Chacon transformation

The standard three-cut Chacon transformation is an invertible measure-preserving transformation built by cutting and stacking with spacer vector $(0,1,0)$ at every stage. Cut the current tower into three equal subcolumns, place one spacer above the middle, and stack left to right. With initial width $2/3$ and height one on a unit interval, level counts and widths are $h_j=(3^{j+1}-1)/2$ and $w_j=2/3^{j+1}$. Tower measure tends to one, using total spacer measure $1/3$. Tower words obey $W_{j+1}=W_j{W}_{j}1W_j$.