论文标题
在三维图灵样模式中对子结构的实验视觉引导研究
Experimental visually-guided investigation of sub-structures in three-dimensional Turing-like patterns
论文作者
论文摘要
在1952年的论文“形态发生的化学基础”中，艾伦·图林（Alan M. Turing）提出了一个用于形成皮肤模式的模型。虽然花了几十年的时间，但通过找到相应的自然现象（例如在斑马鱼的皮肤图案中。更令人惊讶的是，看似无关的模式形成也可以通过模型进行研究，例如白蚁山周围的植物斑块形成。 1984年，戴维·A·杨（David A.从这个模型中，得出了三维图灵样模式的概念。 在本文中，我们认为在三维空间中对模式形成的概括。我们对模式的不同子结构进行分类特别感兴趣。通过提供不同结构的示例，我们证明了关于这些结构在三维图灵样模式中的猜想。此外，我们在视觉实验的指导下进行了调查 - 这些子结构如何分布在离散模型的参数空间中。我们发现了零和一维的子结构以及二维子结构的两个版本，并使用我们的实验发现来为三维图灵样模式和较高维度的情况制定了几种猜想。
In his 1952 paper "The chemical basis of morphogenesis", Alan M. Turing presented a model for the formation of skin patterns. While it took several decades, the model has been validated by finding corresponding natural phenomena, e.g. in the skin pattern formation of zebrafish. More surprising, seemingly unrelated pattern formations can also be studied via the model, like e.g. the formation of plant patches around termite hills. In 1984, David A. Young proposed a discretization of Turing's model, reducing it to an activator/inhibitor process on a discrete domain. From this model, the concept of three-dimensional Turing-like patterns was derived. In this paper, we consider this generalization to pattern-formation in three-dimensional space. We are particularly interested in classifying the different arising sub-structures of the patterns. By providing examples for the different structures, we prove a conjecture regarding these structures within the setup of three-dimensional Turing-like pattern. Furthermore, we investigate - guided by visual experiments - how these sub-structures are distributed in the parameter space of the discrete model. We found two-fold versions of zero- and one-dimensional sub-structures as well as two-dimensional sub-structures and use our experimental findings to formulate several conjectures for three-dimensional Turing-like patterns and higher-dimensional cases.
