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Over the last 40 years, applied mathematicians and physicists have proposed a number of mathematical models that produce structures exhibiting a fractal dimension. This work has coincided with the discovery that objects with fractal dimension are relatively common in the natural and human-produced worlds. One particularly successful model of fractal growth is the diffusion limited aggregation (DLA) model, a model as notable for its simplicity as for its complex and varied behavior. It has been modified and used to simulate fractal growth processes in numerous experimental and empirical contexts. In this work, we present an alternative fractal growth model that is based on a growing mass that bonds to particles in a surrounding medium and then exerts a force on them in an iterative process of growth and contraction. The resulting structure is a spreading triangular network rather than an aggregate of spheres, and the model is conceptually straightforward. To the best of our knowledge, this model is unique and differs in its dynamics and behavior from the DLA model and related particle aggregation models. We explore the behavior of the model, demonstrate the range of model output, and show that model output can have a variable fractal dimension between 1.5 and 1.83 that depends on model parameters. We also apply the model to simulating the development of polymer thin films prepared using spin-coating which also exhibit variable fractal dimensions. We demonstrate how the model can be adjusted to different dewetting conditions as well as how it can be used to simulate the modification of the polymer morphology under solvent annealing.

近四十年来，应用数学家与物理学家已提出诸多可生成具有分形维度（fractal dimension）结构的数学模型。此类研究与一项发现同期开展：具备分形维度的物体在自然及人工生成的世界中实则颇为常见。其中一款尤为成功的分形生长模型为扩散限制聚集（diffusion limited aggregation, DLA）模型，该模型以简洁性与复杂多样的行为表现同样闻名。该模型已被改进并应用于诸多实验与实证场景中的分形生长过程模拟。在本研究中，我们提出一款新型分形生长模型：其核心基于不断生长的团块，该团块会与周围介质中的粒子结合，并在生长与收缩的迭代过程中对粒子施加作用力。最终生成的结构为扩散型三角网络，而非球体聚集体，且该模型在概念上简洁明了。据我们所知，该模型具有独创性，其动力学特性与行为模式均与DLA模型及相关粒子聚集模型存在差异。我们对该模型的行为特性展开探究，展示了其输出结果的变化范围，并证实模型输出可呈现1.5至1.83之间的可变分形维度，该维度取值取决于模型参数。此外，我们将该模型应用于旋涂法制备的聚合物薄膜生长过程模拟——此类薄膜同样具备可变分形维度。我们还展示了如何针对不同脱湿条件调整该模型，以及如何利用该模型模拟溶剂退火条件下聚合物形貌的演变过程。