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Maths of Planet Earth | Limitless Applications

Mathematical Concepts 13. Fractal tree rings

Published on December 12th, 2013 | by Daphane Ng

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Fractal tree rings

Mandelbrot spread the word that clouds are not spheres and mountains are not triangles; he explained they are fractal shapes, with fine detail at every possible scale and a self-similar geometry. Big bits look like smaller bits. A recent development in fractal geometry is the idea of a “fractal transformation”. Fractal transformations are typically self-similar and ‘rough’ on all scales. This is very different to regular Euclidean transformations that are well suited to describing the motion of planets but ill-suited to describing the growth of a tree or the beat of your heart.

Imagine an idealised tree stump with the circular growth rings showing the passage of the years. Now look at this photo of a real tree stump and its real growth rings. It looks just as if a fractal transformation has been applied to the idealised tree stump to produce the reality of growth over the years.

Ref: Barnsley, M & Vince, A 2013, ‘Fractal homeomorphism for bi-affine iterated function systems’, International Journal of Applied Nonlinear Science, vol. 1, no. 1, pp. 3-19.

Louisa Barnsley[subscribe2]

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