In 'Space-Filling Curves' by Hans Sagan is presented equation defining the Peano curve.
Peano, defined a map $f_p$ from $I$ to $Q$ in terms of the operator $kt_j = 2-t_j(t_j = 0, 1, 2)$ as follows: $f_p(0_3·t_1t_2t_3t_4...) = \begin{bmatrix}0_3·t_1(k^{t_2}t_3)(k^{t_2+t_4}t_5)...\\0_3·(k^{t_1}t_2)(k^{t_1+t_3}t_4)...\end{bmatrix}$, where $k^v$ denotes the $v$th iterate of k.
Where $0_3·...$ denotes a number in base-3. I do not know how to use this formula. Is $k = 2/t_j - 1$ and $k^v$ the $v$th power of $k$? What does it mean that he defined the curve in terms of the operator?