Fractals can be strange. They're not quite full shapes, but they're definitely more than just lines. This thought led to the idea of the Hausdorff Dimension, placing fractals in between dimensions.
0:00 Dimensions
0:19 How long is the coastline of Britain?
2:10 Fractals
3:16 Hausdorff Dimension
6:13 Fractals with Integer Dimension?
7:42 What Dimension is the coastline of Britain?