Fractal Inspired Art and Culture

In a 1904 letter to Emile Bernard, Paul Cézanne wrote, “everything in nature is modeled according to the sphere, the cone, and the cylinder. You have to learn to paint with reference to these simple shapes; then you can do anything.”

In contrast, in the Fractal Geometry of Nature Benoit Mandelbrot takes a different point of view: “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.”

To the extent that the arts are informed by nature, we should not be surprised to find fractal aspects in the visual arts. The extent of this presence, much of it largely unconscious, may be a surprise. Fractals may have become a cliché in modern computer graphics, but they have a long and rich history in art

Although not being defined or labelled until 1976 fractals have been observed  throughout history, manifesting themselves visually throughout different cultures through artefacts and artworks resonating strongly throughout many if not all major world cultures and religions as shown here.

 

This an image from the Medieval Celtic Book of Kells (597 A.D)

    

These are black and white Persian Rug examples

The above image is a birds-eye architectural plan of an ethiopian village. fractals

are evident throughout African art and culture, however this was my favourite.

The image on the left is a traditional Islamic artwork, whereas the image on

the left is a computer generated rendering of the Mandelbrot set.

The similarities are obvious and evident.

The above depicts and ancient Egyptian symbolism, again a fractal.

 

This symbol is a well known Jewish icon.

For me, most interestingly of the religious symbols is this one from

Hinduism

 The Italian renaissance and dutch matters even took influence from unknowingly observing fractals in nature. by using a method of iteration with the desired material the artist were able to create increasingly realistic natural forms.  For example The Dutch painter Jan Van Goyen (1596-1656) was capable of creating realism a picture with “small efforts” from stains of colors. Compare Van Goyen’s painted clouds with the typical fractal computer-generated “cloud”

Left is a section of a painting of Goyen’ Two men on a Footbridge

over a stream. To the right is a cloud generated by an iteration computer

system.

The next number of  posts will be regarding artists that have not only worked around the concepts of fractals but also artists that have influenced me within my own work.

 

 

 

 

 

Fractals: The Blueprints for Chaos

“Fractals are not just artificial constructs, they shape us and the world we live in.” (Gleick – 1987).

Fractals for me, explain all natural phenomenon. While fractal geometry was conceived at the beginning of the 20th century, it was not until the advancement of the super computer that we have been able to see the complete implication and brilliance of fractals. I don’t claim to be an authority or expert on the subject, but I’ll try and explain here what little I know.

The notion behind fractals is moderately humble and apparent when described simply. But the arithmetic used to cultivate those concepts is not as easy. A fractal is a geometric figure with two distinct properties. Primarily, it is Irregular, fractured or fragmented. Moreover, it is Self-similar; that is, the figure appears similar no matter how great the scale of magnification. These objects display self-similar structure over an extended, but finite, scale range.

Alex Grey

Benoit Mandelbrot, now known as the ‘father or fractals’, devised the term fractal to define such figures, stemming from the Latin word “fractus” meaning broken, fragmented, or irregular. He also outlined astonishing parallels in appearance concerning some fractal sets and numerous natural geometric patterns. Consequently, the term “natural fractal” refers to natural phenomena that are similar to fractal sets, such as the path followed by a dust particle as it bounces about in the air.

“Fractal Geometry plays two roles. It is the geometry of deterministic chaos and it can also describe the geometry of mountains, clouds and galaxies.” – (Benoit Mandelbrot – 1984)

The majority of objects in nature do not adhere to simple traditional geometric forms. Clouds, trees, and mountains typically do not resemble circles, triangles, or squares.  Within the natural world there are no straight lines or smooth edges. A sunflowers pattern for growth, the faultless symmetry of a microbe, the striped coat of a zebra, the barreling of ocean waves, or the harmonized turns and swoops of a flock of starlings twirling amongst trees prior to landing on a telephone wire. How can all those individuals part of the flock evade collisions or confrontations with their neighbors? How do they orchestrate these elegant, precise and instantaneous movements in such a sizeable group?These are a small number of thousands of additional examples are the kaleidoscope of patterns and forms that nature gifts us over a lifecycle.

         

             

Take a tree, for example. Preference a specific branch and examine it thoroughly. Then select a collection of leaves on that branch. In Chaology (the study of chaos) all three of the matters described – the tree, the branch, and the leaves – are identical. For many, the term chaos insinuates randomness, unpredictability and possibly even untidiness. Chaos is actually extremely structured and adheres to certain patterns and algorithms. The complications occur in finding these elusive and sophisticated patterns. One purpose of examining chaos through fractals is to grasp the patterns in the dynamical organization found in nature that superficially appear unpredictable and incomprehensible.  To many Chaologists, the examination of chaos and fractals is beyond just an innovative and fresh field of science that fuses mathematics, theoretical physics, art, and computer science – it is a revolution. It is the breakthrough of a new geometry, one that helps us in defining and understanding the infinite universe we live in; one that is in constant motion, not as static depictions in textbooks. Today, fractal geometry has increasing implementations and applications, from predicting stock market prices to making new discoveries in theoretical physics.

Timm Dapper

Mathematicians have attempted to describe fractal shapes for over one hundred years, but with the processing power and imaging abilities of modern computers, fractals have enjoyed a new popularity because they can be digitally rendered and explored in all of their fascinating beauty. However beautiful these renderings are, for me they don’t compare to fractals that form in nature. Are visual intakes are saturated with the computer generated images representing fractals, so much so that for many they define fractal geometry. I feel that a reason for creating my video may be an attempt to disperse the brilliance of fractal geometry.

                                                                                   

Computer generated Fractals

For a clear introduction to fractals (including an interesting fractal-generating application for Macintosh), go to:

astronomy.swin.edu.au/pbourke/fractals/ fracintro.