Under nitrogen deprivation, multicellular filaments of the cyanobacterium Anabaena undergo a process of development forming a one-dimensional pattern of nitrogen-fixing heterocysts separated by ~10 photosynthetic vegetative cells. The nature of the steady-state primordial fluctuations in gene expression along a filament under abundant nitrogen conditions that eventually result in a fully-developed pattern after nitrogen deprivation is unknown. HetR is a transcription factor essential for heterocyst differentiation. We studied the protein noise and statistics of gene expression using a chromosomal translational hetR-gfp fusion in wild-type and mutant strains under steady-state growth in rich-nitrogen conditions. We found that basal expression of the HetR inhibitor PatS, cell-cell communication influenced by SepJ and positive auto-regulation are essential determinants of fluctuations in hetR expression and its distribution along filaments. The characteristic spatial range of correlation between the fluctuations of HetR along filaments, circa three to five cells, sets the scale for cellular interactions along a filament.