My design exposes two kinds of resources:
I would like clients to be able to request random images by their tag(s). For example
I agree with Triptych on this one. In a way adding random to the end of the URI makes it feel like an operation, but if it is scoped to a tag then you're really just refining the context.
In his example of:
/image/tagged/sometag/random
images resource -> tagging scope (all images with tags) -> specific tag (all images with tag X) -> random (a resource from the scoped list of images with tag X)