A rhizome is a horizontal subterranean plant that produces shoots above and roots below--the external surface of roots closely adheres to soil particles and debris. It is neither a root, nor a plant. It resides in the nether region in-between--that spaciality. For Deleuze and Guattari, this provides the perfect metaphor for their brand of "philosophy" as set in distinction to "tree" philosophy--a philosophy of deep roots, a philosophy with a foundation, upon which knowledge can be erected. I once received this cartoon on a philosophy instructor's syllabus:
 

In light of Deleuze and Guattari, I can only chuckle. As if chaos is unsystematic.... : )