1. 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
2. How would you
describe the
pattern that
forms?
Why are there no
dots in the largest
white triangular
area?
Can you explain
this pattern?
4. 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?
5. 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
1515 6
11 3535 2121 77
6. 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
1515 6
11 3535 2121 77
