A visualization of the dyadic odometer as an en:interval exchange transformation. This uses the standard mapping from en:Cantor space {0,1}N{\displaystyle \{0,1\}^{\mathbb {N} }} to the en:unit interval on the real number line, given by (b0,b1,b2,⋯)↦x=∑n=0∞bn2−n−1{\displaystyle (b_{0},b_{1},b_{2},\cdots )\mapsto x=\sum _{n=0}^{\infty }b_{n}2^{-n-1}} to visualize the action of the odometer T{\displaystyle T} defined by T(1,…,1,0,bk+1,bk+2,…)=(0,…,0,1,bk+1,bk+2,…).{\displaystyle T\left(1,\dots ,1,0,b_{k+1},b_{k+2},\dots \right)=\left(0,\dots ,0,1,b_{k+1},b_{k+2},\dots \right).}
Own work
Linas