# Fractals - PowerPoint PPT Presentation

1 / 9

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.

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

Fractals

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 - - - - - - - - - - - - - - - - - - - - - - - - - -

## Fractals

• Two important properties of a fractal F

• F has detail at every level.

• F is exactly, approximately or statistically self-similar.

1/3

1/3

1

1/3

1/3

Generator

Iteration 0

Iteration 1

Iteration 2

Iteration 3

### Fractal Tree

Generator

Iteration 1 Iteration 2 Iteration 3 Iteration 4 Iteration 5

### Fractal Fern

Generator

Iteration 0 Iteration 1 Iteration 2 Iteration 3

### Fractal Landscapes

• fractals: not just for “showing math”

• triangle subdivision

• vertex displacement

• recursive until termination condition

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

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

• divide in half

• randomly displace

• scale variance by half

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