Research On Geometric Fractal Of The Birch Growth

Fractal geometry is a discipline that takes irregular shapes and complex systems as research objects.Objects with fractal characteristics are self-similar in structure,and the degree of space occupied is measured by the fractal dimension.Fractal dimension is the result of self-similarity and can be used to characterize the common fe atures of objects at different scales.Fractal geometry is widely used in ecology and has become an important tool for ecology research.This paper uses the fractal theory to study the branching structure characteristics and growth rules of birch trees in Chongli District of Zhangjiakou City,and calculates the cross-sectional integral fractal dimension,length fractal dimension and biomass fractal dimension using the breast diameter and the number of branches at each level as scale indicators.This paper also analyzes the influence of tree size and forest type on fractal dimension.The main research results are as follows:(1)The branch cross-sectional area of birch trees accumulates according to the fractal law,and the distribution of branch cross-sectional areas at all levels is similar.For the population of birch trees,there is a good dynamic relationship between the breast diameter of the birch tree and the total cross-sectional area,and the integral cross-sectional dimension of the dynamic cross section is 1.650;for the individual birch trees,the number of branches and the average cross-sectional area of the birch tree.There is a good static relationship,and its integral dimension of static section is 0.893.The cross-sectional integral dimension represents the horizontal space utilization of trees to a certain extent.The results show that the larger the tree,the greater the horizontal space utilization and the stronger the ability to occupy horizontal space.The degree of competition for horizontal space within birch species is less than that between birch and larch species.(2)The branch lengths of birch trees accumulate according to the fractal rule,and the branch length distribution at all levels is similar.For the birch tree population,there is a good dynamic relationship between the DBH diameter and the total length of the birch tree,and the dynamic length fractal dimension is 1.291;for the birch tree individuals,the number of branches and the average length of the birch tree have a good relationship static relationship,the static length fractal dimension is 0.499.The length fractal dimension represents the vertical space utilization rate of the trees to a certain extent.The results show that the birch trees in the middle growth period have the highest vertical space utilization rate and the strongest ability to occupy vertical space.The degree of competition for vertical spaces within birch species is less than that between birch and larch species.(3)The branched biomass of birch trees accumulates according to the fractal rule,and the biomass distribution of its branches at all levels is similar.For the population of birch trees,there is a good dynamic relationship between the DBH of birch trees and the total biomass,and the fractal dimension of dynamic biomass is 1.964;for the individuals of birch trees,the number of branches of birch trees and the average biomass.There is a good static relationship,the static biomass fractal dimension is 1.172.Biomass fractal dimension represents the biomass allocation ratio of trees to a certain extent.The results show that the larger the tree,the greater the biomass allocation ratio,and the more energy is transferred from the previous branch to the next level.The positive effect of the competition between birch and larch species on the biomass allocation ratio is greater than that within the birch species.As a symbol of the complexity of the spatial pattern of objects,fractal dimension reflects the inherent properties of objects.The fractal dimension of the birch tree provides a useful indicator for understanding its space utilization rate and controlling its growth and development process,which has a certain theoretical value for the construction of the ecological environment,and at the same time provides a certain degree for revealing the distribution law of natural space and resources basis.