The first pattern is probably the most used out of all of them and should be familiar sounding if you listen to a lot of country or folk music. The thumb plays steady quarter notes throughout moving between the two lowest strings while the index finger play the G string and the ring finger plays the B string. The picking pattern for this lick is Thumb-Middle-Thumb-Index repeated over and over.
The second pattern uses an identical bass pattern with the thumb but flips the order of the syncopated notes. This time the picking pattern is Thumb-Index-Thumb-Middle. Notice in the last bar of each pattern (over the G chord) how the top note moves. This is showing a bit of how you can do small movements around the chord voicing to add a bit of melody to your accompaniment. Listening to great solo guitar players like Chet Atkins and Tommy Emmanuel can help give you some ideas on other ways to add more melody to your travis picking.
The third pattern again keeps the same steady quarter note bass pattern in the thumb but this time adds playing two notes at the same time. This pattern is almost identical to the first but instead of playing every note by itself, the first thumb and middle finger notes are played together. Doing this puts more of an emphasis on each down beat.
The last pattern expands on the third by also playing the second and fourth beats together. Like the other patterns, the bass pattern in the thumb remains the same. The only thing that is changing is the upper part of each chord.
Try working this patterns in different keys and on different voicings across the neck. They also sound good when played fast as well. See my other lesson on rockabilly rhythm guitar for ideas on how you can use this technique with electric guitars over faster music.