Development of multicellular organisms requires the generation of gene expression patterns that determines cell fate and organ shape. Groups of genetic interactions known as Gene Regulatory Networks (GRNs) play a key role in the generation of such patterns. However, how the topology and parameters of GRNs determine patterning in vivo remains unclear due to the complexity of most experimental systems. To address this, we use the zebrafish notochord, an organ where coin-shaped precursor cells are initially arranged in a simple unidimensional geometry. These cells then differentiate into vacuolated and sheath cells. Using newly developed transgenic tools together with in vivo imaging, we identify jag1a and her6/her9 as the main components of a Notch GRN that generates a lateral inhibition pattern and determines cell fate. Making use of this experimental system and mathematical modeling we show that lateral inhibition patterning is promoted when ligand-receptor interactions are stronger within the same cell than in neighboring cells. Altogether, we establish the zebrafish notochord as an experimental system to study pattern generation, and identify and characterize how the properties of GRNs determine self-organization of gene patterning and cell fate.