On a piece of paper, draw a triangle (any triangle -right angled, equilateral, isosceles, scalene). Colour one of the vertices red, the second blue, and the third green.
Next, take three dice – one red, one blue, and one green.
Now draw a point in the triangle. This point is the seed for the game. Then roll the die. Whichever die shows the highest number (throw again if there is a tie for the highest), draw a point halfway inbetween the seed and the appropriately colored vertex. Now do the same, using your new point as the seed for the next. After a few rolls you might have a drawing like this:
Now continue in this fashion for five rolls of the dice. Then rub out all the points except the most recent seed and the coloured points.
Now carry on but don’t erase any points.
Can you guess what pattern your points are going to make? You might be surprised!
You might want to use technology to help you find out. Here are some instructions for using geogebra.