FRACTALS&POETRY

OVERVIEW Benoit Mandelbrot

earthquakes,

patterns of vegetation in a swamp,

the way neurons fire when humans search through memory

the coastlinesnowflake

FRACTALS – ETYMOLOGY FRACTUS

BROKEN FRAGMENTEDMandelbrot 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

iteration

A fractal might have dimension of 1.6 or 2.4.

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

If you could fold the paper about 50 times, it would look like this:

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 oneSo that to know a man is to beThat man, to know a place is to beThat place, and it seems to come to that;And if to know one man is to know allAnd if one's sense of a single spotIs 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

There are two clusters,

each made of two clusters (the left is less clear than the right),

each made of two occurrences.