Since this region is composed of 45-45-90 triangles, there are two types of tiles. One is formed by putting two triangles together by their hypotenuses, a square is formed. Putting two triangles together by their legs will form a larger 45-45-90 triangle. Since some of the vertices project eight edges, fortresses converge much slower than simpler regions like Aztec Diamonds and Hexagons. However, once randomized, a fortress seems to exhibit behavior like that of an Aztec Diamond. The arctic boundary, however, is not believed to be circular and is still being researched. This may prove for challenging that the Aztec Diamond and Hexagon since large samples are difficult to produce and its shape is most likely more complex.
Note: clicking the mouse within the applet will pause or resume the randomization process.