Operationalization of Fractal Forms and Generative Processes in Management: The Mathematical Dimension of Fractal and Generative Forms
Purpose: In creating the Categories of Ontology, Aristotle conceptualized one of them, a very important one, in a philosophical sense. It constitutes his understanding and perception of the space around us. He called this category extension. The second understanding of the space around us comes from Descartes and is a mathematical approach, measurable by the Euclidean metric. The main goal of this article is to analyze non-differentiable objects and processes. It analyzes structures that do not have a continuous ontology. This will be presented mathematically – operationally – using representative examples related to our reality. Design/Methodology/Approach: The two philosophies mentioned above influence the way objects are understood and studied within the framework of the resulting methodologies. One methodological category encompasses formal models and methods, the other, content-based ones. It is precisely their application to the study of real and mental processes that is discussed in this article. After all, the central concern with these two categories of our Ontology concerns their formal approach. Practical implications: One could say this: Science possesses proven methods for studying everything. And these are called classical methods. But recently, newer methods have emerged within science. And they bring to our understanding a new perspective on certain processes in our environment. And this has practical implications. Analysis of the relationship between old and new. The achievements of new methods offer the possibility of their different practical applications. They also indicate where they can be applied and what they can achieve for management practice. Originality/value: The originality of the article's content lies in the authors' operational demonstration of examples of the relationship between the characteristics of fractal and generative processes. This also applies to human-created scientific objects. This constitutes an additional contribution in the form of methods for analyzing the dilemmas of contemporary management and our environment. Generativity has been known in science for years. Fractality has been recognized somewhat more recently. However, this article combines these two categories and demonstrates, in addition to their distinctiveness, the characteristics of their possible interrelationships. These two distinct varieties do not compete for primacy, but only for the primacy of a better understanding of our surroundings.