摘要或動機

本研究首先確認培地茅根系具有碎形之基本特性，再進一步以方格覆蓋法計算之碎形維度來分析培地茅根系在不同時間及環境因素下的生長。主要探討碎形維度與抓地力之關係，並設計以實際根系模型來加以模擬，並發展出一可描述抓地力與碎形維度及深度關係的方程式。我們的結論為：（1） 經由方格覆蓋法之計算，培地茅此種植物，不管是整個根系或單枝根，均具有碎形基本特性，適合進一步實驗研究。（2） 碎形維度會隨著培地茅生長時間增長而增加，並且在自然光照及30℃左右會有較大值，而種植於土壤中根系發展較廣，其碎形維度比種植於沙耕中來的高。（3） 實驗結果顯示，抓地力受碎形維度及根系深度兩因素影響，而培地茅根系對土壤有較強的抓地力，推測是因為兩者根系皆又深又長，土中培地茅根碎形維度較大，接觸面積較廣，而又進一步以矽膠模型做實驗驗證。（4） 矽膠模型之目的在於減少難控制之自然變因，實驗之前，測量了根系模型與洋菜凍之基本性質，實驗結果顯示抓地力與碎形維度及根系深度皆呈正向關係，可用數學方程式加以描述。This project is mainly a research into the fractal dimension of the vetiver root system. First, we confirm the vetiver root system has the basic fractal structure by checking its self-similarity, then using box-counting method to calculate fractal dimension. We begin with a fundamental investigation into the relation between different time and environmental factors and fractal dimension. Then we move to our main point: the relation between fractal dimension and its pull-out resistance. In the next step, we make a fundamental silicon model, simulating the vetiver root system, to continue our experiments. In the end, we develop a formula that can describe the relation between its pull-out resistance, roots depth and fractal dimension. Here are our conclusions: （1） After using box-counting method to calculate fractal dimension, we discover that not only the whole vetiver root system but also a single vetiver root has the basic fractal structure. （2） Fractal dimension increases when time goes on. Also the value of fractal dimension is larger in natural sunlight and the temperature at about 30℃.The vetiver root system grows more widely in soil than those in sand. That’s why it has larger fractal dimension. （3） Data shows that its pull-out resistance is influenced by both fractal dimension and the depth of the roots. The vetiver roots, in the meantime, show greater pull-out resistance than some other plants. Thus we draw the assumption that the vetiver root system grows deep and wide, and in natural soil its fractural dimension is greater and reaches greater area. Therefore, a silicon model is constructed to further confirm the findings of the experiment.（4） The design of the silicon model is to reduce the uncontrollable variables in nature. Before starting the experiment, we measured some basic characteristics of the silicon model, including density and angle of repose. Furthermore, the experiment demonstrates that pull-out resistance and fractural dimension have a commensurate mutual relation: the stronger the pull-out resistance, the wider the fractural dimension and the deeper the root system. Thus we derive a math formula to describe this relation.