Self-Similarity Some examples. Self-Similarity in the Koch Curve Fractals usually possess what is...

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Self-Similarity Some examples

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Transcript of Self-Similarity Some examples. Self-Similarity in the Koch Curve Fractals usually possess what is...

Page 1: Self-Similarity Some examples. Self-Similarity in the Koch Curve Fractals usually possess what is called self-similarity across scales. That is, as one.

Self-Similarity

Some examples

Page 2: Self-Similarity Some examples. Self-Similarity in the Koch Curve Fractals usually possess what is called self-similarity across scales. That is, as one.

Self-Similarity in the Koch Curve

Fractals usually possess what is called self-similarity across scales.

That is, as one zooms in or out the geometry/ image has a similar (sometimes exact)

appearance.

Page 3: Self-Similarity Some examples. Self-Similarity in the Koch Curve Fractals usually possess what is called self-similarity across scales. That is, as one.

Self-Similarity in the Mandelbrot Set

Page 4: Self-Similarity Some examples. Self-Similarity in the Koch Curve Fractals usually possess what is called self-similarity across scales. That is, as one.
Page 5: Self-Similarity Some examples. Self-Similarity in the Koch Curve Fractals usually possess what is called self-similarity across scales. That is, as one.
Page 6: Self-Similarity Some examples. Self-Similarity in the Koch Curve Fractals usually possess what is called self-similarity across scales. That is, as one.

Self-similarity in Nature

Page 7: Self-Similarity Some examples. Self-Similarity in the Koch Curve Fractals usually possess what is called self-similarity across scales. That is, as one.

Natural: A picture of a fernHow do plants do it?

Mathematical: plant growth as simulated by a simple iterative procedure.

Page 8: Self-Similarity Some examples. Self-Similarity in the Koch Curve Fractals usually possess what is called self-similarity across scales. That is, as one.
Page 9: Self-Similarity Some examples. Self-Similarity in the Koch Curve Fractals usually possess what is called self-similarity across scales. That is, as one.

Is this a large piece of rugged terrain photographed from an aeroplane, or the side of a mountain, or a patch of dirt on the scale of a few meters, or a magnification of the surface of a rough rock?

Whichever it is, it could also easily be imagined to be any one of the others. So one could start at the large scale view from the air and apply successive zooms down to a microscopic scale, the surface maintains self similarity across those scales.


Self-Similar Sierpinski Fractals - University of California, Santa

Self-Similar Sierpinski Fractals - University of California, Santa

Fractals & Self Similarity

Fractals & Self Similarity

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

Self Similarity in Music

Self Similarity in Music

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

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

Self-similarity Properties of Natural Imagespapers.nips.cc/paper/1460-self-similarity-properties-of...Self-similarity Properties of Natural Images 839 linear) exponents: once the kernel

Self-similarity Properties of Natural Imagespapers.nips.cc/paper/1460-self-similarity-properties-of...Self-similarity Properties of Natural Images 839 linear) exponents: once the kernel

Fractals, Self-similarity and Hausdorff Dimensiontreiberg/FractalSlides.pdfUndergraduate Colloquium: Fractals, Self-similarity and Hausdor Dimension Andrejs Treibergs University of

Fractals, Self-similarity and Hausdorff Dimensiontreiberg/FractalSlides.pdfUndergraduate Colloquium: Fractals, Self-similarity and Hausdor Dimension Andrejs Treibergs University of

Fractals and Self-Similarity

Fractals and Self-Similarity

Scaling, Self-similarity, and Fractals - Mathkorevaar/fractals/fractalpictures.pdf · Scaling, Self-similarity, and Fractals • “Scaling” an object means stretching or shrinking

Scaling, Self-similarity, and Fractals - Mathkorevaar/fractals/fractalpictures.pdf · Scaling, Self-similarity, and Fractals • “Scaling” an object means stretching or shrinking

Hutchinson Fractals Self-Similarity

Hutchinson Fractals Self-Similarity

Fractals and the Mandelbrot Set - Meetupfiles.meetup.com/17097262/Peter's Fractal Notebook.pdf · And hence the reason that the Mandelbrot Set –Fractals and Self-Similarity have

Fractals and the Mandelbrot Set - Meetupfiles.meetup.com/17097262/Peter's Fractal Notebook.pdf · And hence the reason that the Mandelbrot Set –Fractals and Self-Similarity have

Fractals: A Brief Overview - Brothers Technology demonstrate a fourth type of symmetry; they possess “self-similarity.” Self-similar objects appear the same under magnification.

Fractals: A Brief Overview - Brothers Technology demonstrate a fourth type of symmetry; they possess “self-similarity.” Self-similar objects appear the same under magnification.

Complex Systems - Shlomo Havlinhavlin.biu.ac.il/PCS/lecture1.pdf · Complex Systems Shlomo Havlin Content: 1. Fractals: Fractals in Nature, mathematical fractals, self- similarity,

Complex Systems - Shlomo Havlinhavlin.biu.ac.il/PCS/lecture1.pdf · Complex Systems Shlomo Havlin Content: 1. Fractals: Fractals in Nature, mathematical fractals, self- similarity,

Creating Self Similar Tiling Patterns and Fractals using ...

Creating Self Similar Tiling Patterns and Fractals using ...

Fractalsreckert/460/lect25_2010_Fractals.pdfFractals Fractals Beautiful designs of infinite structure and complexity Qualities of Fractals: – Fractional dimension – Self similarity

Fractalsreckert/460/lect25_2010_Fractals.pdfFractals Fractals Beautiful designs of infinite structure and complexity Qualities of Fractals: – Fractional dimension – Self similarity

Chapter 6: Proportions and Similarity · fractals and nongeometric iteration. 280 Chapter 6 Proportions and SimilarityProportions and Similarity. ... 282 Chapter 6 Proportions and

Chapter 6: Proportions and Similarity · fractals and nongeometric iteration. 280 Chapter 6 Proportions and SimilarityProportions and Similarity. ... 282 Chapter 6 Proportions and

Fractals - SCCGsccg.sk/~samuelcik/fractal/Fractals_2.pdf · 2015. 2. 26. · Classical fractals Deterministic Self-similarity Approx. 100 years old Good for modeling Worst approximation

Fractals - SCCGsccg.sk/~samuelcik/fractal/Fractals_2.pdf · 2015. 2. 26. · Classical fractals Deterministic Self-similarity Approx. 100 years old Good for modeling Worst approximation

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

What are fractals? › “A fractal is an object or quantity that displays self-similarity, in a somewhat technical sense, on all scales. The object need.

What are fractals? › “A fractal is an object or quantity that displays self-similarity, in a somewhat technical sense, on all scales. The object need.

Chaos, fractals and self-organization in coastal ...download.xuebalib.com/xuebalib.com.20315.pdf · Chaos, fractals and self-organization in coastal geomorphology: simulating dune

Chaos, fractals and self-organization in coastal ...download.xuebalib.com/xuebalib.com.20315.pdf · Chaos, fractals and self-organization in coastal geomorphology: simulating dune