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Page 1: TEDxFulbright2017FractalsCS380 Talk 1mathcircle.berkeley.edu/sites/default/files/handouts/2020... · Fractals - the geometry of nature ... Use Machine Learning to find DNA for classification:

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• ``

Prof. Bernt WahlFractals - the geometry of nature

Page 2: TEDxFulbright2017FractalsCS380 Talk 1mathcircle.berkeley.edu/sites/default/files/handouts/2020... · Fractals - the geometry of nature ... Use Machine Learning to find DNA for classification:

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“ Mountains are not cones, clouds are not spheres and bark is not smooth nor does lightning travel in a straight line.”

Benoit Mandelbrot

Fractals: The Geometry of Nature

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Gallery of Monsters

Art Architecture

Page 4: TEDxFulbright2017FractalsCS380 Talk 1mathcircle.berkeley.edu/sites/default/files/handouts/2020... · Fractals - the geometry of nature ... Use Machine Learning to find DNA for classification:

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Linear Fractals Nonlinear Fractals

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Fractal Classes

Page 5: TEDxFulbright2017FractalsCS380 Talk 1mathcircle.berkeley.edu/sites/default/files/handouts/2020... · Fractals - the geometry of nature ... Use Machine Learning to find DNA for classification:

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World of Mathematics

Page 6: TEDxFulbright2017FractalsCS380 Talk 1mathcircle.berkeley.edu/sites/default/files/handouts/2020... · Fractals - the geometry of nature ... Use Machine Learning to find DNA for classification:

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Linear Fractals

Page 7: TEDxFulbright2017FractalsCS380 Talk 1mathcircle.berkeley.edu/sites/default/files/handouts/2020... · Fractals - the geometry of nature ... Use Machine Learning to find DNA for classification:

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Koch Curve

Page 8: TEDxFulbright2017FractalsCS380 Talk 1mathcircle.berkeley.edu/sites/default/files/handouts/2020... · Fractals - the geometry of nature ... Use Machine Learning to find DNA for classification:

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Dragon Curve

Page 9: TEDxFulbright2017FractalsCS380 Talk 1mathcircle.berkeley.edu/sites/default/files/handouts/2020... · Fractals - the geometry of nature ... Use Machine Learning to find DNA for classification:

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Measuring a Coastline

Page 10: TEDxFulbright2017FractalsCS380 Talk 1mathcircle.berkeley.edu/sites/default/files/handouts/2020... · Fractals - the geometry of nature ... Use Machine Learning to find DNA for classification:

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Nonlinear Fractals

Page 11: TEDxFulbright2017FractalsCS380 Talk 1mathcircle.berkeley.edu/sites/default/files/handouts/2020... · Fractals - the geometry of nature ... Use Machine Learning to find DNA for classification:

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Mandelbrot and Julia Sets

Page 12: TEDxFulbright2017FractalsCS380 Talk 1mathcircle.berkeley.edu/sites/default/files/handouts/2020... · Fractals - the geometry of nature ... Use Machine Learning to find DNA for classification:

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Fractals in Our World

Page 13: TEDxFulbright2017FractalsCS380 Talk 1mathcircle.berkeley.edu/sites/default/files/handouts/2020... · Fractals - the geometry of nature ... Use Machine Learning to find DNA for classification:

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Culture

Page 14: TEDxFulbright2017FractalsCS380 Talk 1mathcircle.berkeley.edu/sites/default/files/handouts/2020... · Fractals - the geometry of nature ... Use Machine Learning to find DNA for classification:

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Art

Page 15: TEDxFulbright2017FractalsCS380 Talk 1mathcircle.berkeley.edu/sites/default/files/handouts/2020... · Fractals - the geometry of nature ... Use Machine Learning to find DNA for classification:

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Fashion

•https://youtu.be/luRhy2aimRI

Page 16: TEDxFulbright2017FractalsCS380 Talk 1mathcircle.berkeley.edu/sites/default/files/handouts/2020... · Fractals - the geometry of nature ... Use Machine Learning to find DNA for classification:

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Elm tree branch with .

Trees

Fractal out line of a European beech with

Acacia or Umbrella Tree with

Use Machine Learning to find DNA for classification: structure patterns, randomness

Penta Flakes and Fractals for High school students [20th Century Geometry]

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Gradients on Fractals - Jan Römanjanroman.dhis.org/finance/Related to Fractals/fractals/fractals.pdf · Gradients on Fractals Alexander Teplyaev1 Department of Mathematics, McMaster

CHRONICLE OF MEETINGS ON FRACTAL GEOMETRY (Chronicle... · CHRONICLE OF MEETINGS ON FRACTAL GEOMETRY ... ON FRACTALS AND/OR SELF-SIMILAR RANDOM PROCESSES, ... Statistics, Fractals

Fractals - Binghamton › ~reckert › 460 › lect25_2009_Fractals.pdf · Fractals Fractals Beautiful designs of infinite structure and complexity Qualities of Fractals: – Fractional

10. MOLECULAR GEOMETRY AND CHEMICAL BONDING …teachers.sduhsd.net/kshakeri/AP_Chemistry_Pages/Handouts/Chapter... · 10. MOLECULAR GEOMETRY AND CHEMICAL BONDING THEORY ... Each N–H

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STATISTICAL PROPERTIES OF RANDOM FRACTALS ...lib.tkk.fi/Diss/2002/isbn9512262053/isbn9512262053.pdfJoonas Asikainen: Statistical properties of random fractals: geometry, growth and

Fractals - University of Calgary in Alberta · 2002. 4. 17. · Fractals Self Similarity and Fractal Geometry presented by Pauline Jepp 601.73 Biological Computing. Overview History

Quasiconformal geometry of fractals - International Congress of

Fractals: properties and applicationsConclusions: Fractal properties •Fractals exhibit fractal dimensions: all objects whose dimension is not an integer are fractals. •Fractals

1 The Geometry of Linear Programs –the geometry of LPs illustrated on GTC Handouts: Lecture Notes 15.053February 5, 2002

Analytic Geometry Handouts (1)

1: Geometry and Distance - Harvard Mathematics Departmentknill/teaching/summer2017/handouts/week1.pdf · 1: Geometry and Distance The geometry of Euclidean space like the plane R2

Time Series via Fractals Geometry

GEOMETRY INSTITUTE - DAY 4Project MATHEMATICS! (1995) TEXTEAM Geometry Institute 4.6 THE TUNNEL OF SAMOS ... • Applications • Trigonometry • Fractals (will be looked at on Day

Lectures on fractal geometry and dynamics - math.huji.ac.ilmath.huji.ac.il/~mhochman/courses/fractals-2012/course-notes.june... · Lectures on fractal geometry and dynamics Michael

GLSL Geometry Shaders - Oregon State Universityweb.engr.oregonstate.edu/~mjb/cs519/Handouts/geometry_shaders.2pp.pdf · 1 mjb –February 15, 2018 1 Computer Graphics GLSL Geometry

Introduction to Fractals and Julia Sets · 1.1 Fractals and a fresh look at the world Much of classical geometry is concerned with the study smooth and regular forms. Indeed, throughout

Lectures on fractal geometry and dynamicsmath.huji.ac.il/~mhochman/courses/fractals-2012/course-notes.marc… · Fractal geometry and its sibling, geometric measure theory, are branches

PMA443 Fractals 2009{10 1 Introduction to · PDF filePMA443 Fractals 2009{10 1 Introduction to fractals ... ‘Fractals everywhere 2/e’ ... Gerald A Edgar ‘Classics on Fractals’

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