1 Choose a point inside the triangle and make a mark there with a dry wipe pen

2 Roll the die and use the result to select the appropriate corner of the triangle

3 Mark a new point half way between that corner and your previous mark

4 Repeat steps 2 and 3

The chaos game - instructions

How would you describe the pattern that forms?

Why are there no dots in the largest white triangular area?

Can you explain this pattern?

Sierpinski triangle

Now make your own Sierpinski triangle.

How many triangles do you need to draw in at each stage? What is the pattern?

How much of the remaining area are you shading in at each stage?

The connection with Pascal’s triangle

By filling in the number of routes to each block, construct a few more lines of Pascal’s triangle.

Now colour in the blocks that contain even numbers. What do you notice? Why do you think this happens?

1

1

11

1

1

1

1

1

1

1

1

1

2

3

4 6

10

20

5

6

3

4

10

5

15

15

6

11 35

35

21

21

77