Koch island and archipelagoIn figure 1 the triangular extension is placed above the input line segment, and we call this the Koch function of type 1. It is also possible to place the triangular extension below the input line segment, as shown in figure 3, which is then called the Koch function of type 2.
Figure 3. The Koch function of type 2 Let us now begin with a perfectly shaped island of equilateral triangle. By some miraculous geological forces, the sides of triangle bulge outwardly to form an equilateral triangular extension of the type 1 Koch function and thereby resulting in a Star of David, as shown in figure 4. Using Prog#3b you may step through development of the Koch island up to the 4th generation, which is also called the Koch flake. Now, consider the Koch function of type 2, instead. This means a cataclysmic sinking of triangular landmass along each triangle side, and thus gives rise to three diamond shaped landmasses, similar to the Mitsubishi emblem. By Prog#3c you can iterate the type 2 Koch function four times to obtain three chains of small islands, and hence the Koch archipelago.
Figure 4. First iteration of the Koch functions of type 1 and 2
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