The understanding of the emergence of network structures is fundamental to describe biological networks like blood vessels and interconnected neuron systems. The vision is to develop biology-influenced computer devices whose design is inspired by the neural networks of the brain. Compared to artificial intelligence that relies on algorithms to process information, neuromorphic computing uses hardware that mimics the function of the brain. In this talk, we present diffusion-type models describing phenomena from cell biology, which may lead to biological or artificial networks. We report on some models, explain their key features, and present first numerical simulations.