The Growth Competition Model And Realization Of The Natural Tree

The growth of natural trees is an optimization process, during which branches grow outwards and upwards due to the phototropism of the natural tree. Meanwhile, branches may fall because they lack sunshine and nourishment. This process is always accompanied with the growing of new branches and the falling of old ones. After years of continuous evolution, the shape of the trees becomes stable. So the stable shape is formed from the continuous adjustment of the trees to the environment, and it is an optimum result.Based on the theory mentioned above, a competition model of natural trees is established in this thesis to simulate their growing process. It is later applied to solve optimization problems such as curve fitting.From the point of biology, the growth of natural trees is a very complicated process, which is influenced by many environmental factors such as light, moisture, precipitation and temperature. Through the understanding and analysis of the growing process of natural trees, we conclude four basic characteristics that will influence their growth: phototropism, geotropism, competition and stochastic growth. Based upon the antinomy-unification principle in the growth of natural trees, we only take into account the influences of sunshine and nutrition. Then we use sunshine-fitness function and nutrition factor to describe such growth characteristics as phototropism and geotropism. Meanwhile, competition plays a key role in the growth of natural trees, which is presented as the competitions for resources and spaces, the restraint of branches and change of growing patterns. The interconnections between branches are restraining. The concepts of branching and layering are introduced in this thesis taking use of the characteristics of competition and stochastic growth. By grasping these major characteristics, the complicated growing process of natural trees is generalized so as to obtain the competition model.In this thesis, we program in VC++6.0 and display the 3D simulated tree obtained from the model mentioned above. We simulate the patterns of natural trees and better understand the growing mechanisms. Then we use this optimum growing process for the solution of curve fitting problem. A sunshine-fitness function is established based on the phototropism of natural trees. Curve fitting is conducted by approaching the data series via polynomials. Making use of the nutrition factor and the sheltering factor, the pattern of natural trees gradually approaches the optimum solution of the desired problem.In this thesis, the curve fitting results of two typical oscillation functions are compared with that from standard Genetic Algorithm (GA). Results show that our model runs faster, occupies less memory and has higher fitting accuracy. The overall better performance of our model proves the rationality and effectiveness of the competition model. It can be used in a lot of optimization applications such as the structure optimization of tree antennas.