Fractals and the Mandelbrot Set

I have to confess that not only did I fail French at school I didn't do particularly well in mathematics. The latter was mainly because my father, who left school at 14, loved doing my homework and I loved him doing it for me! But I have an artistic mind, I love patterns, and I love nature. Put these elements together and you arrive at The Mandelbrot set which is a fractal and popular outside mathematics because it's aesthetically appealing.

Put simply a fractal is a never-ending pattern. Fractals are images of dynamic systems and nature is full of them in the structure of plants, trees, rivers, mountains, clouds, cyclones. Look at the incredible pattern made by sand, a photo taken by Mukesh Srivastava.
I find them most amazing in plants. The first is an aloe and have no idea what kind of leaf the second image is.
And we all love clouds which are made up of fractals.
Look at a river system. This is a Google Earth photo of the tributaries joining the Rio Grande at Elephant Butte Reservoir.
There are some more incredible examples on this link.
All of these shapes have something in common. They are all complicated and irregular which makes them difficult to tame mathematically but a joy to an artist, particularly photographers and digital creators. Look closely at a fractal, and you will find that the complexity is still present at a smaller scale. A small cloud is similar to the whole thing.

A Maths visionary Benoit Mandelbrot discovered what is called the Mandelbrot Set in 1979. He declared: Clouds are not spheres, mountains are not cones, coastlines are not circles referring to the chaos and irregularity of the world as roughness and saw it something to be celebrated saying it would be a shame if clouds really were spheres.

The Mandelbrot Set is an Abstract Fractal which can be generated by a computer calculating a simple equation over and over. And this allows us to see mathematics visualised in a most glorious and remarkable way. It's a swirling, feathery, seemingly organic landscape that is reminiscent of the natural world, but is nonetheless completely virtual. Makes me wish I'd taken more notice of my maths teachers in school! This is what a mandelbrot might look like.

The fractal mathematics Mandelbrot pioneered, together with the related field of chaos theory, lifts the veil on the hidden beauty of the world. It inspired scientists in many disciplines - including cosmology, medicine, engineering and genetics - and artists and musicians, too. As such, it reminds us that the world is complex - and delightfully unpredictable.

Fractal Art also called Mandelbrot Art, developed from the mid 1980s, is created using fractal generating software and then representing the results as still images, animations, and media. It is a genre of computer art and digital art which are part of new media art. There are different types of fractal images which we wont go into. It is rarely drawn or painted by hand.

To end up today let's take a quick look at some of the fractal artists.

Hamid Naderi Yeganeh is an Iranian mathematical artist.

William Latham a British artist , has used fractal geometry and other computer graphics techniques in his works.

American Vicky Brago-Mitchell

Helene Kippert is a Western Australian fractal artist and I will leave you with a sample of her work.

If you're interested in this type of art here are some names of artists to check out.
Scott Draves is credited with inventing flame fractals
Carlos Ginzburg has explored fractal art and developed a concept called "homo fractalus" which is based around the idea that the human is the ultimate fractal
Merrin Parkers from New Zealand specialises in fractal art.

Desmond Paul Henry was one of the first British artists to experiment with machine-generated visual effects. Tomorrow's Blog is going to be dedicated to his work because his artistic career was launched by none other than my favourite artist and hero Lawrence Lowry who painted the people of Manchester and who definitely was not an abstract artist. Don't you just love how the chaos of the art world always turns up unexpected links and patterns!

Anne Newman

Oil Painter in realistic genre style, predominantly buildings and people. To continue the discussion contact Anne on or phone +61 407 516 522

Melbourne, Victoria, Australia

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