  Basso-Dixon integrals evaluate rectangular fishnets -- Feynman graphs with
massless scalar propagators which form a $m\times n$ rectangular grid -- which
arise in certain one-trace four-point correlators in the `fishnet' limit of
$\mathcal{N}=4$ SYM. Recently, Basso {\it et al} explored the thermodynamical
limit $m\to\infty$ with fixed aspect ratio $n/m$ of a rectangular fishnet and
showed that in general the dependence on the coordinates of the four operators
is erased, but it reappears in a scaling limit with two of the operators
getting close in a controlled way. In this note I investigate the most general
double scaling limit which describes the thermodynamics when one of two pairs
of operators become nearly light-like. In this double scaling limit, the
rectangular fishnet depends on both coordinate cross ratios. I show that all
singular limits of the fishnet can be attained within the double scaling limit,
including the null limit with the four points approaching the cusps of a null
square. A direct evaluation of the fishnet in the null limit is presented any
$m$ and $n$.
