Fractals
NSW Syllabus

NSW Secondary High School Stage 5 Mathematics � Additional Content

Dr T, 2004

To see a World in a Grain of Sand
And a Heaven in a Wild Flower,
Hold Infinity in the palm of your hand
And Eternity in an hour.

William Blake, "Auguries of Innocence" (c. 1803)

A fractal is infinitely detailed, with parts of itself similar to all of itself.

The pictures below illustrate the structure of some of the more well known self-similar fractals. Click to animate.

There are links to worksheets to help you explore the many interesting patterns and relationships in various fractals.

Suggestion: Read the "notes on series" before attempting the worksheets.

notes on series

Sierpinski Fractals

Sierpinski Carpet

worksheet

Sierpinski Triangle

worksheet

Fractal Trees

Binary Tree Construction

worksheet

H Fractal

worksheet

Binary Tree in Motion

Fibonacci Tree Construction

worksheet

Fibonacci Tree Patterns

Pythagoras Trees

Symmetric Pythagoras Tree

worksheet

Asymmetric Pythagoras Tree in Motion

Pythagoras Tree with Hexagons

Pythagoras Tree with Octagons

Koch Snowflakes and Modified Snowflakes

Koch Snowflake

worksheet

Koch Anti-Snowflake

worksheet

Torn Square Construction

Torn Square in Motion

Square Snowflake

worksheet

Square Anti-Snowflake

worksheet

Minkowski Sausage

worksheet

Cantor Dust

worksheet

Cantor Square Dust

Hilbert Space Filling Curve




Back to Resources Back to Top

Produced by Dr T
2004

 

Hosted by www.Geocities.ws

1