[grvbck]

Next week on Show HN: I made a fractal font with unlimited scaling

[perihelions]

You can take a glyph from that font, cut up and rearrange it, and come out with two copies of the original size. Saves money on printer ink

[tempfile]

Turing actually addressed this in his argument!

> If these sets are restricted to be measurable

measurable sets are not Banach-Tarski-able :)

[ashton314]

This is a deep joke and hilarious. Thank you for sneaking in a Banach-Tarski reference here

[myhf]

assuming you are willing to spend an infinite amount of time doing the cutting

[byteknight]

I smell a supertask

[daedalus_j]

The Minds from The Culture scifi series have something like this... The top level glyph is the base meaning and you can encode essentially infinite depth of meaning beyond that... Of course you have to go multidimensional at some point, so you can't really print it out beyond a few layers of resolution...

[flir]

This reminds me of a design for analogue TV from the late 80s/early 90s. Instead of the electron gun scanning in horizontal lines, it follows a space-filling, non-crossing, self-similar curve. Want to upgrade the resolution? Just build a TV that renders the curve one generation deeper, and stuff more data into the analogue broadcast signal. Older TVs can still render the new signal, maybe with a slightly higher noise floor.

(Anyone know what I'm talking about? I assume it was obsoleted by digital solutions, but I'd like to know if there were any serious flaws in the design).

[FredPret]

I think arcade games worked like that. Looked it up and oscilloscopes do, too:

https://en.m.wikipedia.org/wiki/Vector_monitor

[namanyayg]

The concept you're talking about is a Hilbert Curve. But this is the first time I've heard it applied to analogue tv.

https://en.m.wikipedia.org/wiki/Space-filling_curve

[flir]

Yeah, in my memory the pattern was specifically a Hilbert Curve but rotated 45deg (that can't be right, can it? That would just make things harder). I must have seen it between 1987 and 1997.

Ah! Found this: https://www.ripcorddesigns.com/blog-news/who-needs-rastas-an... - there's even a patent! I was searching on space-filling curve, not Hilbert curve.

[pyinstallwoes]

That would be quite the glyph / language.

Perhaps the sense of "I" can be that base, which then allows the expansion of I, I, I (sense of I around I) which expands to in front, behind, etc.

[kazinator]

The closed-form math formulas giving the glyphs of the font have to be written on a square piece of paper with limited resolution ...