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  • branching pattern  (3)
  • 1
    Electronic Resource
    Electronic Resource
    Generation and visualization of root-like structures in a three-dimensional space (1997)
    Springer
    Plant and soil 197 (1997), S. 9-18 
    Details
    ISSN: 1573-5036
    Keywords: branching pattern ; recursive model ; root architecture ; three-dimensional structure ; visualization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Abstract In his Notebooks Leonardo da Vinci describes his diameter squared rule for the branching of above-ground tree parts. We now apply this branching-rule to the study of root-branching. Repeated application of this rule in a recursive computer program (ArtRoot) produces the diameters of the branches. An algorithm in this recursive program calculates the orientation of the branches in a three-dimensional space. From these data three-dimensional root-like structures are visualized by a computer program (PLUTON) designed to draw three-dimensional molecular structures. The visualization shows that starting from a relatively simple, symmetrical structure of dichotomous branching, more complex, asymmetrical root-like structures arise even if only a few parameter values are changed. The introduction of randomness into parameter values produces structures that differ considerably in their architecture. An extra force has been added in order to influence the orientation of new branches in space and to increase the flexibility of the structure formation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004236626479
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Proximal root diameter as predictor of total root size for fractal branching models (1994)
    Springer
    Plant and soil 164 (1994), S. 107-117 
    Details
    ISSN: 1573-5036
    Keywords: branching pattern ; dichotomy ; fractal characteristics ; herringbone ; methods of root research ; root diameter ; specific root length
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Abstract In a fractal branching pattern the same rules govern branching at each subsequent level. The initial size (diameter) and the essential branching rules thus contain the information required to construct the whole pattern. If root branching patterns have fractal characteristics, measurement of the proximal root diameter at the stem base and the branching rules as observed anywhere in the root system, would be enough to predict total root length, root diameter distribution and root length per unit dry weight (specific root length). A ‘pipe stem’ model is used to derive algebraic relations between total root size and proximal root diameter for two classes of branching patterns, determinate and proportionate. To predict total root length from the proximal root diameter, at least information is needed on the minimum root diameter, the average length of internal and external links (segments) and the proportionality factor between total cross sectional areas before and after branching. For the length of the longest root or the specific root length further information on the branching rules is needed, as it is highest for determinate and proportionate branching rules, respectively.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00010116
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  • 3
    Electronic Resource
    Electronic Resource
    Proximal root diameter as predictor of total root size for fractal branching models (1994)
    Springer
    Plant and soil 164 (1994), S. 119-127 
    Details
    ISSN: 1573-5036
    Keywords: branching pattern ; root architecture ; root diameter ; root strategy ; specific root length
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Abstract If root systems have scale-independent branching rules, the total number of links in the root system can be predicted from the ratio of the largest and smallest root diameter. In Paper I we presented an algebraic model for a dicho-syntomous pattern (the simplest form of proportionate branching forming two equal branches at each node) and a herringbone branching model (the simplest form of determinate branching rules). Here, we present a recursive computer model and its results to analyze intermediate patterns, derived from allotomous proportionate branching (with unequal branches). The numerical and algebraic model gave the same results when applied to the same situation and parameter values. For practical applications of the relations found, a test is required on whether or not the underlying assumptions are met. To illustrate such a test, measurements of the branching pattern were made on Mondriaan's Red Tree painting. For patterns such as this tree a slight dependency of the proportionality factor on root diameter and random variability of several parameters may have to be included.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00010117
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