FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY

在过去的几十年里，涉及复杂几何、模式和尺度的现象研究经历了惊人的发展。在这相对较短的时间内，几何和/或时间尺度已经被证明代表了在物理、数学、生物学、化学、经济学、技术和人类行为等不同寻常的领域中发生的许多过程的共同方面。通常，一个现象的复杂性表现在其底层复杂的几何结构中，在大多数情况下可以用具有非整数(分形)维数的对象来描述。在其他情况下，事件在时间上的分布或各种其他数量的分布显示特定的缩放行为，从而更好地理解决定给定流程的相关因素。在相关的理论、数值和实验研究中，将分形几何和尺度作为一种语言，使我们能够更深入地了解以前难以解决的问题。其中，通过应用尺度不变性、自亲和性和多分形性等概念，对增长现象、湍流、迭代函数、胶体聚集、生物模式形成、股票市场和非均匀材料有了更好的理解。专门研究上述现象的期刊的主要挑战在于其跨学科的性质;我们致力于汇集这些领域的最新发展，以便就自然界和社会中复杂的时空行为采取各种方法和科学观点进行富有成效的相互作用。

The investigation of phenomena involving complex geometry, patterns and scaling has gone through a spectacular development 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, 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.