Transcript Fractals-in-Poetry-PowerPoint - Colby

FRACTALS
&POETRY
OVERVIEW

Benoit Mandelbrot
earthquakes,
patterns of vegetation in a swamp,
the way neurons fire when humans search through
memory
the coastline
snowflake
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).
FRACTAL
FEATURES
self-similarity
recursive structure
fractal dimension
A fractal might have dimension
of 1.6 or 2.4.
iteration
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 )
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.

ITERATIONS
ITERATIONS
FRACTALS IN ART
Jackson Pollock.
ACTION PAINTING
chaotic dripping and splattering, fractal patterns in
his work (VIA COMPUTER ANALYSIS)
 African art and architecture


Escher
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
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.
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
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There are two clusters,

each made of two clusters (the left is less clear than
the right),

each made of two occurrences.