Plant-cell expansion is controlled by cellulose microfibrils in the wall with microtubules providing tracks for cellulose synthesizing enzymes. Microtubules can be reoriented experimentally and are hypothesized to reorient cyclically in aerial organs, but the mechanism is unclear. Here, Arabidopsis hypocotyl microtubules were labelled with AtEB1a-GFP (Arabidopsis microtubule end-binding protein 1a) or GFP-TUA6 (Arabidopsis alpha-tubulin 6) to record long cycles of reorientation. This revealed microtubules undergoing previously unseen clockwise or counter-clockwise rotations. Existing models emphasize selective shrinkage and regrowth or the outcome of individual microtubule encounters to explain realignment. Our higher-order view emphasizes microtubule group behaviour over time. Successive microtubules move in the same direction along self-sustaining tracks. Significantly, the tracks themselves migrate, always in the direction of the individual fast-growing ends, but twentyfold slower. Spontaneous sorting of tracks into groups with common polarities generates a mosaic of domains. Domains slowly migrate around the cell in skewed paths, generating rotations whose progressive nature is interrupted when one domain is displaced by collision with another. Rotary movements could explain how the angle of cellulose microfibrils can change from layer to layer in the polylamellate cell wall.