Jurassic Park fractal (Dragon curve)

Have you ever read Michael Crichton's book, Jurassic Park? On such book it appears a very weird shape called dragon curve. And of course, it is a fractal. Today we'll discover more things about it.

 

After watching the videos you have to construct such a fractal using a strip of paper. You have to fold the strip very careful from left to right, several times. Do at least 4 iterations and see what happens.

Pythagorean tree

Another quite amazing fractal is the Pythagorean Tree. Do you know why it has such a name? Let's try to construct one!

Koch snowflake

Taken from https://smist08.wordpress.com/tag/koch-snowflake/

Today we are going to learn about one of the first fractals that where studied. Watch the following two videos and afterwards try to do the related activities.

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Activities

1. Draw a Koch snowflake in a triangular grid. Do at least 3 iterations.
2. Why is the Koch snowflake considered a fractal?
3. Why the Koch snowflake is said to have an infinite perimeter? Explain it with your own words and equations.
4. What happens if you perform an infinite number of iterations?
5. How do you know that the area enclosed by the Koch Snowflake is finite?
6. What is the Australian coastline paradox?
7. Why the Australian and the English coastlines are said to be fractals?
8. What do the Australian coastline and Koch Snowflake have in common?

Fractals and infinite series

Doodling in math: Infinity elephants

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Activities

After watching the video, try to solve the following qüestions:

1. What is an infinite series? Can you give an exemple?
2. What does it mean that an infinite sum approaches to 1? Explain it with your own words
3. Which relationship exist between fractals and infinite series?
4. What is an Apollonian gasket? How is it generated?
5. Try to drawn a fractal that yields into an infinite series. You can take the ones that appear in the video as an exemple. 

A Giant Sierpinski's Triangle

Taken from http://paulbourke.net/fractals/gasket/

Today we'll face a challenge: we'll design a giant Sierpinski's Triangle made of all your individual ones. In order to construct such a figure, we have to organize the work:

• Gather in groups of 4 or 5 people
• Within your group you should draw a scheme of a giant Sierpinski's triangle using the 26 small triangles we built in class:
• Take the measurements of one small triangle
• Make a sketch of the big composition with all the measurements
• How many small triangles will you use?
• How long is the side and the height of the big triangle?
• Will the big triangle fit in a wall of our school corredor?