This is a sweet groove from the song "Liquid Fire" by Gojira, on their album L'Enfant Suavage:
The idea here is fairly simple, but somewhat difficult to execute. The hands merely are a 16th note paradiddle. The right hand is on the bell of the ride, and the left hand is on the snare. Every time the left hand starts a paradiddle, it is played as a rimshot, and the rest are played as ghost notes.
The tricky part is the foot pattern! The feet are playing a grouping in 5/16; three consecutive 16th notes, followed by an 8th note rest. This pattern in 5/16 doesn't line up with the quarter note. In fact, it takes five quarter notes to line back up.
The problem is that the paradiddle doesn't line up evenly with those five quarter notes. After five beats, the paradiddle will be starting on the left hand. It then will be another five beats before the foot pattern and quarter note lines up again! However, this time the paradiddles, quarter note, AND foot pattern will all be in sync.
It makes more sense if you think about all of them in terms of 16th notes. A quarter note is four 16th notes long (1e+a), the foot pattern is five 16th notes long (XXX - -), and the paradiddle is eight 16th notes long (RLRRLRLL). So we're dealing with three different groups of 16th notes, 4, 5, and 8. What we need to understand is how they all line up.
The paradiddles and quarter notes line up easily; 4 fits evenly twice into 8, so the paradiddle lines up with every other quarter note. The foot pattern is not so simple, since 4 does not fit evenly into 5. We need to find the least common multiple of 4 and 5, which is 20. That is fine, but we have new problem. Our paradiddle, which has 8 notes, does not fit evenly into the 20! This means that when the 5 and 4 line up, we will be halfway through the paradiddle. Now, we need to find the least common multiple of 4, 5, and 8, which is 40. So, in the space of 40 16th notes (which is 10 quarter notes) we can evenly fit the 8 note paradiddle, 5 note foot pattern, and the quarter note pulse. That is the full length of the pattern, before it repeats!