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7.2.3.1 Connection to Biodiversity with Fractals
Benoit Mandelbrot’s (1983) book the “The Fractal Geometry of Nature” applied
fractal geometry to common natural phenomena, such as coastlines, rivers, trees,
leaves and snowflakes. The book argues that fractals are an essential tool for understanding the natural world (Mandelbrot 1983). Mandlebrot (1983, p. 1) reasoned
that “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”, but are rather comprised of fragmented, self-similar repeated patterns. Figure 7.1 shows examples of
fractals that occur in nature.
Ecologists have used fractal geometry to determine the biodiversity of an environment (Tokeshi and Arakaki 2012). The fractal dimension, D, has been used to
determine habitat quality (Imre and Bogaert 2004), landscape structure and composition (Pe’er et al. 2013), habitat complexity (Dibble and Thomaz 2009) and species
richness (Stevens 2018). The relative lack of fractals has been used to identify manmade landscapes (Pe’er et al. 2013). Irme and Bogaert (2004) used fractals to determine the habitat quality of 49 pine tree (Pinus sylvestris L.) woodlots in Belgium.
The authors hypothesised that if the woodlots were created due to habitat fragmentation − the process through which large habitats are broken up into small parcels
− then the fractal dimensions of the boundaries of these habitats should all be similar (Imre and Bogaert 2004). Fractal similarity for the boundary shape of the woodlots was found, highlighting that the 49 patches of woodland were once one large
pine forest and were created as a result of habitat fragmentation. Dibble and Thomaz
(2009) examined whether fractal dimension D scores could quantitatively describe
the complexity of 11 species of aquatic plants, and if the D score could be used to
predict density of invertebrates found within these aquatic plants. D scores were a
good predictor of plants’ complexity; plant species with high numbers of finely dissected leaves or roots had higher D scores compared to plants with single leaves.
Furthermore, a significant relationship was found between D score and density of
invertebrates; more complex plants, as measured by D score, were associated with
a greater number of invertebrates. Stevens (2018) investigated whether fractal
dimensions of the tree silhouette of a habitat would differ based on the species richness of plants, animals and fungi in that habitat. There was a significant difference
in D scores between high or low species rich habitats; D scores were higher in tree
silhouettes of high species-rich habitats compared to tree silhouettes of low speciesrich habitats.
7.2.3.2 Fractal Dimension and Preference
Could the fractal dimension D predict environmental preference? Initially, inconsistent results were found, with studies showing preference for fractal patterns with
both high and low D scores (Taylor 2001). Thinking that perhaps this inconsistency
was related to the source of the D scores, Spehar et al. (2003) investigated preference for fractals generated by nature (e.g. trees, mountains, clouds), human beings
7 Theoretical Foundations of Biodiversity and Mental Well-being Relationships
7.2.3.1 Connection to Biodiversity with Fractals
Benoit Mandelbrot’s (1983) book the “The Fractal Geometry of Nature” applied
fractal geometry to common natural phenomena, such as coastlines, rivers, trees,
leaves and snowflakes. The book argues that fractals are an essential tool for understanding the natural world (Mandelbrot 1983). Mandlebrot (1983, p. 1) reasoned
that “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”, but are rather comprised of fragmented, self-similar repeated patterns. Figure 7.1 shows examples of
fractals that occur in nature.
Ecologists have used fractal geometry to determine the biodiversity of an environment (Tokeshi and Arakaki 2012). The fractal dimension, D, has been used to
determine habitat quality (Imre and Bogaert 2004), landscape structure and composition (Pe’er et al. 2013), habitat complexity (Dibble and Thomaz 2009) and species
richness (Stevens 2018). The relative lack of fractals has been used to identify manmade landscapes (Pe’er et al. 2013). Irme and Bogaert (2004) used fractals to determine the habitat quality of 49 pine tree (Pinus sylvestris L.) woodlots in Belgium.
The authors hypothesised that if the woodlots were created due to habitat fragmentation − the process through which large habitats are broken up into small parcels
− then the fractal dimensions of the boundaries of these habitats should all be similar (Imre and Bogaert 2004). Fractal similarity for the boundary shape of the woodlots was found, highlighting that the 49 patches of woodland were once one large
pine forest and were created as a result of habitat fragmentation. Dibble and Thomaz
(2009) examined whether fractal dimension D scores could quantitatively describe
the complexity of 11 species of aquatic plants, and if the D score could be used to
predict density of invertebrates found within these aquatic plants. D scores were a
good predictor of plants’ complexity; plant species with high numbers of finely dissected leaves or roots had higher D scores compared to plants with single leaves.
Furthermore, a significant relationship was found between D score and density of
invertebrates; more complex plants, as measured by D score, were associated with
a greater number of invertebrates. Stevens (2018) investigated whether fractal
dimensions of the tree silhouette of a habitat would differ based on the species richness of plants, animals and fungi in that habitat. There was a significant difference
in D scores between high or low species rich habitats; D scores were higher in tree
silhouettes of high species-rich habitats compared to tree silhouettes of low speciesrich habitats.
7.2.3.2 Fractal Dimension and Preference
Could the fractal dimension D predict environmental preference? Initially, inconsistent results were found, with studies showing preference for fractal patterns with
both high and low D scores (Taylor 2001). Thinking that perhaps this inconsistency
was related to the source of the D scores, Spehar et al. (2003) investigated preference for fractals generated by nature (e.g. trees, mountains, clouds), human beings
7 Theoretical Foundations of Biodiversity and Mental Well-being Relationships