What can be referred to as a "Stomp-Knockdown" texture is common in new construction across the mid-west portion of the United States. As the name implies this texture is created by using a brush to stomp patterns in drywall mud across the surface being textured. Once the basic pattern is created a knockdown knife is used to smooth the high spots. A very similar texture used in the southern part of the U.S. is termed "French Lace."
As with any texture, all-purpose joint compound or topping compound should be used as these types of mud contain more glue like properties which allow the mud to adhere properly to the drywall surface. Key to the look of this texture is the consistency of drywall mud used. Water is used to thin the texture mud considerably. The consistency of mud used for stomp knockdown is by far thinner than that used for any other step in drywall finishing. A gauge to determine drywall mud consistency is to watch the vortex created by a drywall paddle as it spins mud in a five gallon bucket. Using an electric spade handle drill spinning at 500rpm/rev, the paddle should create a vortex in the mud that extends three quarters of the way to the bottom of the bucket.
Drywall mud is applied to the surface being textured using a paint roller with a heavy nap or an airless paint sprayer. Most professionals prefer a heavy duty airless sprayer to apply the texture as this is much quicker and it is easier to control the amount of texture applied. Not to be over emphasized is the importance of keeping the amount of mud applied consistent across the entire area. This step is critical in creating an even consistent stomp knockdown texture.
Once texture mud has been applied to the surface a special brush is used to stomp patterns in the mud. The preferred style brush to use has stiff bristles aligned in an oval pattern across a wooden base that attaches to an extension pole. These brushes are referred to as "crows-foot" brushes. The best of which come as double headed brushes to speed application.
Finally, once the texture has set slightly, a long flat knife is used to smooth out the surface of the texture. To understand the process, imagine knocking the tips off of stalactites hanging from the ceiling. If done before the drywall mud has sufficient time to set the entire pattern may be smeared, ruining the desired effect. If the mud has set too firmly before it is knocked down, dried pieces of mud are dragged through the surface ruining the underlying pattern. Care must be taken when determining when to start knocking down this texture.
Below are a few more examples of Stomp-Knockdown textures
If you have seen stomp knockdown texture you are probably also familiar with rosebud stomp. These two textures are both used extensively in the midwest united states. Take a look at this article about Rosebud stomp drywall texture.