11
Sep
15

self-similarity

Ever since the late 1970s when I bought the book The Powers of Ten by husband-and-wife design team Charles and Ray Eames, I have had a growing sense that there are many similarities between the microscopic world and the greater Universe.

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Lately, partially due to Matt’s wise-ass comment to a recent post, I have been considering this notion…

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…and stumbled upon the idea of “self-similarity” in nature. It has been popularized since the discovery in 1978 of fractals by designer Loren Carpenter, who was looking for a way to render mountains in animated films for Boeing Aircraft. Carpenter found these fractals in the work of mathematician Benoit B. Mandelbrot, which has to do with the fractal geometry of nature. Mandelbrot said you could create fractals by taking smooth-looking shapes and breaking them into 4 pieces, then repeating the same process on each of the 4 pieces, and repeating it over and over again.

For example:

Von_Koch_curve.

Carpenter decided to do this on his computer, and he was able to create convincing mountains that became a sensation in the field of computer animation.

In mathematics, a self-similar object is exactly or approximately similar to a part of itself (i.e. the whole has the same shape as one or more of the parts). Many objects in the real world, such as coastlines, are statistically self-similar: parts of them show the same statistical properties at every scale. Self-similarity is a typical property of fractals.

1024px-Flickr_-_cyclonebill_-_Romanesco.

In nature, the same principle seems to apply. Trees and their branches are one of the most familiar examples of fractals and self-similarity in nature. If you observe the branching nodes of a tree, you see that the pattern of branching repeats (at least approximately) throughout the tree. From the trunk to the uppermost branches, the same basic pattern of branching is repeated at a smaller and smaller scale—just like fractals. Yet, the impression created by the whole organism is highly irregular.

I am no mathematician, but I do have a background as a visual artist and a deep interest in the natural world. After the last few weeks, I have come to the conclusion that I owe it to myself to move on beyond the past and focus more on the wonders of the natural world, and the correspondences, similarities and connections that unify the Universe and make its grandest and most humble features so beautiful.

I have been on this path for some time, but it’s time for a renewed effort. Who knows where it will take this blog?

۞

Groove of the Day

Listen to the Beatles performing “Mother Nature’s Son”

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Weather Report

89° and Partly Cloudy

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1 Response to “self-similarity”


  1. September 11, 2015 at 12:17 pm

    Danny –
    As usual we have been on the same road. when i met Charles and Ray Eames at their Walker show i started looking into their work and the first work was ‘ The Powers of Ten ‘ it changed my perception as it did yours.
    Happy Trails my friend. I love you & like you, Dusty


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