In extant vertebrates, natural motifs such as coat markings, spongy bone structures, neuronal arborescence or collective swarms correspond to diverse pattern types, from fractals to periodic stripes or tessellations, and so on. In this subphylum, evolution produced an apparent paradox: a given pattern may vary tremendously in its extent, periodicity or regularity, but follows general geometrical trends and is produced with meticulous precision. In this review, we discuss the role of self-organization, a patterning strategy in which spontaneous order arises through local interactions without gradient formation, in shaping both natural pattern differences and common themes. Mathematical models evidenced a wide high adaptability of self-organizing dynamics, long-advocating for their contribution to natural pattern diversity. Recent empirical and theoretical approaches taking into account network topologies and natural variation also replaced outcomes of self-organization in more constrained biological contexts, shedding light on mechanisms ensuring pattern fidelity.

中文翻译：

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作为自组织结果的脊椎动物模式的趋势和变化。

在现存的脊椎动物中，诸如外套标记、海绵状骨骼结构、神经元树状结构或集体群等自然图案对应于不同的图案类型，从分形到周期性条纹或镶嵌，等等。在这个亚门中，进化产生了一个明显的悖论：一个给定的模式可能在其范围、周期性或规律性上发生巨大变化，但遵循一般的几何趋势并以一丝不苟的精度产生。在这篇综述中，我们讨论了自组织的作用，这是一种模式化策略，在这种模式化策略中，自发秩序通过局部相互作用而没有梯度形成，在塑造自然模式差异和共同主题方面。数学模型证明了自组织动力学具有广泛的高适应性，长期倡导它们对自然模式多样性的贡献。