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| rn | N(rn) | 1/rn | Log(1/rn) | Log(N(rn)) |
|---|---|---|---|---|
| 1 | 1 | 1 | 0 | 0 |
| 1/3 | 6 | 3 | .477 | .778 |
| 1/9 | 36 | 9 | .954 | 1.556 |
| 1/27 | 216 | 27 | 1.431 | 2.334 |
| 1/81 | 1296 | 81 | 1.908 | 3.113 |
| 1/243 | 7776 | 243 | 2.386 | 3.891 |
| Here is the log-log plot. |
| Here we compute the exact value of the dimension. |
| We can cover this fractal with 6 boxes of side 1/3. Self-similarity guarantees we need 36 boxes of side 1/9, and in general, 6n boxes of side 1/3n. | |||||||||||||||||||||||||||||||||||
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| From this, we fill in the table | |||||||||||||||||||||||||||||||||||
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Return to Box-Counting Dimension Practice Problems.