Icelandic Landscapes and Self-Similarity

In the winter of 2017 my wife and I visited Western Iceland. The following thoughts were written shortly after the trip, and were supposed to be part of a bigger essay. If you enjoy dark atmospheres and landscapes put on some Auen and grab a mug of Earl Grey.

This island is marked by otherness. Driving on its roads feels like exploring an alien planet from a roving vehicle.?

The landscape is characterised both by beauty and sublime. Beauty is given by the self-similarity of its geological formations. This similarity is not an exact replication, but rather variation on a certain theme - a phenomenon showing the same statistical properties at many scales. In Charles Jencks' words, "Fractals, the fractional dimensions lying between the customary one, two and three-dimensions, can be found throughout all of nature. They measure the crinkliness of things, like a wad of paper squeezed together, or the coastline of Scotland, which is so complex in its doubling back that it approaches three dimensions. Clouds, coastlines, snowflakes, ferns and trees are fractals showing an important quality that Benoit Mandelbrot pointed out: self-similarity" - 'The Architecture of the Jumping Universe', Charles Jencks.

This fractal character of natural landscapes holds a spell over all of us; it is the hidden secret behind our fascination with the constantly changing, though closely related shapes of the ocean waves; the contours of clouds, forests or mountains. It is one of the striking features of Icelandic landscapes.?

One must keep in mind that natural self similarity goes beyond pure mathematical fractals; there are no perfect golden spirals or perfect numeric ratios in nature, just as there are no perfect lines or circles. Despite being more adequate to describe natural realities, fractals are still mental abstractions just like Euclidean forms. From an aesthetic perspective, the absolute order of mathematical representations loses its self similar quality and degenerates into monotony or self-sameness. Once we have comprehended the rule of a fractal shape, it loses some of its enticing qualities and it becomes boring. At the opposite spectrum lies the equally disturbing aesthetic experience of encountering a composition with no discernible ordering principle, one in which parts have nothing in common and the relationships between them are chaotic. We could therefore picture 'self-similarity' as the climax of a hyperbola, that critical point between too much chaos and too much order, in which we perceive things to be beautiful. That aesthetic emotion is not reserved to the perception of natural phenomena; it can be experienced while perceiving man-made artefacts as well, provided they meet the criteria of self-similarity by being situated on the same critical point between accident and planning.

The terrain of the island is constantly changing under the actions of volcanoes, tectonic plates and glaciers, which can also be represented as nonlinear occurrences (like strange attractors) that disturb the fractal shapes of the rocks, leading to a composition in which no two shapes are identical, in which nothing is 'tiling'. This 'unity with variety' (C. Jencks) underlies every object or composition that we find beautiful.

When we combine all these rules (fractals + strange attractors + other nonlinear occurrences) into a single composition with enough skill, we obtain a geometric composition in which no two shapes are identical, in which nothing is 'tiling'; the perception of self similarity is undistinguishable from that of natural landscapes.

The sublime character of the landscapes is given by the atmospheric elements - low clouds, rain, mist, the contrast between sunlit and shaded areas. If you are interested in the aesthetic category of 'sublime', I have written a few articles on the topic, starting with this one: https://www.wyrdtree.co.uk/4-archviz-theory-the-aesthetic-category-of-sublime/