All characters fit within a 5 pixel square, and are safe to draw on a 6x6 grid. The design is based off of lcamtuf's 5x6 font-inline.h, which is itself inspired by the ZX Spectrum's 8x8 font.
5x5 is the smallest size that doesn't compromise legibility:
Five by five is actually big enough to draw most lowercase letters one pixel smaller, making them visually distinct from uppercase.
Narrower 4x5 and 3x5 dimensions are possible, but would require sacrificing the M, dotted zero, and reduce U/V/Y distinctiveness.
There's no artistic reason to make all characters five wide just because a few must be... but a using a constant width makes programming a lot easier: The length of a string on screen is always 6 times the number of characters.
It also makes compact layouts much safer: There's no need to worry that a number will overflow because "8978" is longer than "1111".
The whole font takes up just 350 bytes of memory, which makes it ideally suited to 8-bit microcontrollers like the AVR128DA28 (16 kB of RAM) These are cheap, low power and robust... but they fall short on graphics:
Even a low-resolution 384x288 display has 110 thousand pixels: way too big to fit in the AVRs memory.
... except most projects don't need anywhere near that many pixels. A 160x128 or 128x64 OLED is more practical and cheaper — but these need hand-drawn, pixel-efficient fonts to make good use of them.
For reference, here's a vector font rendered at a similar scale:
Antialiasing, several megabytes of code, a megabyte of font data, and it's still terrible compared 350 hand-crafted bytes.
Pixels aren't perfect squares, so the font won't actually look like the rendering at the top of this post: This is it on an actual screen:
I actually really like the pseudo-dropshadow effect created by the subpixels. This won't happen on monochrome displays, but the font will still look smoother than you might expect.
The gaps between pixels really help sell the "e" and "g", but this same effect should allow...
While 5x5 is the smallest no-compromise resolution, a 3x5 isn't too bad:
The "M", "W" and "Q" suffer, but it's still got a distinct O and zero. Something like this might actually be a good option if you need to cram (50%) more columns into a display.
That's still readable, so what about 3x4?
At this size, there's no way to have a distinct upper and lowercase, so I've picked whatever style works the best in the limited space. The numbers have also taken a hit, but still work ok.
How about 3x3?
The main loss was the numbers, but the letters don't include any duplicates and are somewhat recognizable.
This font is hugely improved by being displayed on real hardware:
That means it's still too big. How about 2x3?
Ok, this is getting ridiculous. Most letters are unrecognizable, and there are quite a few duplicates. In case you couldn't tell, the bottom line reads "Hello World".
Flipping the aspect ratio to a 3x2 makes it a lot better:
More letters have horizontal detail (M, W, N, Q, G, P, etc) then have vertical detail (E, F). The bottom line reads "you can probably read this", although you might have to squint or zoom out.
... and for the sake of completeness, a 2x2:
On paper, there are 16 possible 2x2 images, but one of them is blank and 5 of them are shifted copies of another one. That leaves 10, just enough to do all the digits... but because they have no resemblance to the originals, it's more of a secret code than a font.
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