Can gzip be a language model?

A while back I wrote about language modeling without neural networks, where I generated Shakespeare with an unbounded n-gram model: no weights, no training, just counting. Fortuitously, I came across the paper Language Modeling is Compression, which mentioned the compression–prediction equivalence:

every prediction model is inherently a compressor, and all compression algorithms are prediction models.

This led to the natural question: can gzip do language modeling?1 No neural network, no learned parameters, nothing. Just the compressor that ships with your operating system. You prime it with a corpus, give it a normal text prompt, and it continues that prompt by searching for the byte sequences that compress best. Here’s some real, unedited output after priming it on tiny Shakespeare: