What would happen if we used just three vertices
|
As with the square, we start with a point in the triangle. (In this example, it's on the edge of the triangle, but that's still in the triangle.) |
Each move is half-way between where we are and a corner of the triangle, so we never leave the triangle. |
Because we select the corners randomly, no part of the triangle is preferred over any other. |
So since some parts of the triangle fill in, all parts must fill in. |
Thus played with three vertices of a triangle, the chaos game should fill in the triangle. Right? |
Here is the answer. |
Perhaps we should rethink the reasons given at the end of Chaos Game Examples. |
Here are four more Chaos Game examples. Try to determine the shape before running the program or looking at the answer. |
Example 1: vertices the corners of a
square, |
Example 2: move the top right
vertex to the left, |
Example 3: five vertices, four the
corners of a square, one at the center of the square, |
Example 4: five vertices, four the
corners of a square, one at the center of the square, |
Return to the Chaos Game.