During yesterday’s group work, which included a discussion of Pascal’s Triangle, I overheard some groups mention Sierpinski’s Triangle, which they had seen some in Geometry last year. That led to today’s opener, an applet from the awesomely mathy site Cut The Knot:
In the “Chaos Game” a point be-bops about a triangle under specific rules:
- The red point starts one of 3 randomly selected vertices of the triangle.
- Next, one of the 3 vertices is randomly selected, and the red point moves half-towards this new point.
- The process is repeated over and over, and all landing points are marked.
At first, I have the applet run slowly, and students don’t quite absorb what is happening. But as we speed up the animation, something interesting develops….
Our old friend, Sierpinski’s Triangle! Later in the period we saw this famous structure again when discussing Pascal’s Triangle and factors. Check out this cool coloring remainders applet and have fun!