Fractals

 

 

Fractals are an amazing phenomenon.
You'll find them everywhere.

Both in nature and in art.

 

Or in artful nature, like this beautiful picture I captured two years ago on a winter morning 😉

 

The first time I heard about fractals, was when I wandered through a book shop some years ago. 

Although the subject sounded very interesting and I wanted to know more about it, life happened.

 

Till one freezing morning in January, two years ago. 

There were those magnificent frost flowers on the window like the one above and this one:

My interest in fractals revived.

 

But what is a fractal exactly?

Simply put, it's a complex geometric figure containing a particular motif that repeats itself over and over, on an ever smaller scale. A very simple mathematical formula is repeatedly applied (= recursion).
This principle constantly occurs in nature: trees, ice crystals, clouds, coastlines, ...
Although these things sometimes look whimsical and random, they are all shaped according to a fractal motif.
The term 'fractal' was coined by the French-American mathematician Benoît Mandelbrot (1924-2010, born in Poland).

 

Fourth grader Nicole Kershaw made a very interesting visual overview with some of the many examples of fractals in nature:

 

 

Are you interested in a more extensive presentation by Benoît Mandelbrot himself?
Then you can listen to his TED Talk:

 

Following books of him are still on my 'to be read'-list:

 

The Fractalist (Benoît Mandelbrot)

A fascinating memoir from the man who revitalized visual geometry, and whose ideas about fractals have changed how we look at both the natural world and the financial world.

Benoit Mandelbrot, the creator of fractal geometry, has significantly improved our understanding of, among other things, financial variability and erratic physical phenomena. In The Fractalist, Mandelbrot recounts the high points of his life with exuberance and an eloquent fluency, deepening our understanding of the evolution of his extraordinary mind. We begin with his early years: born in Warsaw in 1924 to a Lithuanian Jewish family, Mandelbrot moved with his family to Paris in the 1930s, where he was mentored by an eminent mathematician uncle. During World War II, as he stayed barely one step ahead of the Nazis until France was liberated, he studied geometry on his own and dreamed of using it to solve fresh, real-world problems. We observe his unusually broad education in Europe, and later at Caltech, Princeton, and MIT. We learn about his thirty-five-year affiliation with IBM's Thomas J. Watson Research Center and his association with Harvard and Yale. An outsider to mainstream scientific research, he managed to do what others had thought impossible: develop a new geometry that combines revelatory beauty with a radical way of unfolding formerly hidden laws governing utter roughness, turbulence, and chaos.

Here is a remarkable story of both the man's life and his unparalleled contributions to science, mathematics, and the arts.

 

The Fractal Geometry of Nature (Benoît Mandelbrot)

Clouds are not spheres, mountains are not cones, and lightning does not travel in a straight line. The complexity of nature's shapes differs in kind, not merely degree, from that of the shapes of ordinary geometry, the geometry of fractal shapes.

 

Now that the field has expanded greatly with many active researchers, Mandelbrot presents the definitive overview of the origins of his ideas and their new applications. The Fractal Geometry of Nature is based on his highly acclaimed earlier work, but has much broader and deeper coverage and more extensive illustrations.

 

 

When I saw the following book on NetGalley, I couldn't resist to download it:

 

 
This is a book for art lovers, designers, and art-loving techies everywhere. A coffee-table art book filled with lush art plates that speak to the senses, the fractal images within reflect the beauty and mystery of the natural world, and demonstrate the power of computer-aided design in creating original works of art.

 

My review of this book can be read here.

 

 

Do you know other interesting books, websites, movies, ... about fractals?
Don't hesitate to let me know in the comments 😉