A dyadic square is a closed square of the form
![Q_(j,l,k)=[j2^(-k),(j+1)2^(-k)]×[l2^(-k),(l+1)2^(-k)],](/images/equations/DyadicSquare/NumberedEquation1.svg) |
where 
,
, and 
are integers. Its side length
is 
. For fixed 
, the dyadic squares tile the plane.
Two dyadic squares at possibly different scales have disjoint interiors,
or one is contained in the other.
Dyadic squares provide a hierarchy of locations and scales in harmonic analysis and geometric analysis. For example, they index the sum in the analyst's traveling salesman theorem.
