Fractals
Download
1 / 9

Fractals - PowerPoint PPT Presentation


  • 192 Views
  • Uploaded on

Fractals. Two important properties of a fractal F F has detail at every level. F is exactly, approximately or statistically self-similar. Koch Fractals (Snowflakes). 1/3. 1/3. 1. 1/3. 1/3. Generator. Iteration 0. Iteration 1. Iteration 2. Iteration 3. Fractal Tree. Generator.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Fractals' - temima


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Fractals

Fractals

http://www.ugrad.cs.ubc.ca/~cs314/Vjan2010



Koch fractals snowflakes
Koch Fractals (Snowflakes)

1/3

1/3

1

1/3

1/3

Generator

Iteration 0

Iteration 1

Iteration 2

Iteration 3


Fractal tree
Fractal Tree

Generator

Iteration 1 Iteration 2 Iteration 3 Iteration 4 Iteration 5


Fractal fern
Fractal Fern

Generator

Iteration 0 Iteration 1 Iteration 2 Iteration 3


Fractal landscapes
Fractal Landscapes

  • fractals: not just for “showing math”

    • triangle subdivision

    • vertex displacement

    • recursive until termination condition

http://www.fractal-landscapes.co.uk/images.html


Fractal dimension

D = log(N)/log(r) N = measure, r = subdivision scale

Hausdorff dimension: noninteger

Fractal Dimension

  • Koch snowflake

coastline of Britain

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

http://www.vanderbilt.edu/AnS/psychology/cogsci/chaos/workshop/Fractals.html


1d midpoint displacement
1D: Midpoint Displacement

  • divide in half

  • randomly displace

  • scale variance by half

http://www.gameprogrammer.com/fractal.html


Mandelbrot set
Mandelbrot set

Demohttp://juliamap.googlelabs.com


ad