That’s some high IQ usage of a meme. Lemme see if I’m getting this right:
the total area of the image ( = RHS of the equation) is 1
you divide the image into 4 parts so that the area of 1 part is is 1/4 ( = 1/2^(2*1)). You take the first three quarters and leave the fourth quarter for recursion (I’ll call it x1). That gives you 3(1/4) + x1 = 1
now you take x1 and do the same with it. This time, the area of each sub-quarter is 1/16 ( = 1/2^(2*2)). Three such sub-quarters and a leftover x2 gives you 3(1/16) + x2 = x1. Put this back into the first equation to get 3(1/4 + 1/16) + x2 = 1.
repeat until infinity; each time the area of the resulting tile is 1/4 of the previous tile (which is the 2n in the exponent part)
Edit: imma remove all markdown since it doesn’t seem to work, at least on liftoff. Enjoy the lisp-like mess
I’m pretty sure it’s 3. I think the proof works by taking a 1 x 1 square and splitting into quarters (1/4 = 1/2^2). So we say we have 3 full quarters and then 1 remaining quarter which we then split up again. And if you keep doing that you will fill in the full square. 3/4 + 3/16 + 3/64 and so on
No, it’s a normal multiplication by 3, and it makes sense.
3 times the sum expands to: 3 * 1/4 + 3 * 1/16 + 3 * 1/64 + 3 * 1/256 + …
Which is essentially what the picture shows: The main meme is three quarters filled with whole pictures, the fourth quarter being the inset of the sub meme, which is made up of three sixteenths of whole pictures and the fourth sixteenth is made up of the next layer of inset meme etc.
It’s a sum with n from 1 to infinity. The first value with n=1 is 3/4, with n=2 it’s 3/16. And if you keep adding those terms as n goes to infinity it approaches 1 but never gets there.
Then if you look back at the meme, you could zoom in for infinity and always find a smaller square.
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