We present a unified model for the growth of a population of cells. We propose that sigmoidal growth in cellular systems is a self-organised process due to long-range interactions among the cells. The interaction is mediated through diffusive substances produced by them. The model considers a competition between cell drive to replicate and inhibitory interactions that are modeled by a power law of the distance between the cells. The different classes of solutions (Logistic, Richards-like, Gompertz, and Exponential) are determined by a relation between the interaction length and the fractal dimension of the cellular structure.