Fractal Drawing!

What is a FRACTAL?

MATERIALS

• A piece of paper
• Something to draw with

First, a Binary Tree

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1. Start at the top of your paper with one short vertical line.
2. Split the line into two lines, both going down left/right.
3. Repeat step 2! A very simple fractal shape. Eventually it will get hard to fit in all the pairs of lines!

Next, Sierpiński Triangle

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• Draw a very large equilateral triangle, as big as you can.
• Draw an upside down equilateral triangle inset inside the larger triangle, each point touching an edge.
• Repeat step 3 on each of the resulting 3 smaller triangles, continuing to do so until the triangles get too small.

Then, Koch Snowflake

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• Draw a very large equilateral triangle, as big as you can.
• In the middle of each edge, erase ⅓ of the line.
• Draw two lines to connect it in an equilateral triangle.
• Repeat steps 2 and 3 for each newly made triangle until the triangles get too small to continue.

Then, an H-Tree

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• Draw a line in the center of your paper.
• On the ends of your line, draw perpendicular lines. This should form an H shape.
• Repeat step 2 on the end of every line until the H’s get too small for you to keep going!

Now, The Dragon Curve

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• Draw a short line in the center of your paper.
• Draw a copy of that line rotated 90 degrees at the end of the line.
• Rotate a copy of the whole shape 90 degrees and draw it at the end of the previous line you just drew.
• Repeat step 3! The copied shape will get bigger and may overlap other parts of the whole fractal as you go.

Finally, Sierpiński Carpet

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• Draw a large square on your paper, as big as you can.
• Divide the square into 9 equally sized smaller squares.
• Fill in the center smaller square of the 9.
• For each of the 8 remaining squares, repeat step 2.
• Keep repeating until the squares get too small!