From the article: "Civilization Without Writing -- The Inca and the Quipu" by Marcia Ascher and Robert Ascher (also authors of "Code of the Quipu: A Study in Media, Mathematics and Culture", publisher and date unknown)
"A quipu is a collection of cords with knots tied in them. The cords were usually made of cotton, and they were often dyed one or more colors. When held in the hands, a quipu is unimpressive; surely, in our culture, it might be mistaken for a tangled old mop. (...)
"Quipus probably predate the coming to power of the Incas. But under the Incas, they became part of statecraft. (...)
"There are several extremely important properties of quipus.... First of all, quipus can be assigned horizontal direction. (...) Quipumakers knew which end was which; we will assume that they start at the looped aends and proceed to the knotted ends. Quipus can also be assigned vertical direction. Pendant cords and top cords are vertically opposite to each other with pendant cords considered to go downward and top cords upward. (...) Quipus have levels. Cords attached to the main cord are on one level; theur subsidiaries form a second level. Subsidiaries to these subsidiaries form a third level, and so on. Quipus are made of cords and spaces between cords. (...) Larger or smaller spaces between cords are an intentional part of the overall construction. (...)
"As well as having a particular placement, each cord has a color. Color is fundamental to the symbolic system of the quipu. (...) Basically, the quipumaker designed each quipu using color coding to relate some cords together and to distinguish them from other cords. (...) Additional cord colors were created by spinning the colored yarns together. Two solid colors twisted together gives a candy cane effect, two of these twisted together using the opposite twist direction gives a mottled effect, and the two solid colors can be joined so that part of the cord is one color and the rest of it is another color. (...)
"For the most part, cords had knots tied along them and the knots represented numbers. But we are certain that before knots were tied in the cords, the entire blank quipu was prepared. The overall planning and construction of the quipu was done first, including the types of cord connections, the relative placement of cords, the selection of cord colors, and even individual decorative finishings. (...) The quipumaker's recording was nonlinear. (...) A group of strings occupy a space that has no definite orientation; as the quipumaker conmnected strongs to each other, the space became defined by the points where the strings were attached. (...) Essentially then, the quipumaker had to have the ability to conceive and execute a recording in three dimensions with color."