  We propose a discrete analogue of null geodesics in causal sets that are
approximated by a region of 2d Minkowski spacetime, in the spirit of Kronheimer
and Penrose's "grids" and "beams" for an abstract causal space. The causal set
analogues are "ladder molecules", whose rungs are linked pairs of elements
corresponding loosely to Barton et al's horizon bi-atoms. In 2d a ladder
molecule traps a ribbon of null geodesics corresponding to a thickened or
fuzzed out horizon. The existence of a ladder between linked pairs of elements
in turn provides a generalisation of the horismotic relation to causal sets.
Simulations of causal sets approximated by a region of 2d Minkowski spacetime
show that ladder molecules are fairly dense in the causal set, and provide a
light-cone like grid. Moreover, similar to the uniqueness of null geodesics
between horismotically related events in the spacetime, in such causal sets
there is a unique ladder molecule between any two linked pairs which are
related by the generalised horismotic relation.
