A self-avoiding walk (SAW) is a sequence of moves on a grid that does not visit the same point more than once. SAWs are used to study how networks form, including social networks, biological networks and computer networks, and have provided inspiration to scientists, artists and designers. Here we describe a collaborative project which aims to deliver public engagement activities that embrace creative thinking to explore SAWs through the medium of hand embroidery. We introduce the physics of SAWs and then present an activity which uses materials from hand embroidery to explore these concepts. Specifically, the activity makes use of a Maker Kit which contains all the materials needed to create SAWs on an embroidery hoop. We evaluate the impact of the Maker Kits and reflect on the opportunities provided by a creativity-led engagement activity for physics teaching and research.