Mathematics in Nature and in Art

posted in: Art. Nature. Technology | 1

From paintings and monuments inspired by mathematics of nature, to complicated and beautiful shapes created from simple math equations

The tight connection between Art and Mathematics is fascinating ; they have had a long historical relationship dating back to 2,560 BC. From artists and architects inspired by mathematics in creating their paintings and monuments, to mathematicians developing mathematical models which result in amazing complex patterns and designs.

“The universe is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures. Artists who strive and seek to study nature must therefore first fully understand mathematics. On the other hand, mathematicians have sought to interpret and analyze art through the lens of geometry and rationality. ” – Galileo Galilei

 

Going back in history, evidence of mathematics influence has been seen as far back as 2,560 BC; in monuments such as the Great Pyramids and the Coliseum. Also, painters and philosophers observed geometric shapes and patterns in nature and made use of mathematics in their work; incorporation of realistic shadows, angle of lights, reflections, and perspectives. Piero della Francesca (c.1415-1492), an early Renaissance artist, was also a mathematician and authored many books on perspective and geometry. Graphic artist M.C. Escher (1898—1972) was known for his mathematically inspired work; he used polygons or shapes such as squares, and triangles to create his art.

In conjunction with the artists’ use of mathematics in art, mathematicians have developed mathematical functions that can result in fascinating and complex patterns and shapes.

One example is Fractal art. Fractals represent objects with self-similarity; each shape is made of smaller copies of itself. Fractals are seen in nature in many instances such as trees, roots of trees, the human heart, lungs, kidney, vegetables, mountains, sand dunes, granite patterns, and many more. Have you ever looked down from the window on a plane and noticed the pattern of rivers? This is an example of fractals in nature; small rivers combine to form the larger river. Cauliflower is another interesting example of Fractals seen in nature.  If you look at the shape of a cauliflower, then cut it into pieces, each small piece looks like the larger piece but it’s smaller.

 

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Photo by Azi Sharif

 

 

Fractals in the world of mathematics are beautiful complex images that can be produced by iterating simple equations. One of the most well known examples of Fractals is the Mandelbrot set invented by Benoit Mandelbrot. It shows how iteration of a simple equation can result in amazing shapes with such complications, harmony and beauty.

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                                               Mandelbrot set applet 

And more fascinating images created by Math!

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Wolfram Demonstration Projects, Flower Fractals

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Wolfram Demonstration Projects, Generating Patterns Similar to Peruvian Textiles