Trichome patterning in Arabidopsis is a model for the generation of a spacing pattern from initially equivalent cells. We show that the TRIPTYCHON gene that functions in lateral inhibition encodes a single-repeat MYB-related transcription factor that lacks a recognizable activation domain. It has high sequence similarity to the root hair patterning gene CAPRICE. Both genes are expressed in trichomes and act together during lateral inhibition. We further show that TRIPTYCHON and CAPRICE act redundantly in the position-dependent cell fate determination in the root epidermis. Thus, the same lateral inhibition mechanism seems to be involved in both de novo patterning and position-dependent cell determination. We propose a model explaining trichome and root hair patterning by a common mechanism.