1. Under Choose Map, select Koch. Under Boxes, select size 16.
2. Under Boxes the offset x and y can take any values from 0 to the size of the boxes. For example, at size 16 setting the offsets to 8 puts the corners of the squares in the centers of the offset = 0 squares.
3. Do the box-count for x- and y-offsets of 0. Record the count.
4. With x- and y-offsets ranging from 0 to 15 (Do you see why offset = boxsize does not move hte grid?), there are 256 combinations of offsets. This is far too many to explore, so select several and count the boxes. Record the counts, along with the offsets.
5. Among those tried, select the grid offset that gave the largest difference in count from the offsets of 0. Use this offset with all box sizes to estimate the dimension of the Koch curve.
6. Compute the Koch curve dimension with offests 0. We know the dimension of the Koch curve is about 1.26. Is either experimental answer close? What questions does this suggest about the general process of computing box-counting dimensions?
Return to Procedure.