Explore Sierpinski's Triangle 2

Making Sierpinski's Triangle… Again Let's do something completely different: Draw three dots to represent the corners of an equilateral triangle. Label one dot with "1 & 2", one dot with "3 & 4", and the last dot with "5 & 6". Roll a six-sided die to select a current location (start at the dot matching the number rolled). Roll a die to choose a target destination dot. Find the point exactly half-way between your current location and your target destination. Draw a dot there. This is now your new current location. Repeat steps 4 and 5, ad infinitum. To see this in action, press the "Start" button to the right (the bottom-left corner is 1 & 2, the top corner is 3 & 4, and the bottom-right corner is 5 & 6). Give it a few seconds - the Sierpinski Triangle gradually appears. But wait - there was nothing random about what we did last time. This time it turns out, if the process isn't random, we won't see the whole triangle. What's going on? Take a detour to Cantor Dusts. Take a detour to Chaos Games. Continue with Explore Sierpinski's Triangle.