*Many people have taken up gardening or some other plant-related hobby during the pandemic. It seems that when we have the opportunity, we surround ourselves with nature. I will try to answer why this might be the case.*

*Many people have taken up gardening or some other plant-related hobby during the pandemic. It seems that when we have the opportunity, we surround ourselves with nature. I will try to answer why this might be the case.*

###### Photo by Ceci Freeman on Unsplash

###### Photo by Ceci Freeman on Unsplash

As I am writing these lines, I am looking at my fern plant that I bought over two weeks ago. There were several reasons for this: first, people say it is the most efficient humidifier of air, so I thought I will act on this. Second, I remember my mom making necklaces of fern roots when I was a child and we happened to be in the forest, and this brings pleasant memories. Third, there is something that I find beautiful about ferns: their large, divided leaves. I find there is something magical about that pattern repeating itself over and over again, with the largest leaves situated near the base of the plant and the smallest leaves growing outward.

As I came to discover, objects with this feature contain fractals – geometric features that have the property of ‘self-similarity’ or recursion on different scales of magnitude or dimension. The extent of this self-recursion can be understood as complexity. There are different kinds of fractals, though – statistical and exact fractals. Statistical fractals are those found in nature, and there is an element of randomness included in their construction, as compared to exact fractals, whose repeating patterns involve precise repetition of patterns, and these are usually produced by computers (Bies Blanc-Goldhammer, Boydston, Taylor, & Sereno, 2016). For the purposes of this essay, I will focus on statistical fractals, as those are the most researched when it comes to people perceiving them, and discussing statistical fractals as ‘nature-bearers’ can also bring more light to why I like my fern plant so much.

All statistical fractals are not the same, and there are several criteria by which they can differ. One of the most researched criteria to divide fractals is the aforementioned dimension or complexity, which can be seen as the rate at which the pattern increases in structure from coarse to fine scales, with higher fractal dimension patterns having more fine structure (Bies et al., 2016). Research has found that people have a preference for fractals of low to intermediate dimension. For example, when people are required to choose which landscape they prefer, they are more likely to choose landscapes that include a fractal pattern of low to intermediate dimension. This was calculated from the contours of the landscape silhouette (Hagerhall, Purcell, & Taylor, 2004) using the box counting method, which is based on covering the landscape picture with computer-generated mesh of rectangles, counting the number of boxes that contain part of the pattern, and then repeating this procedure for smaller and smaller size of computer-generated boxes. Not only preference is affected by fractal geometry, but also people’s stress response, which is alleviated by perceiving fractals in a low to intermediate dimension. For instance, looking at such fractals reduces the participant’s stress levels measured as skin conductance response, more than looking at fractals of any other dimension (Wise & Taylor, 2002). As such, we will discuss possible reasons behind this ‘fractal love’ when fractals are of low to intermediate and also how we can bring fractals into our lives to feel more relaxed.

“Humans find objects that resemble savanna appealing and calming because savanna is the environment where early humans lived.”

One of the most iterated hypotheses for why people like some fractals and find them calming is an evolutionary one: the savanna hypothesis. This hypothesis states that humans find objects that resemble savanna appealing and calming because savanna is the environment where early humans lived. It was the environment that offered the best chances for survival by providing both a good view of the surrounding landscape, and protection from predators. According to the hypothesis, humans inherently prefer some environments over others, and that the savanna is likely associated with positive feelings of security (Joye, 2007). These notions have been supported by empirical evidence, as research shows that looking at savanna landscapes while being subject to stressful experimental situations provided the greatest dampening of physiological stress response as compared to looking at a forest landscape or an artistic painting (Taylor, 2006).

As stated, an important part of the savanna hypothesis is the extension of affect to any object resembling savanna. To support this part of the hypothesis, evolutionary psychologists argue that perceiving savannas or anything similar to them would evoke the pleasant feelings connected to savanna which would thus elicit positive affect or dampen negative affect (Joye, 2007). In the search of the criterion by which to judge what is this ‘something that resembles savanna’, scientists have analysed landscapes of savanna for their complexity and patterns, and came to the conclusion that one characteristics of savannas is that they have fractal pattern of low to intermediate complexity (Joye, 2007), making such fractals a geometric abstraction of savannas. Therefore, if an object contains fractal patterns of low to intermediate complexity, it is hypothesized that it will remind us of ‘our homeland’, savanna, and will elicit positive affect.

Arguably, looking at savanna landscapes or stimuli containing fractals has a restorative effect. However, as with any evolution-laden hypothesis, the savanna hypothesis is hard to test. There are countless explanations for what can be appealing about savannas – the colour palette, for instance. The same goes for fractals – we can like them but we can only speculate why we do. Claiming, with certainty, that it is because it reminds us of the savanna would be a logical fallacy of affirming the consequent: if something resembles savanna, it produces liking, but if something produces liking, it doesn’t necessarily mean it is because the thing resembles a savanna, even if there might be reasons for assuming so. We can only make probability claims – it seems likely that fractals of certain complexity are associated with savannas because they are full of such fractals, and savannas do make us calm. It would also be useful to know how to act on this knowledge.

**Fractal mining**

We established that surrounding ourselves with fractal geometry has the potential to increase our well-being and we hypothesized why this might be so. It is also in place to discuss how to expose ourselves to fractals of low to intermediate dimension, do some ‘fractal mining’, in order to maximise the utility of this geometrical phenomena. It must be pointed out, however, that it is not the fractal geometry per se that makes us feel good, after all, it is only a mathematical abstraction. Rather, the association of fractal geometry with nature or savannah is important, with nature or savannah eliciting positive affect. Nevertheless, there are several ways in which to include fractal geometry in our surroundings, given that people display preference for fractals irrespective of the method used to generate them (Taylor, 2006) – by making use of natural elements, art, and architecture. All three solutions will be discussed in turn.

The first and the most straightforward solution is to surround oneself with as much nature as possible, since nature already includes a range of fractal objects with low to intermediate complexity (Taylor, 2006), such as mountains, clouds, rivers, trees, or my fern plant. Nature is not restricted to live plants – pictures and other representations of nature are effective as well. The second option is to look for and make use of art that has fractal elements to them. For instance, Jackson Pollock, an American abstract painter, used fractal patterns in his poured paintings, as well as Leondardo da Vinci in his sketch The Deluge (Taylor, Spehar, Van Donkelaar, & Hagerhall, 2011). The third option for surrounding oneself with fractal geometry is by architecture that uses fractal elements as its building principles. Such elements can be natural elements or simply self-repeating patterns. An example of using natural patterns is Gaudí‘s Sagrada Família in Barcelona in which he masterfully included several natural elements, such as structural trees or flowering structures (Joye, 2007). An example of using self-repeating, not necessarily natural patterns in architecture are Gothic cathedrals or the Eiffel tower in Paris (Taylor, 2006). Therefore, there seem to be countless opportunities to bring fractals close to us – buying ferns, setting fractal paintings as wallpapers or visiting sites with organic architecture in Barcelona.

“It is also unclear whether fractals are associated specifically with savannahs or nature in general.”

Surrounding oneself with fractals is helpful because fractals likely reduce stress. There seems to be a preference for particular types of fractals, those that are low and medium in complexity. The savanna hypothesis offers an explanation for why this particular type of fractals is appealing to humans: savanna landscapes contain low to medium complexity fractal patterns and looking at this type of patterns evokes associations with the savanna, the most advantageous environment to live, in human evolution. Therefore, perceiving this specific type of fractals brings with it the positive evolutionary associations that then reduce stress. Fractals of low to intermediate complexity can be found throughout nature, art and architecture.

Research findings on fractals need to be interpreted with caution, though. Much of the research on human perception of fractals is preliminary and includes mostly the analysis of stimuli that reduced stress reaction the most. When it is found that it is the fractal element that is present in the calming stimulus and not in the ineffective stimulus, it is then inferred that the fractal pattern is responsible for the calming effect. Although likely, there are surely other potential explanations for the calming effect of specific stimuli on stress reaction, but they remain yet to be discovered. It is also unclear whether fractals are associated specifically with savannahs or nature in general, even though the former is a part of the latter and therefore alike. In short, the experimental approach to fractal patterns is in its infancy.

However, the fractals bring to the fore a more general topic, that is, the limits of our knowledge, and the role that intuition plays in it. Before it was known that fractal geometry is appealing, people nevertheless admired nature, and created paintings and architectural pieces that contained fractals with the ‘desired’ level of complexity, for instance the already mentioned gothic cathedrals from the 15th century. Such human creations are actually omnipresent and it is likely that they came about by overtly copying nature, or simply creating patterns that ‘feel good while looking at’. However, only after realising the likely ingredient that makes these human creations appealing – fractals – can we truly appreciate the genius of some artists and architects, and also find new ways of introducing fractal geometry into our surroundings. Therefore, intuition in this case seems to be the first apostle of an effect taking place, an ‘observation’ in the empirical cycle of science, while only the rigorous testing reveals whether it is actually fractal geometry perceiving which makes us more at ease and finally provides the means for systematic disseminating fractal geometry around us. <<

#### References

*– Bies, A. J., Blanc-Goldhammer, D. R., Boydston, C. R., Taylor, R. P., & Sereno, M. E. (2016). Aesthetic responses to exact fractals driven by physical complexity. Frontiers in Human Neuroscience, 10.*

*– Hagerhall, C. M., Purcell, T., & Taylor, R. (2004). Fractal dimension of landscape silhouette outlines as a predictor of landscape preference. Journal of Environmental Psychology, 24, 247–255.*

*– Joye, Y. (2007). Architectural lessons from environmental psychology: The case of biophilic architecture. Review of General Psychology, 11, 305–328.*

*– Taylor, R. P. (2006). Reduction of physiological stress using fractal art and architecture. Leonardo, 39, 245–251.*

*– Taylor, R. P., Spehar, B., Van Donkelaar, P., & Hagerhall, C. M. (2011). Perceptual and physiological responses to Jackson Pollock’s fractals. Frontiers in Human Neuroscience, 5.*

*– Wise, J. A., & Taylor, R. P. (2002). Fractal design strategies for enhancement of knowledge work environments. Proceedings of the Human Factors and Ergonomics Society Annual Meeting, 46, 854–858.*

As I am writing these lines, I am looking at my fern plant that I bought over two weeks ago. There were several reasons for this: first, people say it is the most efficient humidifier of air, so I thought I will act on this. Second, I remember my mom making necklaces of fern roots when I was a child and we happened to be in the forest, and this brings pleasant memories. Third, there is something that I find beautiful about ferns: their large, divided leaves. I find there is something magical about that pattern repeating itself over and over again, with the largest leaves situated near the base of the plant and the smallest leaves growing outward.

As I came to discover, objects with this feature contain fractals – geometric features that have the property of ‘self-similarity’ or recursion on different scales of magnitude or dimension. The extent of this self-recursion can be understood as complexity. There are different kinds of fractals, though – statistical and exact fractals. Statistical fractals are those found in nature, and there is an element of randomness included in their construction, as compared to exact fractals, whose repeating patterns involve precise repetition of patterns, and these are usually produced by computers (Bies Blanc-Goldhammer, Boydston, Taylor, & Sereno, 2016). For the purposes of this essay, I will focus on statistical fractals, as those are the most researched when it comes to people perceiving them, and discussing statistical fractals as ‘nature-bearers’ can also bring more light to why I like my fern plant so much.

All statistical fractals are not the same, and there are several criteria by which they can differ. One of the most researched criteria to divide fractals is the aforementioned dimension or complexity, which can be seen as the rate at which the pattern increases in structure from coarse to fine scales, with higher fractal dimension patterns having more fine structure (Bies et al., 2016). Research has found that people have a preference for fractals of low to intermediate dimension. For example, when people are required to choose which landscape they prefer, they are more likely to choose landscapes that include a fractal pattern of low to intermediate dimension. This was calculated from the contours of the landscape silhouette (Hagerhall, Purcell, & Taylor, 2004) using the box counting method, which is based on covering the landscape picture with computer-generated mesh of rectangles, counting the number of boxes that contain part of the pattern, and then repeating this procedure for smaller and smaller size of computer-generated boxes. Not only preference is affected by fractal geometry, but also people’s stress response, which is alleviated by perceiving fractals in a low to intermediate dimension. For instance, looking at such fractals reduces the participant’s stress levels measured as skin conductance response, more than looking at fractals of any other dimension (Wise & Taylor, 2002). As such, we will discuss possible reasons behind this ‘fractal love’ when fractals are of low to intermediate and also how we can bring fractals into our lives to feel more relaxed.

“Humans find objects that resemble savanna appealing and calming because savanna is the environment where early humans lived.”

One of the most iterated hypotheses for why people like some fractals and find them calming is an evolutionary one: the savanna hypothesis. This hypothesis states that humans find objects that resemble savanna appealing and calming because savanna is the environment where early humans lived. It was the environment that offered the best chances for survival by providing both a good view of the surrounding landscape, and protection from predators. According to the hypothesis, humans inherently prefer some environments over others, and that the savanna is likely associated with positive feelings of security (Joye, 2007). These notions have been supported by empirical evidence, as research shows that looking at savanna landscapes while being subject to stressful experimental situations provided the greatest dampening of physiological stress response as compared to looking at a forest landscape or an artistic painting (Taylor, 2006).

As stated, an important part of the savanna hypothesis is the extension of affect to any object resembling savanna. To support this part of the hypothesis, evolutionary psychologists argue that perceiving savannas or anything similar to them would evoke the pleasant feelings connected to savanna which would thus elicit positive affect or dampen negative affect (Joye, 2007). In the search of the criterion by which to judge what is this ‘something that resembles savanna’, scientists have analysed landscapes of savanna for their complexity and patterns, and came to the conclusion that one characteristics of savannas is that they have fractal pattern of low to intermediate complexity (Joye, 2007), making such fractals a geometric abstraction of savannas. Therefore, if an object contains fractal patterns of low to intermediate complexity, it is hypothesized that it will remind us of ‘our homeland’, savanna, and will elicit positive affect.

Arguably, looking at savanna landscapes or stimuli containing fractals has a restorative effect. However, as with any evolution-laden hypothesis, the savanna hypothesis is hard to test. There are countless explanations for what can be appealing about savannas – the colour palette, for instance. The same goes for fractals – we can like them but we can only speculate why we do. Claiming, with certainty, that it is because it reminds us of the savanna would be a logical fallacy of affirming the consequent: if something resembles savanna, it produces liking, but if something produces liking, it doesn’t necessarily mean it is because the thing resembles a savanna, even if there might be reasons for assuming so. We can only make probability claims – it seems likely that fractals of certain complexity are associated with savannas because they are full of such fractals, and savannas do make us calm. It would also be useful to know how to act on this knowledge.

**Fractal mining**

We established that surrounding ourselves with fractal geometry has the potential to increase our well-being and we hypothesized why this might be so. It is also in place to discuss how to expose ourselves to fractals of low to intermediate dimension, do some ‘fractal mining’, in order to maximise the utility of this geometrical phenomena. It must be pointed out, however, that it is not the fractal geometry per se that makes us feel good, after all, it is only a mathematical abstraction. Rather, the association of fractal geometry with nature or savannah is important, with nature or savannah eliciting positive affect. Nevertheless, there are several ways in which to include fractal geometry in our surroundings, given that people display preference for fractals irrespective of the method used to generate them (Taylor, 2006) – by making use of natural elements, art, and architecture. All three solutions will be discussed in turn.

The first and the most straightforward solution is to surround oneself with as much nature as possible, since nature already includes a range of fractal objects with low to intermediate complexity (Taylor, 2006), such as mountains, clouds, rivers, trees, or my fern plant. Nature is not restricted to live plants – pictures and other representations of nature are effective as well. The second option is to look for and make use of art that has fractal elements to them. For instance, Jackson Pollock, an American abstract painter, used fractal patterns in his poured paintings, as well as Leondardo da Vinci in his sketch The Deluge (Taylor, Spehar, Van Donkelaar, & Hagerhall, 2011). The third option for surrounding oneself with fractal geometry is by architecture that uses fractal elements as its building principles. Such elements can be natural elements or simply self-repeating patterns. An example of using natural patterns is Gaudí‘s Sagrada Família in Barcelona in which he masterfully included several natural elements, such as structural trees or flowering structures (Joye, 2007). An example of using self-repeating, not necessarily natural patterns in architecture are Gothic cathedrals or the Eiffel tower in Paris (Taylor, 2006). Therefore, there seem to be countless opportunities to bring fractals close to us – buying ferns, setting fractal paintings as wallpapers or visiting sites with organic architecture in Barcelona.

“It is also unclear whether fractals are associated specifically with savannahs or nature in general.”

Surrounding oneself with fractals is helpful because fractals likely reduce stress. There seems to be a preference for particular types of fractals, those that are low and medium in complexity. The savanna hypothesis offers an explanation for why this particular type of fractals is appealing to humans: savanna landscapes contain low to medium complexity fractal patterns and looking at this type of patterns evokes associations with the savanna, the most advantageous environment to live, in human evolution. Therefore, perceiving this specific type of fractals brings with it the positive evolutionary associations that then reduce stress. Fractals of low to intermediate complexity can be found throughout nature, art and architecture.

Research findings on fractals need to be interpreted with caution, though. Much of the research on human perception of fractals is preliminary and includes mostly the analysis of stimuli that reduced stress reaction the most. When it is found that it is the fractal element that is present in the calming stimulus and not in the ineffective stimulus, it is then inferred that the fractal pattern is responsible for the calming effect. Although likely, there are surely other potential explanations for the calming effect of specific stimuli on stress reaction, but they remain yet to be discovered. It is also unclear whether fractals are associated specifically with savannahs or nature in general, even though the former is a part of the latter and therefore alike. In short, the experimental approach to fractal patterns is in its infancy.

However, the fractals bring to the fore a more general topic, that is, the limits of our knowledge, and the role that intuition plays in it. Before it was known that fractal geometry is appealing, people nevertheless admired nature, and created paintings and architectural pieces that contained fractals with the ‘desired’ level of complexity, for instance the already mentioned gothic cathedrals from the 15th century. Such human creations are actually omnipresent and it is likely that they came about by overtly copying nature, or simply creating patterns that ‘feel good while looking at’. However, only after realising the likely ingredient that makes these human creations appealing – fractals – can we truly appreciate the genius of some artists and architects, and also find new ways of introducing fractal geometry into our surroundings. Therefore, intuition in this case seems to be the first apostle of an effect taking place, an ‘observation’ in the empirical cycle of science, while only the rigorous testing reveals whether it is actually fractal geometry perceiving which makes us more at ease and finally provides the means for systematic disseminating fractal geometry around us. <<