From the Geometry of Imagination
From the geometry of imagination to the observable world, was accomplished by Benoit Mandelbrot who introduced the concept of ‘self-similarity, in his paper How Long is the Coast of Britain? Science, May 1967.
Abstract.
Geographical curves are so involved in their detail that their lengths are often infinite or, rather, indefinable. However, many are statistically “self-similar,” meaning that each portion can be considered a reduced-scale image of the whole. In that case, the degree of complication can be described by a quantity D that has many properties of a “dimension,” though it is fractional; that is, if exceeds the value unity associated with the ordinarily, rectifiable, curves.
From there, the visual development of fractals was radically enhanced by computer modelling and digital technology.
The phrase ‘often infinite or, rather, indefinable’ is a key to my own perspective and, on occasion, perception.
Not being a mathematician, I came to this many years later. However, I think it was 1970, thereabouts anyway, my cousin and I were staying with a friend on Dartmoor. We all took a dose of LSD. We climbed the hill to Belstone Tor and sat amongst the rocks. The sky was filled with streams of light, the earth was shimmering with fractal patterns. Some time later we had returned to the house. There was a watercolour on the wall. The scene was of a rocky coastline. The waves were breaking on the shore. The gulls were crying. Their calls were quite distinct.
At some point, our friend’s father appeared. He lived nearby. Someone in the village had phoned him to say that his son, who had wandered off, was behaving erratically. They were concerned.
The father wanted to know what the hell was going on. My cousin and I were unable to explain, other than that we were all tripping. I wanted to get back into the painting. The father was perplexed. I could see that he had come to a decision to look elsewhere. “Look he’s disappearing” I observed. He was dissolving into a potential existence to my perception. “Alright I’ll go” he huffed.
