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Fractional Brownian Functions as Mathematical Models of Natural Rhythm in Architecture

机译：分数布朗函数作为建筑中自然节奏的数学模型

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摘要

Carl Bovill suggested and described a method of generating rhythm in architecture with the help of fractional Brownian functions, as they are mathematical models of natural rhythm. A relationship established in the stated procedure between fractional Brownian functions as models of rhythm, and the observed group of architectural elements, is recognized as an analogical relationship, and the procedure of generating rhythm as a process of analogical transfer from the natural domain to the architectural domain. Since analogical transfer implies relational similarity of two domains, and the establishment of one-to-one correspondence, this paper is trying to determine under which conditions such correspondence could be established. For example, if the values of the observed visual feature of architectural elements are not similar to each other in a way in which they can form a monotonically increasing, or a monotonically decreasing bounded sequence, then the structural alignment and the one-to-one correspondence with a single fractional Brownian function cannot be established, hence, this function is deemed inappropriate as a model for the architectural rhythm. In this case we propose overlapping of two or more functions, so that each of them is an analog for one subset of mutually similar values of the visual feature of architectural elements.
机译：卡尔·鲍威尔（Carl Bovill）提出并描述了一种借助分数布朗函数在建筑中产生节奏的方法，因为它们是自然节奏的数学模型。在规定的过程中，作为节奏模型的分数布朗函数与观察到的建筑元素组之间建立的关系被认为是类比关系，而产生节奏的过程则是从自然域到建筑的类比转移过程域。由于类比转移意味着两个域之间的关系相似性以及一对一对应关系的建立，因此本文试图确定可以在何种条件下建立此类对应关系。例如，如果观察到的建筑元素视觉特征的值彼此不相似，以致它们可以形成单调递增或单调递减的有界序列，则结构比对和一对一与单个分数布朗函数的对应关系无法建立，因此，该函数不适合作为建筑节奏模型。在这种情况下，我们建议两个或多个功能重叠，以使每个功能都类似于建筑元素视觉特征相互相似值的一个子集。

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