Fractals, as physical systems, are structures or patterns in nature and materials that exhibit self-similarity or scale invariance over a range of length scales, often characterized by a non-integer (fractal) dimension. They arise in diverse contexts such as aggregation processes, porous media, fracture surfaces, dendritic growth, and critical phenomena. Physical fractals are analyzed using tools like box-counting, correlation functions, and scaling laws to quantify their geometry and its impact on transport, mechanical, or dynamical properties. In experiments and simulations, fractal geometry provides a framework for understanding anomalous diffusion, percolation, roughness, and critical scaling behavior in complex physical systems.
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