This is a way to make the simple, familiar movement of triads around the circle of 5ths act as harmonic substitutions over the ii-V-I pattern. Take a look at the sample below:
By starting from the 3rd of the D-7 chord to extract the F major triad, I move the major triads around the circle, making a shift of a tritone in the middle of the G7 measure, going from Eb major to A major (instead of Ab). If you look it this pattern from a point of view of harmonic relationships, you’ll see there are some fairly rich tensions. For example, b13 (Eb), + 9 (Bb) and +11 (C#). But those tensions become almost secondary, as the ear is drawn to the powerful movement of triads around the circle.
The shift to the tritone creates some surprise, slightly breaking the mundane pattern of the circle. This is a great way to bypass , or at least reframe, the ii-V-I pattern. It should probably be used rather sparingly, as it is a strong, somewhat obtuse sound (click on the link below to hear a midi sample). This etude is composed from various random connections of the triads, so there are no exact patterns per se. For the less advanced student, this is also a great way to get the circle of 5ths in the ears and under the fingers. This, and other concepts of triad substitution are explored at length in my book Melodic Minor Scale Jazz Studies: Organizations and Applications Over Dominant 7th Chords.