What role does mathematics play in designing fractal-like patterns in stone carvings?

Mathematics serves as the foundational framework for designing fractal-like patterns in stone carvings, enabling artists to create intricate, self-replicating designs that exhibit complexity at various scales. Fractal geometry, a branch of mathematics, provides the tools to generate these patterns through iterative processes and recursive algorithms, ensuring precision and symmetry. By applying mathematical concepts such as the Mandelbrot set or Julia sets, carvers can plan and execute detailed motifs that mimic natural forms like mountains, clouds, or leaves, enhancing the aesthetic and symbolic depth of their work. This integration of math not only streamlines the design process but also allows for scalability and reproducibility in artistic expressions, bridging the gap between abstract theory and tangible stone art.