After reading a bit on @warped_wart_wars' Stuff about ϕ topic and the conversation about A Series Paper, I remembered a old project I was going to share, but just forgot to. Originally created because I was inspired by a CGP Grey video. A recursive series of A Series paper.
Press space to render, you can change the ratio of the long side with a slider.
Nice project. I think you should fill with black the part of the stage that isn't part of your largest paper size. It's obvious that the very thin slice on the right can't be part of it, but it took me a while to be sure that the part on the bottom isn't. The brown vertical between the vertical excess and the horizontal excess added to my confusion; if you had a single L-shaped unused region it'd be clearer.
Actually, why do you have unused space in both dimensions? You could scale the largest size up to either the full width or the full height of the stage.
Interesting! Using sqrt 10 makes it not look very interesting, though. Sqrt 3 looks ok.
I guess I could scale it, but I didn't think of doing it when I created this project like a month or so ago, this is only me sharing it just to share it. Besides, the way I've coded this would require me to change the way I made the pattern so I could scale it, unless I'm not seeing something you're seeing. Also, I will say, these 'unused' areas are all part of the greater pattern, they're not exactly unused, even though if you were to zoom out they wouldn't be fully drawn.
Oh! So I'm supposed to imaging a piece of paper a lot bigger than the stage?
Basically, since it is a pattern that can go on forever.
The pattern can, but it's hard to imagine negative size numbers... :~)
Yeah, because A-series paper was named with the largest as A0.
Who is to say any of them are any specific standard? Sorry for posting on a 5 day old thread but I just now decided to reply to this.
I don't understand. Of course it's a standard; that's why you can go into a store and ask for some A4 paper and know what you're going to get!
I am talking about... like... these sizes aren't labeled, so we could be as far down as something hypothetical like A56 or something, or may A982... Sounds stupid but meh, none of this is really specific.
Oh I see. Yes, the standard allows for those, although of course there are practical limits on how small a piece of paper can be manufactured. But I don't think the standard allows for sizes bigger (i.e., smaller size number) than 0.
Just, hypothetically if it could go lower than 0 it could be an infinite pattern.
It can be infinite in the smaller direction already! But yeah, if you want it to get infinitely big you need negative size numbers.
Technically you could have those, ("I'd like a sheet of A negative 5 paper, please") but they aren't made currently. Plus, A0 is already pretty big, so A-5 would be giant.