Abstract
A theory is proposed for the development of filamentous organisms, based on the assumptions that the filaments are composed of cells which undergo changes of state under inputs they receive from their neighbors, and the cells produce outputs as determined by their state and the input they receive. In this first part of this study the inputs are considered to pass only in one direction along the filament. Formal set- theoretical statement of the assumptions, and of some of the theorems derivable from them, is included.