the near infinity of pixels

While I was down an internet rabbit hole, I saw a display of tiny monochrome pixel sprites. They looked so cute and I marvelled at their diversity given the small surface area. And that got me thinking:

if you had a 32x32 pixel square, how many different icons could you make, provided you had to use a minimum of 1 pixel and a maximum of all 1,024?

Sadly my maths isn’t as good at it used to be so I had to look it up and someone had a similar question.

In an article called “The Realm of Finite Possibilities”, A.G. started with a 4x4 square and managed to get 16 different combinations, or $2^4$, where 2 is the number of options (having a black or white square) and 4 are the total number of squares you can fill.

So when you branch out to 32, that’d give you $2^4-1$ (because we don’t want a blank square) which equals… a very large number with 309 digits. Here’s one of the possible icons:

That blew my mind and that was before I considered a colour palette beyond black and white. Of course, most of those combinations would be “noisy” but the fact that you can create so many from a small 32x32 pixel grid is incredible.

Really puts our existence into perspective.