You’re going to need more than a swatch to make these retro “free form” (from a pattern) decor boards — but the good news is that you can use cheap ol’ burlap, as instructed, or any fabric you like (Maybe even old sheets?) The June, 1957, issue of Popular Mechanics describes the DIY project thus:
In addition to being conversation pieces in themselves, decor boards are the answer to the problem of displaying small pictures, curios and other knick knacks in a room of modern furnishings. Besides adding a sharp contrasting background, these “bulletin boards” save the wall from numerous nail holes as they hang like pictures.
Fabric of your choice
Small rubber tacks
And the patterns for “free form” shapes as shown (click to enbiggin’).