Third Homework Set Answers

4a On the left is the completed table, on the right is the graph.
  r    N(r)    1/r    Log(1/r)    Log(N(r))  
.442.50.3980.60
.42166.250.7961.204
.434315.6251.1941.806
.444439.0631.5922.408
.454597.6561.9903.010
.4646244.142.3883.612
The points appear to fall along a straight line; the slope of this line is the box-counting dimension. We measure dim = (3.612 - 0.60)/(2.388 - .398) = 1.513.

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