FRACTAL GEOMETRY: WHAT IS IT, AND WHAT DOES IT DO? · 2006-02-03 · fractal geometry: what is it, and what does it do? author: benoit b mandelbrot created date: 3/20/2003 2:53:46

Download PDF Report

Upload
others
View
2
Download
0

Embed Size (px)

Citation preview

$Page 1: FRACTAL GEOMETRY: WHAT IS IT, AND WHAT DOES IT DO? · 2006-02-03 · fractal geometry: what is it, and what does it do? author: benoit b mandelbrot created date: 3/20/2003 2:53:46$

$Page 2: FRACTAL GEOMETRY: WHAT IS IT, AND WHAT DOES IT DO? · 2006-02-03 · fractal geometry: what is it, and what does it do? author: benoit b mandelbrot created date: 3/20/2003 2:53:46$

$Page 3: FRACTAL GEOMETRY: WHAT IS IT, AND WHAT DOES IT DO? · 2006-02-03 · fractal geometry: what is it, and what does it do? author: benoit b mandelbrot created date: 3/20/2003 2:53:46$

$Page 4: FRACTAL GEOMETRY: WHAT IS IT, AND WHAT DOES IT DO? · 2006-02-03 · fractal geometry: what is it, and what does it do? author: benoit b mandelbrot created date: 3/20/2003 2:53:46$

$Page 5: FRACTAL GEOMETRY: WHAT IS IT, AND WHAT DOES IT DO? · 2006-02-03 · fractal geometry: what is it, and what does it do? author: benoit b mandelbrot created date: 3/20/2003 2:53:46$

$Page 6: FRACTAL GEOMETRY: WHAT IS IT, AND WHAT DOES IT DO? · 2006-02-03 · fractal geometry: what is it, and what does it do? author: benoit b mandelbrot created date: 3/20/2003 2:53:46$

$Page 7: FRACTAL GEOMETRY: WHAT IS IT, AND WHAT DOES IT DO? · 2006-02-03 · fractal geometry: what is it, and what does it do? author: benoit b mandelbrot created date: 3/20/2003 2:53:46$

$Page 8: FRACTAL GEOMETRY: WHAT IS IT, AND WHAT DOES IT DO? · 2006-02-03 · fractal geometry: what is it, and what does it do? author: benoit b mandelbrot created date: 3/20/2003 2:53:46$

$Page 9: FRACTAL GEOMETRY: WHAT IS IT, AND WHAT DOES IT DO? · 2006-02-03 · fractal geometry: what is it, and what does it do? author: benoit b mandelbrot created date: 3/20/2003 2:53:46$

$Page 10: FRACTAL GEOMETRY: WHAT IS IT, AND WHAT DOES IT DO? · 2006-02-03 · fractal geometry: what is it, and what does it do? author: benoit b mandelbrot created date: 3/20/2003 2:53:46$

$Page 11: FRACTAL GEOMETRY: WHAT IS IT, AND WHAT DOES IT DO? · 2006-02-03 · fractal geometry: what is it, and what does it do? author: benoit b mandelbrot created date: 3/20/2003 2:53:46$

$Page 12: FRACTAL GEOMETRY: WHAT IS IT, AND WHAT DOES IT DO? · 2006-02-03 · fractal geometry: what is it, and what does it do? author: benoit b mandelbrot created date: 3/20/2003 2:53:46$

$Page 13: FRACTAL GEOMETRY: WHAT IS IT, AND WHAT DOES IT DO? · 2006-02-03 · fractal geometry: what is it, and what does it do? author: benoit b mandelbrot created date: 3/20/2003 2:53:46$

$Page 14: FRACTAL GEOMETRY: WHAT IS IT, AND WHAT DOES IT DO? · 2006-02-03 · fractal geometry: what is it, and what does it do? author: benoit b mandelbrot created date: 3/20/2003 2:53:46$

$Page 15: FRACTAL GEOMETRY: WHAT IS IT, AND WHAT DOES IT DO? · 2006-02-03 · fractal geometry: what is it, and what does it do? author: benoit b mandelbrot created date: 3/20/2003 2:53:46$

$What does a fractal look like? - Radford Universitywacase/Math 116 Fractals.pdfMath 116 Fractals What is a fractal? A fractal is a geometric figure that is divided into smaller versions$

What does a fractal look like? - Radford Universitywacase/Math 116 Fractals.pdfMath 116 Fractals What is a fractal? A fractal is a geometric figure that is divided into smaller versions

Documents

$ON THE GRAMMARS OF FRACTAL SEQUENCESkmh.diva-portal.org/smash/get/diva2:721238/FULLTEXT01.pdf5 Introduction 1.1 FRACTAL SEQUENCES What defines a fractal sequence? What use do they$

ON THE GRAMMARS OF FRACTAL SEQUENCESkmh.diva-portal.org/smash/get/diva2:721238/FULLTEXT01.pdf5 Introduction 1.1 FRACTAL SEQUENCES What defines a fractal sequence? What use do they

Documents

Is It Live, or Is It Fractal? Bergren Forum September 3, 2009 Addison Frey, Presenter

Documents

$Lois d'échelle et transitions fractal – non fractal en ... · Scaling laws and fractal – non fractal transitions in geography Maxime Forriez*, Philippe Martin* et Laurent Nottale**$

Lois d'échelle et transitions fractal – non fractal en ... · Scaling laws and fractal – non fractal transitions in geography Maxime Forriez*, Philippe Martin* et Laurent Nottale**

Documents

$Introduction to Ultra Fractal · Ultra Fractal has two methods for saving a fractal. The first method saves a copy of the image and all the information needed to regenerate it in$

Introduction to Ultra Fractal · Ultra Fractal has two methods for saving a fractal. The first method saves a copy of the image and all the information needed to regenerate it in

Documents

The Fractal Technique - An Experiential Approach of Fractal Images … · The Fractal Technique - An Experiential Approach of Fractal Images in Reducing Perceived Stress Through Therapy

Documents

$Fractal geometry - mimuw.edu.plpawelst/rzut_oka/Zajecia... · difference between fractal geometry and calculus is that fractal geometry has not solved any problems. It is not even$

Fractal geometry - mimuw.edu.plpawelst/rzut_oka/Zajecia... · difference between fractal geometry and calculus is that fractal geometry has not solved any problems. It is not even

Documents

Rapid Prototyping Using Fractal Geometry - Fractal Navigator

Documents

$bioquest.orgbioquest.org/.../2014/06/Fractal-Analysis-Final2.docx · Web viewA fractal is not in a particular dimension, instead it is between dimensions. Fractals are rough geometric$

bioquest.orgbioquest.org/.../2014/06/Fractal-Analysis-Final2.docx · Web viewA fractal is not in a particular dimension, instead it is between dimensions. Fractals are rough geometric

Documents

$Fractal Robots(difference between nano robots and fractal robots)$

Fractal Robots(difference between nano robots and fractal robots)

Technology

$Fractal Geometries - GOUYET JFjfgouyet.fr › fractal › fractauk › chapter1.pdf · Fractal Geometries 1.1 Introduction The end of the 1970s saw the idea of fractal geometry spread$

Fractal Geometries - GOUYET JFjfgouyet.fr › fractal › fractauk › chapter1.pdf · Fractal Geometries 1.1 Introduction The end of the 1970s saw the idea of fractal geometry spread

Documents

$Fractals in nature. A fractal fern A fractal tree$

Fractals in nature. A fractal fern A fractal tree

Documents

$Fractal self similarity A fractal is a mathematical object that exhibits self similarity — it looks the same at any scale$

Documents

$A Fractal View of Lean - Lean Competency System · What is a Fractal View of Lean? The Fractal Foundation defines fractal as: ... by minimising waste applies at every scale of$

A Fractal View of Lean - Lean Competency System · What is a Fractal View of Lean? The Fractal Foundation defines fractal as: ... by minimising waste applies at every scale of

Documents

$Fractal Image Compression and - Queen's Universityresearch.cs.queensu.ca/.../850/papers/FractalImageCompression.pdf · Fractal image compression versus fractal geometry Whilc the$

Fractal Image Compression and - Queen's Universityresearch.cs.queensu.ca/.../850/papers/FractalImageCompression.pdf · Fractal image compression versus fractal geometry Whilc the

Documents

Fractal It y

Documents

$CONNECTING THE FRACTAL COASTzeta.math.utsa.edu/~yxk833/fractalcoast.pdf · 2. The fractal coast. A coastline is a fractal interface between land and sea. The word “fractal” means$

CONNECTING THE FRACTAL COASTzeta.math.utsa.edu/~yxk833/fractalcoast.pdf · 2. The fractal coast. A coastline is a fractal interface between land and sea. The word “fractal” means

Documents

$Fractals - University of New Mexicojoel/cs351/notes/Fractals-JoelCastellanos.pdf12 What is a Fractal? A fractal is something that is Self Similarity on Multiple Scales. Something is$

Fractals - University of New Mexicojoel/cs351/notes/Fractals-JoelCastellanos.pdf12 What is a Fractal? A fractal is something that is Self Similarity on Multiple Scales. Something is

Documents

On the Application of Fractal Geometry to Stream Networks€¦ · Fractals and Fractal Dimensions Self-similarity and Heavy Tails Fractal Dimension Complexity and Space-filling Fractal

Documents

$THE GLOBAL REVOLUTION IN ENERGY AND WHAT IT MEANS …eolstoragewe.blob.core.windows.net/wm-698609-cms... · Networks and mini-grids are increasingly radial, meshed and fractal, and$

THE GLOBAL REVOLUTION IN ENERGY AND WHAT IT MEANS …eolstoragewe.blob.core.windows.net/wm-698609-cms... · Networks and mini-grids are increasingly radial, meshed and fractal, and

Documents

A Minimal Fractal Music Fractal Music Composition Language

Documents

FRACTAL GEOMETRY: WHAT IS IT, AND WHAT DOES IT DO?

Documents

$Controlling Robots with Fractal Gene Regulatory Networksfractal.org › Fractal-Research-and-Products › Fractal-protein-robots.pdf · Controlling Robots with Fractal Gene Regulatory$

Controlling Robots with Fractal Gene Regulatory Networksfractal.org › Fractal-Research-and-Products › Fractal-protein-robots.pdf · Controlling Robots with Fractal Gene Regulatory

Documents

$Bruce Wayne Fractals. What is a Fractal? According to Benoit Mandelbrot … “A fractal is by definition is a set for which the Hausdorff-Besicovitch dimension$

Bruce Wayne Fractals. What is a Fractal? According to Benoit Mandelbrot … “A fractal is by definition is a set for which the Hausdorff-Besicovitch dimension

Documents

FRACTAL ROBOTS - Study Mafiastudymafia.org/wp-content/uploads/2015/03/mech-FRACTAL-ROBOTS... · CONCLUSION REFERENCES ... Fractal Robots A Fractal Robot physically resembles itself

Documents

Fractal Antennae and Coherence 1 Fractal Antennae and Coherence

Documents

Fractal Image Compression - Springer978-1-4612-2472-3/1.pdf · Preface What is "Fractal Image Compression," anyway? You will have to read the book to find out everything about it,

Documents

$Fractal coding based on image local fractal dimension FRACTAL CODING BASED ON IMAGE LOCAL FRACTAL DIMENSION comparedwithothersfractalimagecompressionmethods. Thepointsconsidered in$

Fractal coding based on image local fractal dimension FRACTAL CODING BASED ON IMAGE LOCAL FRACTAL DIMENSION comparedwithothersfractalimagecompressionmethods. Thepointsconsidered in

Documents

$Analysis and Development of Koch Fractal Dipole … · Analysis and Development of Koch Fractal Dipole ... The fractal conceit is been used for design antennas. The fractal ... “Fractal$

Analysis and Development of Koch Fractal Dipole … · Analysis and Development of Koch Fractal Dipole ... The fractal conceit is been used for design antennas. The fractal ... “Fractal

Documents