Research Article
Exploring the Fractal Parameters of Urban Growth and Form with Wave-Spectrum Analysis
Table 2
Comparison between the fractal dimension values of an imaginary city form and its estimated results from the spectral exponent.
| Length of sample path (N) | Radial dimension | Spectral exponent (β) | Goodness of fit | Estimation of | Estimation of | Square error |
| 256 | 1.0500 | 0.8684 | 0.9919 | 1.4342 | 2.0658 | 0.1476 | 1.2500 | 1.0044 | 0.9943 | 1.5022 | 1.9978 | 0.0636 | 1.5000 | 1.1904 | 0.9950 | 1.5952 | 1.9048 | 0.0091 | 1.6536 | 1.3072 | 0.9946 | 1.6536 | 1.8464 | 0.0000 | 1.7000 | 1.3417 | 0.9944 | 1.6709 | 1.8292 | 0.0008 | 1.7500 | 1.3783 | 0.9942 | 1.6892 | 1.8109 | 0.0037 | 1.9500 | 1.5126 | 0.9933 | 1.7563 | 1.7437 | 0.0375 |
| 512 | 1.0500 | 0.8612 | 0.9903 | 1.4306 | 2.0694 | 0.1449 | 1.2500 | 1.0020 | 0.9938 | 1.5010 | 1.9990 | 0.0630 | 1.5000 | 1.1974 | 0.9950 | 1.5987 | 1.9013 | 0.0097 | 1.6654 | 1.3308 | 0.9947 | 1.6654 | 1.8346 | 0.0000 | 1.7000 | 1.3582 | 0.9946 | 1.6791 | 1.8209 | 0.0004 | 1.7500 | 1.3970 | 0.9944 | 1.6985 | 1.8015 | 0.0027 | 1.9500 | 1.5386 | 0.9934 | 1.7693 | 1.7307 | 0.0327 |
| 1024 | 1.0500 | 0.8557 | 0.9889 | 1.4279 | 2.0722 | 0.1428 | 1.2500 | 0.9998 | 0.9933 | 1.4999 | 2.0001 | 0.0625 | 1.5000 | 1.2026 | 0.9951 | 1.6013 | 1.8987 | 0.0103 | 1.6756 | 1.3512 | 0.9947 | 1.6756 | 1.8244 | 0.0000 | 1.7000 | 1.3715 | 0.9946 | 1.6858 | 1.8143 | 0.0002 | 1.7500 | 1.4124 | 0.9944 | 1.7062 | 1.7938 | 0.0019 | 1.9500 | 1.5605 | 0.9934 | 1.7803 | 1.7198 | 0.0288 |
| 2048 | 1.0500 | 0.8517 | 0.9877 | 1.4259 | 2.0742 | 0.1413 | 1.2500 | 0.9981 | 0.9929 | 1.4991 | 2.0010 | 0.0620 | 1.5000 | 1.2066 | 0.9951 | 1.6033 | 1.8967 | 0.0107 | 1.6846 | 1.3691 | 0.9947 | 1.6846 | 1.8155 | 0.0000 | 1.7000 | 1.3825 | 0.9946 | 1.6913 | 1.8088 | 0.0001 | 1.7500 | 1.4152 | 0.9944 | 1.7076 | 1.7924 | 0.0018 | 1.9500 | 1.5790 | 0.9933 | 1.7895 | 1.7105 | 0.0258 |
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