Nature uses self-organized spatiotemporal patterns to construct systems with robustness and flexibility. Furthermore, understanding the principles underlying self-organization in nature enables programmable design of artificial patterns driven by chemical energy. The related mechanisms are however not clearly understood because most of these patterns are formed in reaction–diffusion (RD) systems consisting of intricate interaction between diffusion and reaction. Therefore, comprehensive understanding of the pattern formation may provide critical knowledge for developing novel strategies in both natural science and chemical engineering. Liesegang patterns (LPs) are one of the typical programmable patterns. This study demonstrates that appropriate tuning of gel concentration distribution is a key programming factor for controlling LP periodicities. The gel distribution was realized in bi- or multilayered gels constructed by stacking agarose gels of different concentrations. Thus, exceptional LP periodicities were achieved locally in bilayered gels. Furthermore, RD simulations revealed that the nucleation process modulated by the gel distribution determines the LP periodicity in bilayered gels. Finally, based on this concept, desired LP periodicities were successfully realized by programming gel distributions in multilayered gels. Thus, deep insights into the fundamental role of nucleation in designing LPs can lead to the practical applications of LPs and the understanding of self-organization in nature.

中文翻译：

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通过沉淀反应的自组织模式的可编程设计。

大自然使用自组织的时空模式来构建具有鲁棒性和灵活性的系统。此外，了解本质上自组织的原理可以实现由化学能驱动的人工图案的可编程设计。但是，有关机理尚不清楚，因为大多数这些模式是在反应扩散（RD）系统中形成的，该系统由扩散和反应之间的复杂相互作用组成。因此，对模式形成的全面理解可能为开发自然科学和化学工程领域的新策略提供关键知识。Liesegang模式（LP）是典型的可编程模式之一。这项研究表明，适当调整凝胶浓度分布是关键的程序设计控制LP周期的因素。凝胶分布在通过堆叠不同浓度的琼脂糖凝胶而构成的双或多层凝胶中实现。因此，在双层凝胶中局部获得了异常的LP周期性。此外，RD模拟表明，由凝胶分布调节的成核过程决定了双层凝胶中的LP周期性。最终，基于该概念，通过对多层凝胶中的凝胶分布进行编程，成功实现了所需的LP周期性。因此，对成核在LP设计中的基本作用的深入了解可以导致LP的实际应用和自然界中对自组织的理解。