*Fractal*

comes from the Latin word *fractus*

(translated as ‘fractured’) and it refers to any irregular,

‘fractured’ looking shape. The term was coined by Benoit Mandelbrot,

the IBM mathematician who first produced computer-generated images of

fractals and mathematically interpreted nature in his book *The
Fractal Geometry of Nature*. The

most famous computer-generated fractal shape is the

*Mandelbrot*

set,related to the

set,

*Julia*

set, and its infinite detail and

set

depth can be described by a very simple equation. A value is fed into

the equation and the result is then fed back into the equation – it

is this recursive nature of the equation which leads to the infinite

nature of the fractal image.

Mandelbrot set

It is

interesting that fractals have existed in nature, yet no-one paid any

real, scientific attention to them until the 1980s. This goes to show

that scientific and mathematical breakthroughs heavily depend on

circumstance. Fractals in nature could only really be understood,

mathematically, once computers were powerful enough to generate

fractal images. This is not to say though that an essential feature

of fractals, *self-similarity*,

had not been understood in the past. Self-similarity is when the

parts of a shape resemble the whole shape or are a copy of the whole shape. The Cantor Set

and the Koch snowflake are prime examples of this.

Koch snowflake, full of repeating triangles

In

fact, some artists have even used self-similarity in their art; for

example, the Japanese artist Hokusai used the repeating pattern of

waves in his well-known painting *The Great Wave Off
Kanagawa*.

A lot of religious

art, particularly art from Eastern religions, make use of

self-similarity and bear some similarities to fractals. Tibetan

*thangka* paintings

would be a good example of this.

Fractal geometry seems to act as a blueprint for many living things. In

nature, fractals are everywhere. The centre of sunflowers, pine

cones, ferns, the shape of lightning and river meanderings, the branching of

trees, veins and blood vessels, lungs, and the countless other forms of other countless plants and animals. It has been said that

nature has exploited fractal geometry because it is the most

efficient way for something to grow or because it is the easiest way

to increase surface area (making it easier for the lungs to absorb

oxygen, for example).

The lungs of a dog

My favourite example of a fractal in nature is the one that most

resembles a computer-generated fractal, called the Romanesco

cauliflower. It is easy to see the repeating pattern of cones. As a

whole, the cauliflower is a large cone, but at any point is another

cone, which contains cones within cones etc. It’s dizzying. But if you want to appreciate how infinite complexity

can arise from simple rules, watch videos of ‘fractal zooming’ on YouTube.

Romanesco cauliflower

The

study of fractals in the 80s and the later computer-generated images

of the Mandelbrot set spawned a whole new type of art called fractal

art.

Fractal art

It’s interesting that a kind of mathematics, belonging to a kind

of science (the science of chaos) would lead to a new aesthetic

appreciation of fractals, shapes which have always existed in nature.

Perhaps the psychedelic art of the 60s though did pre-empt this in

some way, since tie-dye and kaleidoscopic art is very similar to

fractal art. It is also supposed to be very common to see images of

fractals under the influence of LSD, *psilocybin*,

mescaline and DMT.

DMT-inspired art

This seems pretty strange. How could a drug make you see an image

of a fractal? Does the drug make your visual system recursive, so

that shapes and colours are fed into themselves, eventually

producing a fractal image? If that’s what happens, how and why does the drug do this?

High doses of these drugs can make users feel connected with nature, so maybe seeing fractals is part of the visual aspect of that experience, since fractals do have their basis in nature itself.

Fractal

geometry now has a wide-range of applications. They are being applied to

computer chips so that they can store more information and in computer-generated landscapes for films such as *Star Wars *and

*Star Trek*.* *It was

only because of fractal geometry that computers were able to generate

images of mountains and forests which had that realistic, fractured,

irregular shape. There are many other useful applications in video

game design, engineering, medicine and other areas of technology.

Fractal geometry is a very recent kind of geometry so its

implications for the future are not clear.

Computer-generated fractal landscape

It may

even be relevant to physics and our view of reality. Arthur C.

Clarke (author of *2001: A Space Odyssey*), in a discussion with Carl Sagan and Stephen Hawking (which is on YouTube) asked Stephen Hawking if the fundamental nature of

reality could be fractal. In other words, if we keep zooming deeper and deeper

into matter, will we reach some smallest, fundamental particle or string

(if string theory becomes verified in the future) or will the zooming go on forever?. Hawking dismissed

the idea by saying that the deepest level of matter is the Planck length

– nothing can be smaller than this length.

But maybe as particle colliders become

more sophisticated, it will become apparent that material objects are

like fractals, in that they are finite in extent, but they are infinite in

depth. In other words, the object takes up a limited amount of space,

but the depth of the object is never-ending. You could zoom into it

forever. Even if this does not turn out to be true, it’s still a

fascinating fact that fractals are both finite and infinite in this

way.

the recursive nature of the equation hints at the infinite nature of the fractal, but the inverse stumps me. how can there actually be entropy in the universe given that the perceived chaos is susceptible to recursive deconstruction? i am obviously not a scientist so please don't mock me for wondering.