This paper combines the synergies of three mathematical and computational generalizations. The concepts of fractional calculus, memristor and information visualization extend the classical ideas of integro-differential calculus, electrical elements and data representation, respectively. The study embeds these notions in a common framework, with the objective of organizing and describing the "continuum" of fractional order elements (FOE). Each FOE is characterized by its behavior, either in the time or in the frequency domains, and the differences between the FOE are captured by a variety of distinct indices, such as the Arccosine, Canberra, Jaccard and Sørensen distances. The dissimilarity information is processed by the multidimensional scaling (MDS) computational algorithm to unravel possible clusters and to allow a direct pattern visualization. The MDS yields 3-dimensional loci organized according to the FOE characteristics both for linear and nonlinear elements. The new representation generalizes the standard Cartesian 2-dimensional periodic table of elements.

本文结合了三种数学和计算概括的协同作用。分数微积分，忆阻器和信息可视化的概念分别扩展了积分微分微积分，电子元素和数据表示的经典思想。这项研究将这些概念嵌入一个通用框架中，目的是组织和描述分数阶元素（FOE）的“连续体”。每个FOE都在时域或频域中以其行为为特征，并且通过各种不同的指标（例如Arccosine，堪培拉，Jaccard和Sørensen距离）可以捕获FOE之间的差异。差异信息由多维缩放（MDS）计算算法处理，以解散可能的聚类并允许直接模式可视化。MDS会根据线性和非线性元素的FOE特性生成3维基因座。新的表示法概括了标准的笛卡尔二维元素周期表。