Understanding fractals

fractals in nature


Doñana National Park, Andalusia, Spain



Our daily encounters with nature spark endless hours of inspiration and fascination as nature provides infinite puzzles still to be solved. This curiosity is something we try – one way or the other - to incorporate into our designs. One of the true breathtaking subjects of nature is fractals. Unique patterns and structures that are ever present in the nature surrounding us, without giving us a full explanation of their meaning.

Aloe vera plant


Aloe vera plant



We decided to dedicate a little time and space to get you up to date on one of the most amazing mathematics lessons of nature. The term fractal (from the Latin fractus, meaning “broken”) was coined by the mathematician Benoit Mandelbrot in 1975. In his seminal work “The Fractal Geometry of Nature,” he defines a fractal as “a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole.”

Dried mud


Dried mud



In nature, one would assume that we rarely see the same order, which can be found in symmetrical patterns. On a raw winter morning in the forest or a windy day on the beaches of Denmark, it seems as if the only thing characterizing nature is the general unpredictability to shaping.

Frost fractals


Frost fractals



We human beings are designed in a way, where we will always browse for logic and hidden patterns, in order to understand things. In the case of nature, the logics behind shape and form is not visible until we describe them mathematically, but from pure human instinct, we are certain that there is a pattern.

Fractal Plant
Succulent plant



As we dig deeper into the subject of fractals, we understand, that there is no random even in nature. But defining the shapes of nature can certainly be a difficult task. It brings focus to the process, which creates the shape, instead of on the shape itself. Much like the development phase of a textile or print design, where the multiple repetitions, in the end, build the whole picture.

Dragon tree


Dragon tree



One could describe the shape of a tree, as a branch, that continues to recede. The key to the fractal geometry can be found in the algorithmic understanding of the shape it produces. What the trees algorithm is telling the tree is: Continue to create the same structure over and over again, in a smaller and smaller scale. With this kind of repetition, the different parts of a tree all look the same in structure. Break the tip of a branch and what looks like a miniature tree will reveal itself.

Monkey tree flower


Monkey tree flower



This structure, which repeats itself over and over in smaller scales, is called "self-similar". Fractals are always self-similar, with a hierarchical order, which means that the pattern is created over an amount of differences size scales. The log itself represents level one of the hierarchy, the bigger branches the next level and so forth.  

Chambered Nautilus


Chamber of a Nautilus



Another example of a fractal could be a coastal line that seems uneven over distances. But without any point of reference, like a house or cabin on the bay, we would not be able to determine whether the photo was picturing a hundred meter wide bay or the coastal line of an entire country.

Norwegian fjords


Satellite photo of Norwegian fjords

Feet of a gecko


Feet of a gecko



Nature can also create fractals, which are even more organised than the ones of a coastal line. For example with a fern, every new level is an "echo" of the last one, simply smaller, creating an almost perfect copy. Fractal branches are so common in biology, that one must assume, that they place a useful role.

Fern fractals


Leaves of a fern

Dragon fly wings


Wings of a dragonfly



If you compare them to the passages in a lung, or the network of arteries, veins or capillaries in the blood systems, which all come with the same hierarchical structure as seen on trees. It has also been proven, that these networks are the most energy efficient when it comes to the amount of energy needed to transport fluid around.

Australia
Australia's valleys



Besides still being a bit of a scientific puzzle, fractals are just aesthetically pleasing to look at due to their symmetrical order. That’s also why fractals provide an endless source of inspiration for graphic designers and textile producers across the globe. Try having a look in your closet and pull out the vibrant prints or jacquards you might have gathered over the years and most likely you will find reflections of some kind of fractal pattern. If not in there – just take a walk outside and you’ll find that they are everywhere.

romanesco broccoli


Romanesco broccoli