Bandt Christoph, Mekhontsev Dmitry
Institute of Mathematics, University of Greifswald, 17487 Greifswald, Germany.
Sobolev Institute of Mathematics, 4 Acad. Koptyug Avenue, 630090 Novosibirsk, Russia.
Chaos. 2018 Jun;28(6):063104. doi: 10.1063/1.5023890.
By slight modification of the data of the Sierpiński gasket, keeping the open set condition fulfilled, we obtain self-similar sets with very dense parts, similar to fractals in nature and in random models. This is caused by a complicated structure of the open set and is revealed only under magnification. Thus, the family of self-similar sets with separation condition is much richer and has higher modelling potential than usually expected. An interactive computer search for such examples and new properties for their classification are discussed.
通过对谢尔宾斯基垫片的数据进行轻微修改，同时保持开集条件成立，我们得到了具有非常密集部分的自相似集，类似于自然和随机模型中的分形。这是由开集的复杂结构引起的，并且只有在放大时才会显现出来。因此，具有分离条件的自相似集族比通常预期的要丰富得多，并且具有更高的建模潜力。本文讨论了通过交互式计算机搜索此类示例及其分类的新属性。
