Plot the points
| (Log(1/r0),Log(N(r0))) | = (Log(1), Log(1)) | = (0, 0) |
| (Log(1/r1),Log(N(r1))) | = (Log(2), Log(3)) | = (0.301, 0.477) |
| (Log(1/r2),Log(N(r2))) | = (Log(4), Log(10)) | = (0.602, 1.0) |
| (Log(1/r3),Log(N(r3))) | = (Log(8), Log(36)) | = (0.903, 1.556) |
| (Log(1/r4),Log(N(r4))) | = (Log(16), Log(136)) | = (1.204, 2.134) |
| ... |
(the graph shows a greater range, and more widely spaced, points than these) and see if they lie approxiamtely on a straight line of slope 2.
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Indeed, the points do appear to lie approximately along a straight line of slope 2. The fit is not perfect because the squares cover more than the triangle.Return to Box-Counting Dimension of a Filled-in Triangle.