I use the patterns (or filigree) as a form of highlighting / shading. Similar to how an illustrator would use pointillism or cross-hatching to create different values with only two colors. Filigree is a more decorative form of those techniques for my papercrafts. I first draw major line forms to get the flow of the pattern, then fill in the gaps with random swirls or linework to create varied shapes as I go.
How do you come up with such brilliant ideas for patterns? Your papercuts seem very complicated!