论文标题
分形维度和拓扑不变性作为量化Yayoi Kusama绘画中复杂性的方法
Fractal dimension and topological invariants as methods to quantify complexity in Yayoi Kusama's paintings
论文作者
论文摘要
抽象艺术中复杂的模式多次可以被错误地描述为复杂。复杂性可以是整个系统内部动力学的指标，而不论所讨论的系统类型，包括艺术创作。在这项研究中，我们使用两种不同的技术在抽象图像中客观地量化复杂性：分形维数和贝蒂数的值。我们首先通过考虑与点随机分布的合成图像来验证我们的技术，然后将其应用于Yayoi Kusama的一系列“净痴迷”画。令人惊讶的是，我们发现，尽管她在本系列中的作品的分形维度与杰克逊·波洛克（Jackson Pollock）的滴水期相当，这可能表明较高的复杂性，但贝蒂（Betti）数字的价值确实显示出脱节性，而不是很高的复杂性。这与此类作品的视觉评估一致。
Intricate patterns in abstract art many times can be wrongly characterized as being complex. Complexity can be an indicator of the internal dynamic of the whole system, regardless of the type of system in question, including art creation. In this investigation, we use two different techniques to objectively quantify complexity in abstract images: the fractal dimension and the value of the Betti numbers. We first validate our technique by considering synthetic images with a random distribution of dots, to then apply it to a series of `Net obsession' paintings by Yayoi Kusama. Surprisingly, we found that although the fractal dimension of her works in this series is comparable to those by Jackson Pollock in his dripping period, which could indicate a high level of complexity, the value of the Betti numbers do show disconnectedness and not high complexity. This is intuitively in agreement with the visual assessment of such works.
