To begin with, the introduction is a comparison between “the tree” and the “Rhizome”. The two terms are not only applicable on literature, but also in psychology and politics.
Second, in chapter 14 other terms are used which are “smooth space” and “striated space”. In order to show the relation between them, Deleuze gave different models which reveal the aspects of the two spaces.
In both cases (chap 1 and 14) the author is trying to show that the relation between the terms is that of “becoming” of “assemblage”, “deterritorialization” and “reterritorialization” in order to attain “the plane of consistency” which is the outside of all multiplicities or in other words, to reach the exteriority of relations.
Deleuze gave several examples to support his argument. First, he showed psychoanalysis as the closed system where there are always objects and leader. Than, he said that schizoanalysis is a Rhizome and an assemblage of multiplicity of states of the unconscious that has no center. In addition, he gave other examples on linguistics and capitalism.
Further more, the thought, as the author believe, is and assemblage of concepts. It is always in growth and process; it breaks and starts up again.
Later he gave the characteristic of a Rhizome, which are the opposite of the tree or their root. The Rhizome is a connection of different things, it is reducible, it is composed of directions, it is always in the middle intermezzo, it has neither subject nor object, it is not a structure but rather it is made of lines, it is an antigenealogy, it is a short-term memory, it is not a tracing but a map which has multiple entryways and exits (the map is done by tracing), it is acentered, nonhierchial, nonsignifying, it is a relation to everything (book, sexuality…) no matter if those things were natural or artificial, it is an assemblage of plateaus, it is a machinic assemblage of desires plugged to the multiplicity of the outside.
More over, Deleuze said that books are the image of the world; they assemble in heterogeneity with the outside only in a world that reproduces (the becoming world of the book, and the becoming book of the world). The books assure the deterritorialization of the world, but the world affects the reterritorialization of the book which in turn deterritorializes itself in the world. So it is important to make Rhizomes (not roots), multiplicities, to be productive and to make maps and no tracing.
In chapter 14, Deleuze portrayed the same relation but in other terms. He talked about two spaces which exist in mixture. The smooth space is the becoming of the striated space. He explained that in many models. First the technological model where the striated space is the fabric which is a closed system that takes the body and the exterior to a closed area; and weaving nomad is the smooth space that brings the cloth and the house (closed area) to the outside. And after an assemblage of many factors the fabric started to change thus the striated space to become a smooth space. Similar examples were given in the musical model, where he talks about the texture of the music which is in smooth space when it is in continuous development of form. Than in the maritime model, Deleuze said that in the sea there is openness therefore a smooth space and the smooth space of the sea takes the striated to the openness. After that he talked about the mathematical model where he said that the smooth space is nonmetric, in minor geometry and is operative and qualitative; the magnitudes are in the striated space. More in the physical model he said that surplus labor and capitalism are becoming less striated and more smoothed because of the physicosocial concept of work. Finally the aesthetic model: nomad art where there is the haptic space (smooth) where there is close-range vision (like short term memory) and the tactile space (striated) which is long-distance vision (like long term memory). There is the idea of “becoming-artist”. And finally the author talked about the smooth space as an abstract in modern art, a variable direction that describes no outline and restricts no form.