Internet is Beautiful

"640KB ought to be enough for anybody"

I could see reasons.

Like the original twitter concept, where you had to limit yourself. The pics I just saw when opening the link were horrible, but so is twitter, but that's not the point.

If you do pixel paint a good old bitmap, instead of compressing a too high resolution file like you're trying to speed run hemorrhoids, then you could use the standard 32bpp, giving you 16.8 million colors and have pixels to work with. That gives you roughly 300 pixels (or 15x20), which isn't a lot, but still enough room for artistic expression. When I say roughly it's because I can't remember how much is used for metadata, but IRC it's less than 30bytes.

If you play around with the bit depth you'll need a bit more bytes for the header, but you can use a monochrome palette instead and theoretically get it down to 1bpp which should give you close to 8000 pixels, or 80x100.

Is it super duper 8k high def HDR? Of course not, but when you impose a 1kB limit then HD is kinda hard to achieve.

Maybe you can get something more, if you tried manually creating a jpg, like in a hexeditor, but I don't really know, I've only done bitmaps by hand.

Perhaps playing with discrete cosine transform after watching https://m.youtube.com/watch?v=n_uNPbdenRs and https://m.youtube.com/watch?v=Q2aEzeMDHMA you could actually make jpegs by hand.