Persian carpets may not be Persian at all, of course, but Anatolian, or, more broadly, Central Asian.
Geometrically patterned Persian carpets, originally woven by nomadic tribes, are decorated with linear elements composed of vertical, horizontal and diagonal lines, and are formed by a repetition of the same motif. The motif of a carpet can be used to determine the particular tribe, or place of origin.
A pattern, whether in nature or art, relies upon three characteristics: a unit, repetition, and a system of organisation.
Symmetry is a fundamental organising principle in nature and in culture. The analysis of symmetry allows for understanding the organisation of a pattern, and provides a means for determining both invariance and change.
By varying relationships within patterns where symmetry is expected, otherwise predictable and repetitive patterns are transformed into great works of art.
The variations in design occur in the two main parts of the rug: the field, or ground, and the borders, which frame the interior, or the field. Designs are either curvilinear or rectilinear.
The most common motif for Persian rugs, especially the larger ones, is a large central medallion. Yet, even if two carpets have basically the same design, no two medallions are ever exactly the same. Some experts believe that the medallion designs stems from the very religious nature of the weavers and that their inspiration probably came from the artwork and patterns of domes of the mosques.
Always roll carpets against the grain, of course. It is easy to feel that uniform tilt in the fibres. It is also easy to see it in the light. When facing sources of natural light, a carpet will appear lighter with light falling in the direction of the grain, darker when falling against it.