What are fractals?

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What are fractals?

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What are fractals?. What are fractals?. Romanesco. What are fractals?. What are fractals?. What are fractals?. What are fractals?. What are fractals?. What are fractals?. Golden ratio = 1.61803398875. How to create a Koch snowflake:. Fractal dimension? Point = 0-D Line = 1-D - PowerPoint PPT Presentation

Transcript of What are fractals?

$Page 1: What are fractals?$

What are fractals?

$Page 2: What are fractals?$

What are fractals?

Romanesco

$Page 3: What are fractals?$

What are fractals?

$Page 4: What are fractals?$

What are fractals?

$Page 5: What are fractals?$

What are fractals?

$Page 6: What are fractals?$

What are fractals?

$Page 7: What are fractals?$

What are fractals?

$Page 8: What are fractals?$

What are fractals?

Golden ratio = 1.61803398875

$Page 9: What are fractals?$

How to create a Koch snowflake:

$Page 10: What are fractals?$

$Page 11: What are fractals?$

$Page 12: What are fractals?$

$Page 13: What are fractals?$

Fractal dimension?

-Point = 0-D

-Line = 1-D

-Area = 2-D

-Volume 3-D

1.26

$Page 14: What are fractals?$

Four identical line segments that are each 1/3 long, the dimension is log 4 / log 3, which is approximately 1.26.

D = log(4)/log(3) = 1.26

$Page 15: What are fractals?$

1990. Sugihara, G., and R.M. May. Applications of fractals in ecology. Trends in Ecol. and Evol. 5(3): 79-86.

$Fractals - cse.unt.educse.unt.edu/~renka/4230/Fractals.pdfIntroduction In graphics, fractals are used to produce natural scenes with irregular shapes, such as coastlines, clouds, forests,$

Fractals - cse.unt.educse.unt.edu/~renka/4230/Fractals.pdfIntroduction In graphics, fractals are used to produce natural scenes with irregular shapes, such as coastlines, clouds, forests,

$Fractals & Iterative Function Systems - Computer Science · Random Fractals ! Random fractals are " randomly generated curves that exhibit self-similarity, or " deterministic fractals$

Fractals & Iterative Function Systems - Computer Science · Random Fractals ! Random fractals are " randomly generated curves that exhibit self-similarity, or " deterministic fractals

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Fractals, Multi-Fractals, Psuedo- Fractals and Non-Fractals in Energy Spectral Techniques Francis Vaughan (Archimedes Consulting) EAGE Workshop on Non.

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Fractals presentation

Fractals presentation

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

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

$Lecture 13 3.4 Recursive Definitions. Fractals fractals are examples of images where the same elements is being recursively.$

Lecture 13 3.4 Recursive Definitions. Fractals fractals are examples of images where the same elements is being recursively.

Fractals GEOMETRY

Fractals GEOMETRY

Fractals - cs.bham.ac.uk · Fractals are geometric shapes that model structures in nature. They are rough or fragmented geometric shapes that can be subdivided into parts, each of

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Heavenly Fractals

Heavenly Fractals

$Fractals - the ultimate art of mathematics ultimate art … · Fractals - the ultimate art of mathematics Adam Kozak. Outline What is fractal? Self-similarity dimension Fractal types$

Fractals - the ultimate art of mathematics ultimate art … · Fractals - the ultimate art of mathematics Adam Kozak. Outline What is fractal? Self-similarity dimension Fractal types

$Fractalssierra.nmsu.edu/.../math210Fall2014/Lectures/Fractals-web.pdfFractals are shapes which exhibit self-similarity. We’ll explore what this means shortly. The term fractal was$

Fractalssierra.nmsu.edu/.../math210Fall2014/Lectures/Fractals-web.pdfFractals are shapes which exhibit self-similarity. We’ll explore what this means shortly. The term fractal was

Fractals - University of Birmingham · 2012-12-05 · Fractals are geometric shapes that model structures in nature. They are rough or fragmented geometric shapes that can be subdivided

Fractals - University of Birmingham · 2012-12-05 · Fractals are geometric shapes that model structures in nature. They are rough or fragmented geometric shapes that can be subdivided

FRACTALS - How to write a proposal for FRACTALS

FRACTALS - How to write a proposal for FRACTALS

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

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

Fractals, Scaling and Renormalization (1) · Irregular Fractals are not Random! We make them by using an asymmetric or irregular generation rule. They are produced with a deterministic

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Fractals - OpenTextBookStore Fractals are mathematical sets, usually obtained through recursion, that exhibit interesting dimensional properties. We’ll explore …

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$The Broken Past: Fractals in Archaeologywise.fau.edu/~ctbrown/The Broken Past Fractals in... · The Broken Past: Fractals in Archaeology 39 Third, fractals are not only descriptive—they$

The Broken Past: Fractals in Archaeologywise.fau.edu/~ctbrown/The Broken Past Fractals in... · The Broken Past: Fractals in Archaeology 39 Third, fractals are not only descriptive—they

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