扩散重组聚集体:扩散过程中的吸引子?
Diffusion-Reorganized Aggregates: Attractors in Diffusion Processes?
摘要:
基于粒子蒸发、扩散和再沉积的过程迭代地应用于任意形状的二维物体。进化自发地改变对象形态,收敛到分支结构。与初始几何形状无关,长时间后发现的结构呈现分形几何形状,分形维数约为1.75。随着时间的推移不断演变的最终形态可以被认为是该蒸发-扩散-再沉积算子的动态吸引子。这些分形形状的集合可以被认为是扩散控制的自变换过程的{ \em动态平衡}几何。
英文摘要:
A process based on particle evaporation, diffusion and redeposition is applied iteratively to a two-dimensional object of arbitrary shape. The evolution spontaneously transforms the object morphology, converging to branched structures. Independently of initial geometry, the structures found after long time present fractal geometry with a fractal dimension around 1.75. The final morphology, which constantly evolves in time, can be considered as the dynamic attractor of this evaporation-diffusion-redeposition operator. The ensemble of these fractal shapes can be considered to be the {\em dynamical equilibrium} geometry of a diffusion controlled self-transformation process.
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