Fractal word coined

The word fractal was coined by Mandelbrot in his fundamental book.1 It is from the Latin adjective fractus which means broken and it is used to describe objects that are too irregular to fit into a traditional geometrical setting. The most representative property of fractal is its invariant shape under self-similar or self-affine scaling. In other words, fractal is a shape made of parts similar to the whole in some way.61 If the objects are invariant under isotropic scale transformations, they are self-similar fractals. In contrast, the real objects in nature are generally invariant under anisotropic transformations. In this case, they are self-affine fractals. Self-affine fractals have a broader sense than self-similar fractals. The distinction between the self-similarity and the selfaffinity is important to characterize the real surface in terms of the surface fractal dimension. 

In the real world, however, the objects we see in nature and the traditional geometric shapes do not bear much resemblance to one another. Mandelbrot [2] was the first to model this irregularity mathematically clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line. Mandelbrot coined the word fractal for structures in space and processes in time that cannot be characterized by a single spatial or temporal scale. In fact, the fractal objects and processes in time have multiscale properties, i.e., they continue to exhibit detailed structure over a large range of scales. Consequently, the value of a property of a fractal object or process depends on the spatial or temporal characteristic scale measurement (ruler size) used. 

This movement led to the pubUcation by Mandelbrot in 1975 [1] of an essay in which he highlighted the similarities among the then-known continuous, nowhere-differentiable sets. He coined for these sets the term fractal , to emphasize the fact that their Hausdorff dimensions are often fractional. In the words of Dyson [54], fractal is a word invented by Mandelbrot to bring together under one heading a large class of objects that have [played]... an historical role... in the development of pure mathematics . 

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