In mathematical definition, a fractal is a self-similar subset of Euclidean space whose fractal dimension strictly exceeds its topological dimension which in turn involves a recursive generating methodology that results in contours with infinitely intricate fine structures. Fractal geometry has been used to model complex natural objects such as clouds coastlines, etc., that has space-filling properties. In the past years, several groups of scientists around the globe tried to implement the structure of fractal geometry for applications in the field of electromagnetism, which led to the development of new innovative antenna configurations called “fractal antennas” which is primarily focused in fractal antenna elements, and fractal antenna arrays. It has been demonstrated that by exploiting the recursive nature of fractals, several marvellous kinds of properties can be observed in antennas and arrays. The primary focus of this article is to provide a compressed overview of the developments in fractal-shaped antennas as well as arrays over the last few decades where the most prominent contributions mostly from IEEE journals have been highlighted. The open intention of this review work is to show an encouraging path to antenna researchers for its advancement using fractal geometries.

中文翻译：

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分形天线和阵列：回顾和最新发展

在数学定义中，分形是欧几里得空间的自相似子集，其分形维数严格超过其拓扑维数，这反过来又涉及递归生成方法，导致轮廓具有无限复杂的精细结构。分形几何已被用于模拟具有空间填充特性的复杂自然物体，例如云海岸线等。在过去的几年中，全球多组科学家试图将分形几何结构应用于电磁学领域，从而开发出新的创新天线配置，称为“分形天线”，主要专注于分形天线元素和分形天线阵列。已经证明，通过利用分形的递归性质，在天线和阵列中可以观察到几种奇妙的特性。本文的主要重点是简要概述过去几十年分形天线和阵列的发展，其中突出了主要来自 IEEE 期刊的最突出贡献。这项审查工作的公开目的是向天线研究人员展示一条令人鼓舞的道路，以促进其使用分形几何的进步。