![]() ![]() When treating the topic of branches, he states that there are branching patterns with similar qualities occurring in both organic and physical systems, thus implying a universality in the geometry. In The self-made tapestry (Ball, 2001), the author analyses natural occurring fractals. The Mind Unleashed (2014) 30 Beautiful Photographs of Fractals in Nature, accessed Natural occurring fractals can be found in the branching of a tree, the veins of a leaf, mountain ridges, rivers, vegetables and in the bronchial structure of lungs, to name a few. Self similar structures require only one rule, which applies in all scales, and by being information efficient fractal structures are created. In order to minimise the energy and material spent on this information, nature has conceived an impressive ratio between amount of information put into the system and the complexity of the outcome. In nature, energy efficiency is crucial, and high performing structures are created with simple material and the information itself being the key to success. “Fractals are objects with roughness at all scales or, for natural fractals, over at least several orders of magnitude of scales.” (West, Deering, 1994, p.9) Mathematical fractal structures on the other hand, reaches no such limit. Naturally there are physical limitations such as molecule size and finally atom size. Although, when discussing natural occurring fractals, the concept of infinite iterations becomes less useful. The fragmentation tends to recur identically at all scales. Self similarity is another important concept within the field of fractals. The Minkowski curve (fractal dimension: 1.5) fills the plane to a higher degree compared to the Koch curve (fractal dimension 1.26), thus having a larger fractal dimension. The Peano curve has a fractal dimension of 2, implying the curve completely fills a two-dimensional plane when iterated to infinity. The above mentioned curves, Koch, Minkowski and Peano, have different fractal dimensions ranging between 1 and 2. “Fractal dimension (…) is a measure of the extent to which a structure exceeds its base dimension to fill the next dimension” (Bovill, 1996 p.14). Bovill (1996) offers the following definition: When discussing fractals there are a few aspects to consider, one of them is the fractal dimension. Peano curve Bovill, Carl (1996) Fractal geometry in architecture and design.
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