To my knowledge Jerry Bergonzi has been the first to logically organize and teach in a simple and consistent way the pentatonic style first explored by John Coltrane. These approach is presented in the second volume of his jazz improvisation series: "Melodic Structures". These steps are applied over a set of notes, usually a pentatonic, in order to "travel" up and down the scale. For example if the set of notes is the C major pentatonic (C D E G A) and we want apply the ↑-↑-↓↓-↑ pattern starting from the first C we will first have a step forward (C to D), followed by a second step forward (D to E), by a double step backward (E to C) and a final step forward (C to D). Notice how we started from a C and ended on a D. After this the pattern can be repeated, starting from D we have D E G D E, and so on. The final result will be: C D E C | D E G D | E G A E | G A C' G | A C' D' A | C' D' E' C' | ... ("C'" means C one octave higher, "C," would be one octave lower).

This simple device can generate an enormous amount of different musical lines. The pattern does't have any rythmic or harmonic information. Various sets of notes can be used for different harmonic situations and different rythmic groupings can generate the needed variety. For this reason the patterns are usually presented as a continuous stream of notes of identical duration.

We see that we can classify the patterns in a variety of ways. The first thing we noticed with the ↑-↑-↓↓-↑ pattern is that we started from a C and ended on a D. The sum of the steps was equivalent to ↑. Different patterns might "sum up" to double, triple or even bigger steps forward or backward. For this reason we can classify the patterns depending on their "total step".

A second thing we notice is that some patterns are simply the "opposite" of each other, where all the ↑ are replaced by ↓ and viceversa (e.g. ↑-↑-↓↓-↑ and ↓-↓-↑↑-↓). I called these "reverse" patterns.

Finally different patterns can be "modes" of each other. As normal scalar modes are obtained from a "rotation" of the sequence of intervals that make up the scale (E.g. Ionian "2-2-1-2-2-2-1" can be rotated to the left by taking the first whole step "2" and putting it at the end, obtaining "2-1-2-2-2-1-2", that is Dorian) the same we can say for the ↓↓-↑-↑-↑ and ↑-↑-↑-↓↓ patterns.

Not all the patterns we can think of are very useful to create interesting lines. For example we should exclude patterns that have an "total step" of zero (e.g. ↑-↓-↑-↓) since they don't move from their initial position. We should probably also exclude patterns that immediately backtrack (e.g. they have a ↑ immediately followed by a ↓, as ↑-↓↓-↑-↓)

To limit a bit the scope, let's focus on four-note patterns composed only of single and double steps, patterns that are equivalent at max to five forward steps (one octave if our group of notes is a pentatonic). How many possibilities do we have? It turns out we have eight possible "root" patterns that are not modes of each other. Each of them generates four actual patterns (modes), except the symmetrical patterns ↑-↑-↑-↑ (one possible mode) and ↓-↑↑-↓-↑↑ (two possible modes). Strangely enough none of them is equivalent to three forward steps.

Many of these are frequently employed by "pattern" players (Coltrane, McCoy, Brecker, Potter, Bergonzi himself, ...), while others are a bit more unsual. Not many guitarists (or trumpet players) seem to have explored these possibilities, and this style is probably easier to master on sax or piano. Of course wider steps and different lengths (three or five note patterns) are possible, and are often employed by the above players.

You can download a full pdf with the patterns below applied to the basic chord families (Major, Minor, 7, m7♭5, 7♭9)