| 1. (n) This fractal consists of N = 4 pieces, with r1 = r2 = 1/2 and r3 = r4 = 1/4. The dimension, d, is the solution of the Moran equation |
| 2(1/2)d + 2(1/4)d = 1 |
| Taking x = (1/2)d, the Moran equation becomes the quadratic equation |
| 2x2 + 2x - 1 = 0 |
| The positive solution is x = (-1 + √3)/2. |
| Solving x = (1/2)d for d gives |
| d = Log((-1 + √3)/2)/Log(1/2), approximately 1.450. |
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