunity for compression, but mp3, ogg, mp4, png, gif, jpg, etc., are pretty highly compressed. There's a distinction between lossy (jpg, mp3) and lossless (png, AALC) formats. You get smaller files with lossy formats, but you're actually losing some of the original data, whilst lossless codecs allow fully reconstruction of the original source image, audio, or video.
Your comment about simulated universes gets to a key philosophical question about information, truth, and models. Generally, any representation we have of the universe is at best an abstraction of it, and hence a small, lossy, model.
This needn't necessarily be the case:
Compressing arbitrary inputs using emergent properties may never be practical, but in it seems reasonable that you could trade computation for compression to an arbitrary extent (searching an emergent series for chunks of data that match your input).
Then it can be compressed down to an index into the libraryofbabel