Want a fast, self-hosted mirror of your Instagram feed? Here you go.
Almost too easy!!!
The first page of your Instagram feed is baked for very quick loading. All other pages and permalinks are generated per request, but all your photo data is stored locally, in data.php. The only time the Instagram API is called is when you visit /your-repo/update, or if there's no local data at all.
This can be tricky when you're trying to edit your template. I suggest looking at page 2, then running the update script when you're done making changes.
Also, if your local data is up to date, index.html won't be regenerated, but the script is also not smart enough to fill in the gaps, so the only way to force a re-bake is to remove one or more items from the end of data.php (they are ordered chronologically, oldest to newest).