An brief explanation of what linear patterns are with written examples.
A linear pattern, or linear drumming, is a part where only one stroke is played at a time. That means familiar movements such as kick and hi hat or snare and hi hat don't happen. This creates some really interesting and musical parts that can sound really complex. These kind of patterns can be very demanding on hand-foot co ordination as odd and uncomfortable movements are common. However, that means they also make great exercises for improving this area of drumming.
To show the difference in this style of playing and the more conventional non linear style I have provided some written examples. In the groove examples below, the part on the left is linear and the part on the right isn't. As you can see from the notation, linear parts tend to be notated in just one voice.
In this version the ostiatno is the right hand rhythm played on the ride. The kick and snares then do there thing around this.