This cup cozy is inspired by the diamond pattern on the jacket worn by Howl in the Studio Ghibli movie "Howl's Moving Castle." The finished cozy is 3 inches/7 cm tall with a circumference of 10 inches/26cm. This pattern is moderately difficult, and uses overlay mosaic crochet. If you've never tried mosaic crochet before then I recommend you watch some tutorials before attempting this pattern.
Here are some mosaic crochet tutorials that I found useful:

Basic mosaic crochet: https://www.youtube.com/watch?v=HTigdTvdTLQ&t=493s&ab_channel=TinnaThorudottirThorvaldar

This one explains the difference between inset and overlay mosaic crochet (This pattern uses overlay mosaic crochet): https://www.youtube.com/watch?v=Ss9w3q-LUK8&ab_channel=CoolWoolDesign

This pattern also has the option to create one of 2 types of cozies; One with a sealed tube shape, and one that is open and made to accommodate for a cup handle. Which one you choose is dependent on the type of mug or cup you are using it for (With or without a handle).