Get the latest tech news
2-adic numbering for binary tilings
I’ve posted quite a bit about the binary tiling of the hyperbolic plane recently, including what you get when you shrink its vertical edges, a related “nowhe...
That’s why I chose the backwards order of binary digits and backwards choice of what 0 and 1 mean: with the digits in the other order we would get the bit-reversal permutation of these numbers and with the other choice of what 0 and 1 mean they would count down rather than counting up. A tiling has a one-dimensional group of symmetries, obtained by scaling the Poincaré half-plane drawing by a factor of \(2^i\), if and only if its labels are rational numbers whose binary expansions have period \(i\). For instance the unique tiling for which scaling by 2 is a symmetry is the one where all the labels are rational integers.
Or read this on Hacker News