Solid areas are contrary to the nature of tatting, they aren't much fun to work, and they don't add a lot to the design. They are, however, possible; all you have to do is to place chains close together.
Sometimes solid areas are effective; I particularly like Julia E. Sanders' rose with petals that look solid. It was made by working a daisy with picot-fringed mock-ring petals on every fourth picot of the center ring, then working two rows of almost-mock-rings of chain to frame each mock ring, then covering the center with a "flat ball" of crochet. ("Collar in Tatting Appliqué on net," fig. 82 in Tatting Patterns, Dover, 1977 republication of 1915 edition.)
I took it, at first glance, for a stack of carefully-graduated medallions, which sounds like a fertile idea.
Nicholls' Figure 60 shows a "lively German edging" in which a chain folds back and forth to make square spots. I have sketched one possible way to copy the photograph.