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The Fractal World

Erosion

River Basins

River Flow

The Fractal Structure of the Universe

Björn Birnir

Center for Complex and Nonlinear ScienceDepartment of Mathematics

UC Santa Barbara

The Discovery Center June 2011

Birnir The Fractal Structure of the Universe

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The Fractal World

Erosion

River Basins

River Flow

Outline

1 The Fractal World

2 Erosion

3 River Basins

4 River Flow

Birnir The Fractal Structure of the Universe

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The Fractal World

Erosion

River Basins

River Flow

Outline

1 The Fractal World

2 Erosion

3 River Basins

4 River Flow

Birnir The Fractal Structure of the Universe

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The Fractal World

Erosion

River Basins

River Flow

Most things made by nature are fractals

Birnir The Fractal Structure of the Universe

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The Fractal World

Erosion

River Basins

River Flow

Most things made by nature are fractals

Birnir The Fractal Structure of the Universe

Th F l W ld

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The Fractal World

Erosion

River Basins

River Flow

Fractal Nautilus Shell

Birnir The Fractal Structure of the Universe

Th F t l W ld

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The Fractal World

Erosion

River Basins

River Flow

They come in beautiful self-similar shapes

Birnir The Fractal Structure of the Universe

The Fractal World

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The Fractal World

Erosion

River Basins

River Flow

Real Snowflakes

Birnir The Fractal Structure of the Universe

The Fractal World

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The Fractal World

Erosion

River Basins

River Flow

Fractals Shorelines

Birnir The Fractal Structure of the Universe

The Fractal World

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The Fractal World

Erosion

River Basins

River Flow

Fractal Shorelines and Fjords

Birnir The Fractal Structure of the Universe

The Fractal World

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The Fractal World

Erosion

River Basins

River Flow

Our Man-made World Consists of Boxes

Birnir The Fractal Structure of the Universe

The Fractal World

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The Fractal World

Erosion

River Basins

River Flow

We even tried to put the human body into a rectangle

Birnir The Fractal Structure of the Universe

The Fractal World

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Erosion

River Basins

River Flow

Most things made by nature are not rectangular or

circular

Birnir The Fractal Structure of the Universe

The Fractal World

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Erosion

River Basins

River Flow

Leafs and Tree-branches are fractals

Birnir The Fractal Structure of the Universe

The Fractal World

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Erosion

River Basins

River Flow

Fractal lightnings and crystals

Birnir The Fractal Structure of the Universe

The Fractal World

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Erosion

River Basins

River Flow

Perhaps life itself has a fractal structure

Birnir The Fractal Structure of the Universe

The Fractal World

E i

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Erosion

River Basins

River Flow

Outline

1 The Fractal World

2 Erosion

3 River Basins

4 River Flow

Birnir The Fractal Structure of the Universe

The Fractal World

E i

7/28/2019 The Hole Universe Ih Fractal

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Erosion

River Basins

River Flow

ErosionHow does the surface of the Earth evolve?

Birnir The Fractal Structure of the Universe

The Fractal World

Erosion

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Erosion

River Basins

River Flow

River Valleys with Uplift

Birnir The Fractal Structure of the Universe

The Fractal World

Erosion

7/28/2019 The Hole Universe Ih Fractal

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Erosion

River Basins

River Flow

Mountain Ranges are Fractals

Birnir The Fractal Structure of the Universe

The Fractal WorldErosion

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Erosion

River Basins

River Flow

The Merging of the Rivulets

Birnir The Fractal Structure of the Universe

The Fractal WorldErosion

7/28/2019 The Hole Universe Ih Fractal

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Erosion

River Basins

River Flow

Outline

1 The Fractal World

2 Erosion

3 River Basins

4 River Flow

Birnir The Fractal Structure of the Universe

The Fractal WorldErosion

7/28/2019 The Hole Universe Ih Fractal

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Erosion

River Basins

River Flow

The Cache la Poudre River Basin near Ft. Collins, COWe all live in a river basin

Birnir The Fractal Structure of the Universe

The Fractal WorldErosion

7/28/2019 The Hole Universe Ih Fractal

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River Basins

River Flow

The Amazon River Basin

Birnir The Fractal Structure of the Universe

The Fractal WorldErosion

7/28/2019 The Hole Universe Ih Fractal

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River Basins

River Flow

Outline

1 The Fractal World

2 Erosion

3 River Basins

4 River Flow

Birnir The Fractal Structure of the Universe

The Fractal WorldErosion

7/28/2019 The Hole Universe Ih Fractal

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River Basins

River Flow

Meanderings of the Mississippi

Birnir The Fractal Structure of the Universe

The Fractal WorldErosion

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River Basins

River Flow

A Drawing of an EddyStudies of Turbulence by Leonardo da Vinci

Birnir The Fractal Structure of the Universe