What is a rhizome? - simply said, it is a non-hierarchical network - we see Delta-s as such a network...

The classical definition of a rhizome is a horizontal, root-like stem that extends underground and sends out shoots to the surface.

Rhizomes connect plants in a living network.

Rhizome is also a figurative term used by Gilles Deleuze and Felix Guattari to describe non-hierarchical networks of all kinds. Here are a few quotations from their seminal book, A Thousand Plateaus.

"A rhizome as subterranean stem is absolutely different from roots and radicles. Bulbs and tubers are rhizomes. Plants with roots or radicles may be rhizomorphic in other respects altogether: the question is whether plant life in its specificity is not entirely rhizomatic. Even some animals are, in their pack form. Rats are rhizomes... The rhizome itself assumes very diverse forms, from ramified surface extension in all directions to concretion into bulbs and tubers... We get the distinct feeling that we will convince no one unless we enumerate certain approximate characteristics of the rhizome." -p. 7

"A rhizome ceaselessly establishes connections between semiotic chains, organization of power, and circumstances relative to the arts, sciences, and social struggles." -p.7

"Multiplicities are rhizomatic, and expose arborescent pseudomultiplicities for what they are." -p. 8

"The rhizome is an antigenealogy." -p. 11

"Write, form a rhizome, increase your territory by deterritorialization, extend the line of flight to the point where it becomes an abstract machine covering the entire plane of consistency." -p. 11

"We're tired of trees." -p. 15

"To these centered systems [arborescent structures], the authors contrast acentered systems, finite networks of automata in which communication runs from any neighbor to another, the stems or channels do not preexist, and all individuals are interchangeable, defined only by their state at a given moment--such that the local operations are coordinated and the final, global result synchronized without a central agency." -p. 17

"Let us summarize the principal characteristics of a rhizome: unlike trees or their roots, the rhizome connects any point to any other point, and its traits are not necessarily linked to traits of the same nature; it brings into play very different regimes of signs, and even nonsign states. The rhizome is reducible neither to the One nor the multiple... It is composed not of units but of dimensions, or rather directions in motion." -p. 21

"Unlike the tree, the rhizome is not the object of reproduction, neither external reproduction as image-tree nor internal reproduction as tree-structure. The rhizome is an antigenealogy. It is a short-term memory, or antimemory. The rhizome operates by variation, expansion, conquest, capture, offshoots. Unlike the graphic arts, drawing, or photography, unlike tracings, the rhizome pertains to a map that must be produced, constructed, a map that is always detachable, connectable, reversible, modifiable, and has multiple entryways and exits and its own lines of flight. It is tracings that must be put on the map, not the opposite. In contrast to centered (even polycentric) systems with hierarchical modes of communication and preestablished paths, the rhizome is an acentered, nonhierarchical, nonsignifying system with a General and without an organizing memory or central automation, defined solely by a circulation of states." -p. 21

[The quotations above are from A Thousand Plateaus: Capitalism and Schizophrenia by Gilles Deleuze and Felix Guattari. Translated by Brian Massumi. University of Minnesota Press, Minneapolis. 1987.]
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