Four shafts, four blocks...
One of the reasons I decided to include rep weave in A Good Yarn is that it is one of the weave structures with which you can achieve four blocks on four shafts. Others are overshot, crackle and shadow weave.
I threaded a point progression (Block A, B, C, D, C, B, repeat) and am weaving in a straight progression (A, B, C, D).
There is no 'true' plain weave with this weave structure because of the way it is threaded. The treadles are used in pairs and it is dependent upon which of the pair you select for the thick yarn that determines which block is woven.
It takes a little bit for the brain to get comfortable with how it works, but once your brain and feet figure it out, it is simple to sort of 'draw' your pattern. For the purposes of A Good Yarn I am weaving each sample exactly the same.
With four blocks on four shafts, when you want block A to weave you have to choose whether its 'pair' (or shadow) will be block D or block B. When you want block B to weave you have to choose whether it will have block A or block C at the same time. And so on. In this way you can adjust the design and have a pattern that repeats, or constantly changes, always on the twill diagonal.
For more information on how this works I recommend Lucille Landis' book Twills and Twill Deriviatives - the section on shadow weave. The same principle applies to any of the four shaft/four block weaves.
PS - this is one weave where a floating selvedge might come in handy. Since I don't use one I am simply twisting the shuttles around each other at the selvedge to lock the warp ends into the weave structure. It's a personal preference thing.