What is the Philosophical presupposition(s) of Fractal Geometry?

Fractal geometry, as a mathematical and philosophical concept, challenges traditional understandings of shape, space, and structure. It is not merely a branch of mathematics but also a profound philosophical shift in how we conceptualize the natural world, the infinite, and patterns that emerge from chaos. The philosophical presuppositions of fractal geometry are deeply rooted in ideas about self-similarity, scale invariance, complexity, and the nature of reality itself. These presuppositions invite a reevaluation of established ontologies and epistemologies, making it a fertile ground for philosophical reflection.

The first key philosophical presupposition of fractal geometry is the rejection of the classical Euclidean notion of geometry. Euclidean geometry, which emerged from the works of ancient Greek philosophers like Euclid, is based on the assumption that space is smooth, continuous, and can be divided into simple geometric _____ ______ _____ ________ ________ ____ ___ ___ ___ ______ ____.
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