My PhD project studies the evolution of developmental systems. As a case study, we are looking at the gap gene network involved in pattern formation and segment determination during early insect development. My approach focuses on understanding the dynamics implemented by this system and how they constrain, and guide the evolution of developmental patterning processes. During my project, I have used methods from dynamical systems theory - in particular the geometrical analysis of configuration space - to characterise gap gene regulation in Drosophila melanogaster. My analysis reveals a damped oscillator mechanism that underlies the dynamic expression of posterior gap domains. This is a very suprising finding in a long-germband insect, which forms its segments simultaneously, and is similar in kind to the oscillatory mechanism producing segments sequentially in shortgermband embryos. I am currently extending my analysis to characterise the dynamic mechanisms underlying pattern formation by the gap genes in two more species of flies (Megaselia abdita and Clogmia albipunctata). My work raises fundamental questions concerening the evolution of evolving dynamical systems.