  This paper defines the set fib of fibbinary numbers and displays its
structure in the form of a table of a specialised type, and in array form. It
uses the Zeckendorf representation $n \in \mathbf{N}$ to define a bijection
$\mathcal{Z}$ between $\mathbf{N}$ and fib. It is proved that the fibbinary
array is the image under $\mathcal{Z}$ of the famous Wythoff array. The
fibbinary table proves useful pictorial insight into the fractal defined by the
Wythoff array. The Wythoff table, obtained as the image under the inverse of
$\mathcal{Z}$ of the fibbinary table, leads to a simpler view of the fractal,
and may be compared with the (1938) Steinhaus tree.
