what are fractals?

15

What are fractals?

Upload: metea

Post on 06-Jan-2016

66 views

Category:

Documents

1 download

Report

Download

Tags:

Embed Size (px):

DESCRIPTION

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

$Page 1: What are fractals?$

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.

An Exploration of Fractals - vigyanpratibha.invigyanpratibha.in/wp-content/uploads/2019/10/M_Fractals_Students_… · An Exploration of Fractals An introduction to the lesson: What

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

Footprints of bees are fractals, complexity of bee training

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

Chronicle Fractals

Fractals and Chaos - Iowa State Universityorion.math.iastate.edu › dept › thesisarchive › MSM › BrincksMSMF06… · fractals are easier for students to understand than Euclidean

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

FRACTALS - Union University do fractals have to do with chaos? Fractals have some of the same chaotic characteristics. Fractals are: Sensitive to small changes Unpredictable Appear

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

15-fractals - University of Birmingham · 2011. 11. 17. · Fractals are geometric shapes that model structures in nature. They are rough or fragmented geometric shapes that can be

Fractals. Similar Figures Same shape Corresponding angles are congruent Corresponding sides are proportional

Fractals - computergraphics2015.files.wordpress.com€¦ · Classification •Self Similar •fractals have parts that are scaled down versions of the entire object, we construct

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: properties and applications - Applied Mathematics · 2016. 3. 29. · • Fractals are . self-similar. d = 1.2683. Fractals - mathematical objects Mandelbrot set. Variation

FRACTALS IN PUPILLARY OSCILLATION …Fractals can be either statistical or mathematical (Fairbanks & Taylor, 2011). Statistical fractals are common in natural processes and natural

FRACTALS - How to write a proposal for FRACTALS

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’

Fractals Are Really Beautiful Mathematics

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

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

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

Strictly self-similar fractals composed of star-polygons that are … · 2015-02-06 · Strictly self-similar fractals composed of star-polygons that are attractors of Iterated Function

Fractals and Chaos: Things are Complex

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

Heavenly Fractals

Fractals GEOMETRY

Educators’ Guide - Fractal Foundation · Fractals Are SMART: Science, Math & Art! All contents copyright 2009 FractalFoundation ALGEBRAIC FRACTALS We can also create fractals by

Fractals and fractals in nature ● What are fractals? ● A fractal can be defined as a geometric object which repeats itself in his structure in the same

SNOWFLAKES AND FRACTALS PRESENTATION · snowflakes and fractals ... • Snowflakes are not merely frozen water, as they exhibit crystalline structures. • Variations in snowflake

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

Fractals and Art - objects in mind are closer than they appear