Drawing things out is helpful when you're trying to bring an abstract idea to life. If you want a "whirly thing" on your invitation, then use Moleskine Journal (free) to illustrate what you're thinking of, and show it to your wedding planner or paper goods designer. The app takes on the classic Moleskine style and provides you with a complete artist tool set. Choose from different Moleskine styles like plain, ruled, grid, or storyboard.
Just like the real thing, you can save images and other media to the "expandable back pocket." The Moleskine app syncs with Evernote and Dropbox, too!