Mountains, Nature

On fractals and triangles in mountains…

Fractals are in us, and around us, from the infinitesimal to the infinite, they represent that cusp where one is flummoxed about mathematics being an art or a science… a flower to a cosmos, there is a sense of immortality that they exude, a never ending series of patterns mimicked by nature in the cycle of life and death…

In the mountains though, they meet their match in another shape – triangles –  which to the naked eye seem to make the fractals pause… ‘tis a difficult debate… the fickle nature of a Fibonacci against the stout demeanour of a Pythagorean… the former an embodiment of the living in micro, the latter a testament to the orderliness of the macro… in mathematical theory, the golden ratio and the triangle occupy their own separate culverts… in nature, especially mountains, they are inextricably intertwined…

For the pedestrian, life seems more fractal in the flower near one’s feet, and triangles dominate the horizon in large massifs… for centuries intellectuals have pondered over the aesthetic beauty of the former, from flowers to snow flakes to the branches of trees, yet triangles often seem to be under studied…

From the perspective of visual aesthetics, sharp, compact triangles are more appealing… in mountains, peaks with clean, clear lines leading up to the summits, an isosceles with a small base looks more condescending than say, an equilateral massif… as they seem to flatten out, they become less attractive…

And this is where the fun begins… where the triangles seem to become obscure, fractals take over the baton and start imprinting themselves on the senses… think rolling meadows carpeting the milder undulations, in spring, summer and fall, a blasphemy of colours and smells emerge from the fractals, in winters, one can revel in curvaceous geometry of snowflakes

Yet this demarcation is only a theoretical attempt to delineate the two shapes in order to understand one’s own perception… one might think they have a semblance of clarity staring at a triangular massif, yet gaze long enough it will break down into fractals of its own… mountains are curves scolded into lines by geological forces… the ones that comply spire up to dizzying heights yet find themselves cold and lonely, the diffident of the lot remain transfixed at their feet yet are blessed with more life and colour… the irony of it all, they say…

 

Fractals in nature
A snail’s shell is cited as one of the most evident examples of the golden ratio in nature, however, in reality ‘tis actually a variation of the traditional golden spiral

 

Fractals in nature
One can very easily spot fractal patterns in flowers, and for that matter even the occurrence of
irrational numbers in nature

 

Fractals in nature
Lichens are another subset where fractals are very evident, sometimes akin to how the branches of a tree spread out…

 

The triangular crests on the centre and left seem aesthetically more appealing than the smaller domed summits on the right…

 

Fractals in nature
Triangles give a sense of ‘closure’ to the landscape, similar to what one experiences in music where falling fifth chord progressions are perceived to bring about this sense of closure to the song,  the sound seeming complete rather than ending abruptly…

 

Rivers and streams often bisect the landscape into triangles, a pattern that is soothing to the eyes…

Musings on visual aesthetics of mountains…

Author: Parth Joshi

Allured by the outdoors, the author is made up in parts of that quintessential lost soul wreathing under the pangs of biophilia in a desk job, a wannabe elegist mostly ending up in dungeons of poetasters and an optimist waiting for the senility of the modern world to fade away while sampling shoots and leaves. In saner times, he has a keen interest in areas pertaining to tourism, history, agriculture and climate change, especially with respect to historical interpretations, emerging technologies and future livelihoods. An avid trekker, runner, cyclist, birder and photographer, he is more often than not found gloating over anything hinterland, on foot or over computer monitors, and fantasizing solutions that can foster inclusive growth and sustainable livelihoods for communities at the grassroots.

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