Editorial by Jacques Mandelbrojt Benoit Mandelbrot and Fractals in Art, Science and Technology

Journal of the International Society for the Arts, Sciences and Technology

Benoit Mandelbrot, recently deceased French and the same from very close or from afar—this self- Volume 44 Number 2 2011 American mathematician, was born in Warsaw in 1924. similarity corresponds with fractal curves; an example In 1936 he and his family fled the Nazis and in France can be seen in the coast of Brittany. Fractal curves joined his uncle Szolem Mandelbrojt, professor of appear very complex; their degree of complexity is mathematics at Collège de France. After attending defined by theirfractal dimension, which is 1 for simple Ecole Polytechnique, he studied linguistics and proved curves and between 1 and 2 for more complex curves. Zipf’s law. He was an extremely original scientist who Concerning art, René Huyghe in Formes et Forces with the invention of fractals created a new concept [3] makes a distinction between art based on shapes with applications in numerous fields of science and describable by Euclidian geometry, such as are art. His unconventional approach was well accepted encountered in Classical art, and art such as Baroque when he came to IBM in 1958. He was also a professor art, based on the action of forces—for instance shapes at Yale University (1999–2005). In 1981 he published that are encountered in waves, in vortices, etc. We an article in Leonardo [1]. could assert that both Classical and Baroque art can The concept of fractals unites and gives a solid be described geometrically: the former by Euclidian mathematical framework, as Mandelbrot liked to geometry and the latter by fractal geometry. emphasize, to ideas that artists, scientists and philoso- In the sciences, ranging from physics at all scales to phers of art have sometimes intuited more or less economics, fractals give new insights and a suitable clearly. framework for understanding chaos or phenomena Let me start with this striking quotation from that have been outside the mainstream of science due Eugene Delacroix’s Journal in 1857: to their complexity. Concerning technology, Benoit Mandelbrot was the Swedenborg asserts in his theory of nature that each of first to be surprised when he saw weird and complex our organs is made up of similar parts, thus our lungs are made up of several minute lungs, our liver is made up of shapes appear on his computer screen as the result of small livers. . . . I realized this a long time ago: I often said an equation. This was to lead to the Mandelbrot set that each branch of a tree is a complete small tree, that and is the origin of fractal art, a main branch of com- fragments of rocks are similar to the big rock itself, that puter art. each particle of earth is similar to a big heap of earth. . Fractals can subconsciously suggest that each of us . . A feather is made up of millions of small feathers [2]. is a microcosm, an image of the whole world, hence This description by Delacroix corresponds to what their strong appeal. would become clearly defined with fractals. Benoit Mandelbrot, whose ideas apply to so many Perhaps most natural shapes are fractals, unlike domains, is one of the very few true scientists who is shapes corresponding to human-made objects, and known and appreciated far beyond the scientific com- so fractals can be considered a way of freely escaping munity.

the artificial constraints of Euclidian shapes. I recently Jacques Mandelbrojt heard someone suggest that fractal shapes in animals Leonardo Honorary Editor are within their bodies. I would say that animals have 16 October 2010 interior fractal shapes, whereas trees for instance have exterior fractal shapes, because the former interact with the outside world with their interior shapes—to References breathe with their lungs—whereas trees breathe with 1. B. Mandelbrot, “Scalebound or Scaling Shapes: A Useful Distinction their exterior shapes, and an interaction surface is in the Visual Arts and in the Natural Sciences,” Leonardo 14, No. 1, 43–45 larger when it is fractal. (1981). A simple plane curve appears straighter as one 2. Delacroix E. Journal, Paris, Plon 1986. approaches it. Other more complicated curves look 3. Huyghe R. Formes et Forces, Paris, Flammarion, 1971.

98 LEONARDO, Vol. 44, No. 2, p. 98, 2011 ©2011 ISAST

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