Thanks to a request on the Blender Artist forums, I messed around with my carbon fiber material and was able to get it to work as a diagonal weave pattern. The only downside is that the brighter color means it's easier to see the seams between faces so you might need to use a subsurf modifier to get better transitions.
Like the carbon fiber material, your mesh must be UV-Unwrapped in order for it to work.
This weave is called a 2 twill herringbone pattern. It is what is used in most shoe laces, carbon fibre (though not all), cable braiding, etc. Not too bad.
I think that this blend will make great fuel or brake line hose such as used on high performance engines or cars.
This reminds me a bit of the weave on the old fashioned fabric hoses on the "sausage-type" pull-along early vacuum cleaners.
There was a similar weave on fabric-covered electrical power leads, before the less aesthetic black plastic/rubber became the norm.