Application Research Of Fractal Dimension On The Apple Tree Architecture Evaluation

The relationship between the fractal dimension of different age apple trees trained to thinspindle configuration and their shoots characteristics, leaf characteristics, photosynthesisindex, and yield were analysed, which will provide theory basis for evaluating treearchitecture and guiding the production using fratal theory. Meanwhile, computerimplementation of fractal dimension calculation was proposed. The main researchachievements are as follows:（1） The fractal dimension of apple trees of different ages and different cultivars trained tothin spindle configuration have positive correlations with most of their shoots characteristicsand leaf biomass. The whole tree fractal dimension with leaves of Changfu2, Yuhuazaofu,Honggailu, Ligala, Fuhongzaoga and Yanfu6are1.635，1.666，1.647，1.672，1.598，1.573while the fratal dimension without leaves are1.365，1.477，1.372，1.474，1.349，1.341。The rank by total shoots length, dry leaf weight and fractal dimension are almost the same andare Ligala＞Yuhuazaofu＞Honggailu＞Changfu2＞Fuhongzaoga＞Yanfu6.（3） Fractal dimension of different canopy have a connection with the leafphotosynthesis. To the Changfu2apple trees trained to thin spindle configuration, the fractaldimension of the upper and middle and lower6-year old tree at the inner crown are1.620，1.852，1.845while that at the outer crown are1.620，1.852，1.845; the fractal dimension of theupper and middle and lower13-year old tree at the inner crown are1.620，1.852，1.845whilethat at the outer crown are1.620，1.852，1.845; the fractal dimension of the upper and middleand lower18-year old tree at the inner crown are1.620，1.852，1.845while that at the outercrown are1.620，1.852，1.845. The net photosynthetic rate and transpiration rate have littledifferences among the upper and middle crown of different ages: the net photosynthetic raterange from14.9to17.2μmol·m^-2·s-1and the transpiration rate vary between2.1and3.1mmol/（m2·s）. As the tree age increase, the fractal dimension of upper and middle crownincrease and the branch and leaf density increase, which lead to the decrease of the netphotosynthetic rate ranging from6.9to12.8μmol·m^-2·s-1and transpiration rate varying from1.2to1.9mmol/（m2·s） at middle and lower crown. The stomatal conductance demonstratesthe similar trend with transpiration rate. The intercellular CO2concentration present little differences among the five ages ranging from203.0～276.0μmol/mol.（4） The average fractal dimension of6、9、13、18and20years old apple tree with leavesbeing trained to thin spindle configuration form the front and side view are1.672，1.717，1.783，1.825，1.854while that without leaves are1.493，1.606，1.697，1.772，1.804. Theintergral fractal dimension have certain relationship with the yield: the yield reach the topbeing60000kghm^-2or so when the fractal dimension is around1.75; The yield increase as thefractal dimension increase when the fractal dimension is less than1.75; The yield decrease asthe fractal dimension increase when it’s more than1.75. The proper fractal dimension shouldbe1.7～1.8.（5） A new concept of CRL（contribution rate of leaves） was proposed. The CRL ofChangfu2, Honggailu, Ligala, Fuhongzaoga, Yanfu6are16.52%，11.35%，16.73%，11.8%，16.08%，14.79%; The CRL decreases as the age increases for Changfu2apple tree trained tothin spindle configuration which are10.68%，6.34%，4.8%，2.93%，2.7%.