Sierpinski triangle: A local lumberyard has teak wood floor inlays in equilateral triangle of side 1 ft. Since it is too costly to cover the entire floor, a plan is to accent the floor by laying them sparingly in the Sierpinski triangle pattern, as shown in figure 7. With the triangular inlay of side 1ft, it requires 3 inlays for the first Sierpinski triangle of side 2 ft and 9 inlays for the second Sierpinski triangle of side 4 ft, as listed in table 5.

Figure 7. Triangular inlays

Table 5. Floor covering by triangular inlays of side 1 ft.

From the straight-line plot of x versus y in figure 8, we compute the dimension 1.58 by formula (1). Again, it is a non-integer dimension and less than d = 2 for a solid triangle.

Figure 8.  Log-log plot of table 5

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