In 2015, the third author launched a successful Kickstarter campaign to fund the purchase of an industrial knitting machine. The Kickstarter rewards were scarves, each procedurally knitted in a unique two-colour pattern: the output of a elementary cellular automaton. The scarves are double knit (double bed jacquard in machine knitting parlance), meaning that the scarf has two layers of different colours, that swap positions back and forth to produce the pattern on the scarf. This implies that the pattern on the back side of the scarf is the colour reverse of the pattern on the front side. A corresponding “inverse” elementary cellular automaton produces the pattern on the back. We wondered if it would be possible to produce a Möbius strip scarf, in which the front becomes the back whilst seamlessly continuing the development of a single elementary cellular automaton. This paper describes our discoveries.