A Brief History of Strahler Numbers

8 years 26 days ago

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The Strahler number or Horton-Strahler number of a tree, originally introduced in geophysics, has a surprisingly rich theory. We sketch some milestones in its history, and its connection to arithmetic expressions, graph traversing, decision problems for context-free languages, Parikh’s theorem, and Newton’s procedure for approximating zeros of diﬀerentiable functions. 1 The Strahler Number In 1945, the geophysicist Robert Horton found it useful to associate a stream order to a system of rivers (geophysicists seem to prefer the term ‘stream”) [20]. Unbranched ﬁngertip tributaries are always designated as of order 1, tributaries or streams of the 2d order receive branches or tributaries of the 1st order, but these only; a 3d order stream must receive one or more tributaries of the 2d order but may also receive 1st order tributaries. A 4th order stream receives branches of the 3d and usually also of lower orders, and so on. Several years later, Arthur N. Strahler replaced this...

Javier Esparza, Michael Luttenberger, Maximilian S

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