FRACTALS

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FRACTALS

• POETRY

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overview

• Benoit Mandelbrot
• earthquakes,
• patterns of vegetation in a swamp,
• the way neurons fire when humans search through
  memory
• the coastline
• snowflake

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Fractals etymology

• FRACTUS
• BROKEN FRAGMENTED
• Mandelbrot discovered that these chaotic
  structures contained deep logic or patterns,
  which is precisely why he called them fractal
  forms
• each fractal form replicates the form of the
  entire structure (Mandelbrot190).

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Fractal features

• self-similarity
• recursive structure
• fractal dimension
• iteration

A fractal might have dimension of 1.6 or 2.4.
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How to make a fractal

• Fractals are often formed by what is called an
  iterative process. Here's what I mean. To make a
  fractal Take a familiar geometric figure (a
  triangle or line segment, for example) and
  operate on it so that the new figure is more
  "complicated" in a special way.
• Then in the same way, operate on that resulting
  figure, and get an even more complicated figure.
• Now operate on that resulting figure in the same
  way and get an even more complicated figure.
• Do it again and again...and again. In fact, you
  have to think of doing it infinitely many times.
• (http//math.rice.edu/lanius/fractals/iter.html
  ) 

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How to make a fractal

• Start with a large equilateral triangle.
• Make a Star.
• Divide one side of the triangle into three equal
  parts and remove the middle section.
• Replace it with two lines the same length as the
  section you removed.
• Do this to all three sides of the triangle.
• Do it again and again.
• Do it infinitely many times and you have a
  fractal.

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iterations
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iterations
If you could fold the paper about 50 times, it
would look like this
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FRACTALS IN ART

• Jackson Pollock.
• ACTION PAINTING
• chaotic dripping and splattering, fractal
  patterns in his work (VIA COMPUTER ANALYSIS)
• African art and architecture
• Escher

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FRACTALS IN POETRY

• In fractal poetics one poem triggers another
  through the repetition of certain linguistic
  elements or patterns.
• each poem growing by slow, repetitive accretion

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PATTERN OF know IN Wallace Stevens' poem "The
Sail of Ulysses (Canto I)"

• The Sail of Ulysses (Canto I)
• If knowledge and thing known are one
• So that to know a man is to be
• That man, to know a place is to be
• That place, and it seems to come to that
• And if to know one man is to know all
• And if one's sense of a single spot
• Is what one knows of the universe,
• Then knowledge is the only life,
• The only sun of the only day,
• The only access to true ease,
• The deep comfort of the world and fate.

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PATTERN OF know IN Wallace Stevens' poem "The
Sail of Ulysses (Canto I)"

• Note the occurrences of know organize themselves
  into hierarchical clusters, that is, clusters
  within clusters
• There are two clusters,
• each made of two clusters (the left is less clear
  than the right),
• each made of two occurrences.