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Fractals and Fractiles

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The name Fractiles is a combination of the word "fractal", meaning the phenomenon of scaling or the repeating of a pattern on every scale - and the word "tiles".



"Fractal" is a relatively new word, yet it describes something which we recognize intuitively. Fractal refers to a geometric shape that is complex and detailed, yet similar at any level of magnification. Examples include a rugged coastline which when seen from space becomes ever more complex as the viewer moves closer. Coastlines turn into rugged boulders, then into sand, and then finally into sub-atomic particles. Yet at every level of magnification the pattern is similar.
Fern

Europe
Europe
Mathematician Benoit Mandelbrot called those shapes "fractals". He also wrote that fractals are "self-similar" meaning that each portion of a fractal can be viewed as a smaller replica of the whole. If you look closely at a fern, for example, you will see the same pattern reproduced at every level. The leaves seem to be made up of miniature ferns - repeating the shape of the whole in ever decreasing sizes.
We live in a fractal Universe. Our Sun is just one star among billions of stars which make up our Milky Way Galaxy. The Milky Way Galaxy is merely a tiny part of a super galaxy (a galaxy made of galaxies). In the vast expanse of celestial space, a super galaxy is but a tiny replicated part of a super-super galaxy, ad infinitum.
Wales
Wales
Large Boulders
Large Boulders
Similarly, when we zoom in on the world of sub-atomic particles, we find that it is composed of endlessly smaller structures within structures, all of which have similarity of pattern. There is no known limit to how large or small fractals can be. We humans are somewhere on an endless continuum.

Some call the similarity of pattern which exists everywhere from the infinitesimal to the unimaginably vast - the "fingerprint of God".
Pebbles
Pebbles
Sand Magnified
Sand Magnified
The spiritual insight that the Universe is a fractal transforms this earthly world into one of splendour and mutual fusion.

 

To see the World in a grain of Sand
And Heaven in a wild Flower
Hold Infinity in the palm of your hand
And Eternity in an hour.

-William Blake



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