Box-Counting Dimension of the Koch curve

Plotting the points

(Log(1/r0),Log(N(r0)))	= (Log(1), Log(1))	= (0,0)
(Log(1/r1),Log(N(r1)))	= (Log(3), Log(4))	= (0.477, 0.602)
(Log(1/r2),Log(N(r2)))	= (Log(9), Log(12))	= (0.954, 1.079)
(Log(1/r3),Log(N(r3)))	= (Log(27), Log(48))	= (1.431, 1.681)
(Log(1/r4),Log(N(r4)))	= (Log(81), Log(192))	= (1.908, 2.283)
...

(the graph shows a greater range, and more widely spaced, points than these) we see they lie on a straight line of slope about 1.26.

So the box-counting dimension of the Koch curve is about 1.26.

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