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FRACTALS

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

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FRACTALS

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  1. FRACTALS &POETRY

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

  3. 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).

  4. Fractal features self-similarity recursive structure fractal dimension iteration A fractal might have dimension of 1.6 or 2.4.

  5. 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 ) 

  6. 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.

  7. iterations

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

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

  10. 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

  11. 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.

  12. 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.

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