Tuesday, March 27, 2007

Fractals

How do you know when you see a fractal in nature? A fractal is a rough or fragmented geometric shape that can be subdivided in parts, each or which is a reduced size copy of the whole. This means that they usually contain little copies of themselves buried deep within the original (Fractal). Fractals are plentiful in nature. A simple example is twigs on trees look like the branches which they grow on, which look like the tree itself. This fits the profile of fractal as the parts of the tree are copies of the larger unit, the whole tree. With this knowledge, it is easier to see how fractals are hiding in your back yard.There are many different examples of fractals in nature that are sure to stimulate students in a classroom. Maybe the most famous fractal is the snowflake. http://library.thinkquest.org/26242/full/fm/fm33.html
This link illustrates how a snowflake is a fractal. It goes through the steps of creation and provides a visual of the smaller parts being similar to the snowflake as a whole. Viewing this site would give students insight to fractals as they apply to nature. Another famous natural fractal is the fern. Fractals are found in many plants but are very obvious in the fern. Students would be able to recognize the properties of fractals easily. The smaller leafs of the shrub are replicas of the plant as a whole. Providing students with concrete examples of fractals makes learning about them much more simplified. Students can carry their knowledge of fractals into their everyday lives and recognize other examples in nature and manmade objects. There are many other fractals in nature that include clouds, mountains, river networks, cauliflower or broccoli, and systems of blood vessels and pulmonary vessels. Fractals are applicable to a variety of fields such as medicine, business, geology, art, and music. They can be taught using nature’s examples as well as games such as Chaos. http://math.bu.edu/DYSYS/applets/chaos-game.html

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