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The Chaos Game
by Michael Barnsley
1, 2
3, 4
1. Choose a point in the triangle at
random
2. Throw the die
3. Move the point half way
towards that point
4. Go back to 2.
5. After six throws start marking
each point on the OHT with a
5, 6
small dot
6. Keep going
The Chaos Game
Note to teachers:
1, 2
If each group does this on a
piece of acetate then the impact
will be greater when you
superimpose their results onto
an OHP
3, 4
5, 6
Strange Attractors
An explanation of the Sierpinski Triangle
In actuality, the orbit of any
point that starts in any of the
removed triangles will never
“reach” the Sierpinski
triangle (S).
Sierpinski triangle.xls
It will continue to lie in smaller
and smaller removed triangles
until it looks as though it lies on
S.
We say that S is a strange
attractor.
Constructing Sierpinski’s
Triangle