Traditional Rope Coiling
Notes and Resources:
There is a large family of related but slightly different rope coiling techniques, which collectively I'm calling "traditional" coiling in the sense that they're widely preferred by practitioners of Japanese-derived rope styles.
There are (at least) three different ways of forming the coil -- folding, figure 8, and figure 8 with a single fold at the end -- as well as two different general approaches to finishing the bundle: by tucking the bight under the securing wraps, or by passing the bight through the end of the bundle.
Each combination provides a somewhat different compromise in terms of coiling speed, uncoiling speed, security, tangle-resistance, and bundle aesthetics. Which one is right for you comes down to personal preference.
Erin Houdini has an interesting variation on Kink Academy, if you have an account there, as well.