Search results for "Box counting"

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Dimensions of random affine code tree fractals

2014

We calculate the almost sure Hausdorff dimension for a general class of random affine planar code tree fractals. The set of probability measures describing the randomness includes natural measures in random $V$-variable and homogeneous Markov constructions.

Discrete mathematicsCode (set theory)v-variable fractalsApplied MathematicsGeneral MathematicsProbability (math.PR)ta111Dynamical Systems (math.DS)self-similar setsTree (descriptive set theory)Box countingFractalIterated function systemMathematics - Classical Analysis and ODEsHausdorff dimensionClassical Analysis and ODEs (math.CA)FOS: MathematicsAffine transformationMathematics - Dynamical Systems28A80 60D05 37H99RandomnessMathematics - ProbabilityMathematics
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Canopy Architecture Appraisal by Fractal Dimension of 'Flordastar' Peach Trees Grafted onto Different Rootstocks

2007

The objective of this research was to evaluate the modification of canopy architecture of ''Flordastar'' peach (Prunus persica L. Batsch) grafted onto rootstocks with different vigour, by the use of fractal dimension (D). The hypothesis was that different vigour rootstocks are able to modify the complexity of the branching pattern and that this effect can be assessed by a geometric parameter such as the fractal dimension (D) of the 2D projection of tree branching structure. The observations were carried out in a four-year-old experimental orchard of cv. ''Flordastar'' peach trees grafted onto Ishtara, Barrier, GF677 and MrS 2/5 rootstocks. On digital pictures of leafless, dormant peach tree…

The objective of this research was to evaluate the modification of canopy architecture of ''Flordastar'' peach (Prunus persica L. Batsch) grafted onto rootstocks with different vigour by the use of fractal dimension (D). The hypothesis was that different vigour rootstocks are able to modify the complexity of the branching pattern and that this effect can be assessed by a geometric parameter such as the fractal dimension (D) of the 2D projection of tree branching structure. The observations were carried out in a four-year-old experimental orchard of cv. ''Flordastar'' peach trees grafted onto Ishtara Barrier GF677 and MrS 2/5 rootstocks. On digital pictures of leafless dormant peach trees the tree skeleton was manually depicted by an image analysis software to measure total length and angles of insertion of branches. Bitmaps of the skeleton were then subjected to a specific software (FDCALC) able to calculate D by the "box counting" method. To account for the error introduced by analyzing a three dimensional structure with its 2D projection measurements were done on two images per tree taken from two different viewing angles. Results are shown in relation to tree vigour of the scion/stock combination. Fractal dimension was related to the vigour ranking of the graft combinations tested. In particular vigorous scion/stock combinations showed the highest D.HorticultureCanopy architectureHorticultureRootstockFractal dimensionMathematics
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