论文标题
扩散限制在线生长的聚集体的尺寸
The dimension of Diffusion Limited Aggregates grown on a line
论文作者
论文摘要
扩散限制聚集（DLA）已有40年，作为创造分形生长模式的范式示例。尽管有成千上万的参考文献，但对于DLA的分形尺寸$ d $却没有确切的结果。在这封信中，我们宣布在一条线上生长的近距离DLA的确切结果，$ d = 3/2 $。结果依赖于用迭代的保形图表示DLA，从而使一个人证明是自我的，适当的缩放限制和明确定义的分形维度。主要结果的数学证明可在Arxiv：2008.05792中获得。
Diffusion Limited Aggregation (DLA) has served for forty years as a paradigmatic example for the creation of fractal growth patterns. In spite of thousands of references no exact result for the fractal dimension $D$ of DLA is known. In this Letter we announce an exact result for off-lattice DLA grown on a line, $D=3/2$. The result relies on representing DLA with iterated conformal maps, allowing one to prove self-affinity, a proper scaling limit and a well defined fractal dimension. Mathematical proofs of the main results are available in arXiv:2008.05792.
