Patterns

期刊简介：The investigation of phenomena involving complex geometry, patterns and scaling has gone through a spectacular development and applications in the past decades. For this relatively short time, geometrical and/or temporal scaling have been shown to represent the common aspects of many processes occurring in an unusually diverse range of fields including physics, mathematics, biology, chemistry, economics, engineering and technology, and human behavior. As a rule, the complex nature of a phenomenon is manifested in the underlying intricate geometry which in most of the cases can be described in terms of objects with non-integer (fractal) dimension. In other cases, the distribution of events in time or various other quantities show specific scaling behavior, thus providing a better understanding of the relevant factors determining the given processes.Using fractal geometry and scaling as a language in the related theoretical, numerical and experimental investigations, it has been possible to get a deeper insight into previously intractable problems. Among many others, a better understanding of growth phenomena, turbulence, iterative functions, colloidal aggregation, biological pattern formation, stock markets and inhomogeneous materials has emerged through the application of such concepts as scale invariance, self-affinity and multifractality.The main challenge of the journal devoted exclusively to the above kinds of phenomena lies in its interdisciplinary nature; it is our commitment to bring together the most recent developments in these fields so that a fruitful interaction of various approaches and scientific views on complex spatial and temporal behaviors in both nature and society could take place.

【译文】过去几十年里，对涉及复杂几何、模式和缩放现象的研究取得了显著的发展和应用。在这相对较短的时间内，几何和/或时间缩放已被证明是许多在不同领域发生的异常多样化的过程（包括物理学、数学、生物学、化学、经济学、工程和技术，以及人类行为）的共同特征。通常，现象的复杂性质体现在其下复杂的几何结构中，在大多数情况下，这种结构可以用非整数（分形）维度的对象来描述。在其他情况下，事件在时间或各种其他数量上的分布显示出特定的缩放行为，从而更好地理解决定这些过程的有关因素。利用分形几何和缩放作为相关理论、数值和实验研究中的语言，我们能够对以前难以解决的问题有更深入的了解。通过应用诸如尺度不变性、自相似性和多重分形等概念，许多其他现象，如生长现象、湍流、迭代函数、胶体聚集、生物图案形成、股市和非均匀材料，都得到了更好的理解。这本专注于上述现象的期刊的主要挑战在于其跨学科性质；我们致力于将这些领域的最新发展汇集在一起，以便在自然和社会中复杂空间和时间行为的不同方法和科学观点之间产生富有成效的互动。