|
Cantor gasket We can apply the Cantor function not only to triangles (figure 2) but also to a square. This then is the Cantor gasket function, as described by the function diagram of figure 4. It splits an input square into 9 equal squares and throws away the center one. Next, by applying the Cantor gasket function to each of 8 small squares, we get 64 ( = 8 x 8 ) smaller squares of the second generation, and so on. For instance, from the original square of side 13.5cm, there are 8 small squares of side 4.5cm ( = 13.5 / 3 ) of the first generation. We then break up each of the 8 small squares into 9 smaller squares of side 1.5cm ( = 4.5 / 3 ) for the second generation, and so on. With Prog#5c you may step through iterations of the Cantor gasket function up to the fourth generation.
Figure 4. Cantor gasket
|
