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What the heck is a fractal and why you need one in your living room.


Recent scientific evidence proves that viewing natural patterns in nature makes us feel relaxed. How can this be used to our advantage when we might not be able to escape for a walk in a natural area or forest?



I am crouching by the side of the walking path eyeing the best angle for sunlight to filter through a stalk of long grass so I can capture the beauty that called me to stop.


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In my peripheral vision, a pair of men are approaching down the path.

For a split second I contemplate popping up and pushing off before they notice what I am looking at.

No, quickly the decision to finish snapping my shot before standing.

"What kind of berries were you looking at?" asks the man closest, on the inside of the path.

I take a breath and search for a simple response to avoid lengthy explanation. This somehow feels more difficult than stopping the truth that rises and escapes from my lips.

"Actually, I am doing a bit of research on fractals and was looking at the long grass."


Pause.


I can tell this is not what he was expecting from a slightly disheveled looking mom crouching beside a stroller on the side of a walking path with two toddlers.

"Um, I don’t think I am familiar with that word - fractals?" He replies.


Buoyed by my unexpected honesty and the confidence with which it projected, I continue and am pleased at how easily the words string together.

"It means repeating patterns in nature. There is a lot of really good evidence to say that just looking at them can reduce stress and produce other positive responses. I just finished a nature therapy certification and am a nurse by background - I find it really interesting."


The friend of the questioner looks absurdly about to burst out laughing with his mouth drawn into an exaggerated open smile at the unexpectedness of this exchange. His friend stammers out a response along with a forehead salute before turning to resume walking.

"Oh, well, good luck then ... keep up the good work!"



The thing is, fractals are hard to explain. Defined by a complex mathematical equation and a set of not so black and white characteristics, they are even harder to understand.


The good news is that by intentionally placing them around us, we feel relaxed - almost instantly, from seeing, hearing, or feeling their patterns. All we have to know is where to find them and how to access the benefit.


Fractals are repeating patterns found in nature that can be either visual, auditory, or tactile. As an example of a visual fractal, if you look at something on a large scale, it will look similar in shape to smaller components. For example, trees, branches, twigs, leaf veins, and smaller leaf veins all have similar angles and shapes if you examine them independently.


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Fractals were first mathematically defined and named in 1975 by Benoit Mandelbrot (1), who pointed out that infinite examples of fractals can be found in nature (lucky for us).


The interesting part in today's continued research is the effect that engaging with fractals has on humans. As humans are as a part of nature as trees, or clouds, or oceans (all fractals), unsurprisingly, they too contain many fractal structures. Similar to tree root structures is the brachial structure of the lungs, just as the ever branching system of veins to capillaries resembles a watershed map of rivers to streams.



Image drawn / taken and owned by author


Research has now proven that the human eye contains fractal structures that convey images to the brain. The really crazy part is that when the eye detects a fractal pattern that resembles its own, and processes this as vision, it creates a relaxed state in the brain, demonstrated by alpha waves shown on EEG monitoring. In other words, when the human eye views a river, leaf, or tree the brain responds by relaxing the body. (2)



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On a broad scale, the implications of this for designing the world around us are incredible. As Richard Taylor (2021) points out in a systematic review of research on fractals,


... we already have the potential to walk into a room in which the fractal ceilings dampen the noise, the fractal window shades provide an optimal breeze, the fractal solar panels deliver efficient energy to the Sinai lighting, and all of their patterns combine to create a stress-reducing visual environment analogous to the complex scenes of nature. (3)

However, starting now, with reading this article, we can implement this knowledge to the immediate effect of reduced stress. Demonstrated by the relaxed state of body and mind I felt during and after a walk on a gorgeous fall day with the purpose of finding and photographing fractals, despite being up the better part of the previous night with two sick toddlers, this stuff works.


Identifying visual fractals becomes easier the more you see. Take these examples shown in Taylor's review:


Photo credit: Taylor, R.P. (2021) (3)


This image shows examples of statistical tree fractals where each section taken from the larger image appears similar when examined independently (3).


Photo credit: Taylor, R.P. (2021) (3)


Here we can see a fractal cloud where the curves of the smaller shapes appear similar in contour to the larger, overall structure (3).


Now, have a look at these images and see if you can spot the fractal patterns:



Image taken and owned by author



Image taken and owned by author


Hint:



Images taken, modified, and owned by author


So, now that it is a bit easier to identify simple fractal shapes in nature, how can we use this knowledge in day to day life to reduce stress?


On a more broad scale, fractals are all around us and are more and more being used to design architecture, music, art, and a number of other items that make up our environment.


Photo credit: Taylor, R.P. (2021) (3)


Taylor's image highlighting how the Eiffel Tower (a) contains patterns reflective of the fractal shapes on the right (b) (3).


Photo credit: Taylor, R.P. (2021) (3)


A fascinating use of fractals in design whereby the neuron pathways in a human eye are mapped (left), outlined in grey scale (middle), and then used to create the literally, "easy on the eyes" carpet design for a building (right) (3).


Closer to home, and immediately implementable, here are some strategies for the home, which deliver the benefits of fractals to the comfort of home:


  • Houseplants. If you are a green-thumb (or someone in your household is), this is a super-easy way to introduce fractals with the added benefit that they clean the air as well as reduce stress!

  • Open windows. Preferably ones looking out onto either green space, or some kind of natural elements (sky and clouds included!). Weather permitting, this is even better if the windows literally open to let the view as well as the breeze in.

  • Music. Searching "fractal music" identifies a growing body of music designed specifically around fractal patterns. Interestingly, there is also a growing body of research around classical composition that include fractal patterns long before they were "a thing."

  • Art. If the budget allows for a Jackson Pollock painting (prints count), or other work of art with identified fractals, the results are guaranteed "easy on the eyes."


If you are able to access green areas outdoors, getting out into nature, where fractals of all varieties literally abound (bird songs, river patterns, land formations, and of course trees/plants), you are guaranteed maximal fractal immersion. Taking off shoes and adding the kinaesthetic of grass fractals on the feet adds bonus points.



Join the conversation!


  • What ways of incorporating fractals into daily life do you think are most interesting, or implementable?


  • Do you feel city planners should be incorporating fractal design into public spaces?



Please enjoy some additional fractals from our recent adventures!



Image taken and owned by author


Ocean fractals from a retreating tide.


Image taken and owned by author


Dandelion. Fractals are helping us even if we are contemplating cutting them down!



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Fractals remain in death.



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Fern fractals in a Redwood Forest.



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From petal fractal to seed fractal. The beauty of fractals in transformation.



And one more beautifully written fractal quote:


the phenomenon of Fractals stretches out into every branch of human expression and knowledge and leads all of it right back to what it has been created to represent: the beautiful balance between chaos and order within in all that makes up our world, our knowledge of our world, and ourselves. - Jules Ruis (4)

🌱


* Please note, all images taken and owned by the author


(1) Mandelbrot, B.B. (1982) The Fractal Geometry of Nature; WH Freedman: New York, NY, USA.


(2) Williams, F. (2017). The nature fix: Why nature makes us happier, healthier, and more creative.


(3) Taylor, R.P. The Potential of Biophilic Fractal Designs to Promote Health and Performance: A Review of Experiments and Applications. Sustainability 2021, 13, 823. https://doi.org/10.3390/su13020823


(4) Ruis, J. Life is a Fractal Abstraction. http://www.fractal.org/Fractal-abstraction.pdf .

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