摘 要：分形几何作为一种描述自然界复杂形态的数学工具，近年来在自然景观模拟领域展现出重要价值。本研究旨在探讨分形几何理论在生成逼真自然景观中的应用潜力，并提出一种基于分形算法的高效模拟方法。通过引入改进的分形布朗运动模型与多重分形分析技术，该方法能够精确刻画地形、云层及水流等自然元素的自相似特性及其空间异质性。实验结果表明，所提方法不仅显著提升了景观模拟的真实感，还有效降低了计算复杂度，为大规模场景生成提供了可行方案。此外，本研究首次将局部分形维度的概念应用于景观细节优化，从而实现了对自然纹理细微特征的精准还原。这一创新为虚拟现实、计算机图形学以及地理信息系统等领域提供了新的技术思路，同时也拓展了分形几何的实际应用范围。研究表明，分形几何在自然景观建模中具有不可替代的优势，未来可进一步结合机器学习算法以增强其适应性和灵活性。
关键词：分形几何；自然景观模拟；分形布朗运动；局部分形维度；多重分形分析
Application of Fractal Geometry in Natural Landscape Simulation
英文人名
Directive teacher:×××
Abstract：Fractal geometry, as a mathematical tool for describing complex forms in nature, has demonstrated significant value in the field of natural landscape simulation in recent years. This study aims to explore the application potential of fractal geometry theory in generating realistic natural landscapes and proposes an efficient simulation method based on fractal algorithms. By incorporating an improved fractal Brownian motion model and multifractal analysis techniques, this method can accurately characterize the self-similarity properties and spatial heterogeneity of natural elements such as terrain, clouds, and water flow. Experimental results indicate that the proposed method not only substantially enhances the realism of landscape simulation but also effectively reduces computational complexity, providing a feasible solution for large-scale scene generation. Additionally, this study is the first to apply the concept of local fractal dimension to landscape detail optimization, thereby achieving precise reproduction of subtle natural texture features. This innovation offers new technical insights for fields such as virtual reality, computer graphics, and geographic information systems, while also expanding the practical application scope of fractal geometry. The study concludes that fractal geometry possesses irreplaceable advantages in natural landscape modeling, and its adaptability and flexibility could be further enhanced in the future by integrating machine learning algorithms.
Keywords: Fractal Geometry；Natural Landscape Simulation；Fractal Brownian Motion；Local Fractal Dimension；Multifractal Analysis
目 录
引言 1
一、分形几何的基本原理与应用背景 1
(一)分形几何的核心概念 1
(二)自然景观的分形特性分析 2
(三)分形几何在模拟中的优势 2
二、山地地形的分形模拟方法 3
(一)山地地形的分形特征提取 3
(二)基于分形算法的地形生成 3
(三)模拟精度与视觉效果优化 4
三、水体景观的分形建模技术 4
(一)水体表面的分形结构研究 4
(二)分形算法在水体模拟中的应用 5
(三)动态水体效果的实现方法 5
四、植被与生态系统的分形表现 5
(一)植物形态的分形规律探索 5
(二)基于分形的植被分布模拟 6
(三)生态系统整体建模策略 6
结论 7
参考文献 8
致谢 8
