The Fractal Dimension is based upon the Coefficient Index Position number (which maps out Energy) which returned the highest R squared (r^2) result. This is highlighted in BOLD in the table.
| 2-D Structure | d4 wavelet Energy, slope, r^2 | d6 wavelet Energy, slope, r^2 | d8 wavelet Energy, slope, r^2 |
| Fungus DTheor=1.600 Ritz et al. | 20. 6.458e+003 -1.3355 0.9164 21. 3.538e+003 -1.3437 0.9226 22. 1.896e+003 -1.3562 0.9278 23. 5.445e+002 -1.3826 0.9303 24. 8.643e+001 -1.4293 0.9249 Mean: D=1.617 | 20. 5.845e+003 -1.3408 0.9168 21. 3.578e+003 -1.3482 0.9229 22. 1.952e+003 -1.3597 0.9282 23. 8.703e+002 -1.3779 0.9322 24. 2.740e+002 -1.4069 0.9333 25. 4.828e+001 -1.4532 0.9275 26. 1.481e+000 -1.5389 0.8976 Mean: D=1.593 | 20. 6.040e+003 -1.3453 0.9193 21. 3.862e+003 -1.3509 0.9252 22. 2.046e+003 -1.3615 0.9304 23. 9.547e+002 -1.3782 0.9344 24. 3.356e+002 -1.4040 0.9361 25. 8.061e+001 -1.4430 0.9331 26. 6.483e+000 -1.5085 0.9165 Mean: D=1.596 |
| Neurite DTheor=1.210 | 14. 5.062e+003 -1.5909 0.8880 15. 2.595e+003 -1.6228 0.9020 16. 1.174e+003 -1.6582 0.9122 17. 4.084e+002 -1.7025 0.9187 18. 1.032e+002 -1.7601 0.9207 19. 1.201e+000 -1.8938 0.8904 Mean: D=1.240 | 14. 4.828e+003 -1.5883 0.8938 15. 2.971e+003 -1.6159 0.9071 16. 1.618e+003 -1.6429 0.9172 17. 7.964e+002 -1.6720 0.9248 18. 2.666e+002 -1.7115 0.9294 19. 7.432e+001 -1.7621 0.9304 20. 8.931e+000 -1.8379 0.9229 Mean: D=1.238 | 15. 3.517e+003 -1.6083 0.9094 16. 1.941e+003 -1.6310 0.9193 17. 9.046e+002 -1.6584 0.9268 18. 4.142e+002 -1.6893 0.9323 19. 1.393e+002 -1.7292 0.9351 20. 2.816e+001 -1.7858 0.9329 21. 2.703e+000 -1.8690 0.9210 Mean: D=1.271 |
| Vicsek Snowflake DTheor=1.465 | 18. 4.654e+003 -1.4496 0.9248 19. 2.739e+003 -1.4635 0.9310 20. 1.435e+003 -1.4809 0.9360 21. 6.054e+002 -1.5054 0.9393 22. 1.915e+002 -1.5402 0.9396 23. 3.697e+001 -1.5912 0.9341 24. 1.673e+000 -1.6782 0.9103 Mean: D=1.460 | 17. 5.720e+003 -1.4639 0.9196 18. 3.600e+003 -1.4783 0.9268 19. 2.200e+003 -1.4933 0.9328 20. 1.227e+002 -1.5104 0.9377 21. 6.330e+002 -1.5306 0.9415 22. 2.713e+002 -1.5563 0.9438 23. 7.928e+001 -1.5927 0.9430 24. 1.303e+001 -1.6467 0.9358 Mean: D=1.444 | 18. 3.923e+003 -1.4669 0.9201 19. 2.567e+003 -1.4794 0.9323 20. 1.497e+003 -1.4937 0.9374 21. 7.840e+002 -1.5113 0.9415 22. 3.502e+002 -1.5343 0.9442 23. 1.294e+002 -1.5646 0.9449 24. 3.573e+001 -1.6052 0.9424 25. 4.320e+000 -1.6665 0.9314 Mean: D=1.435 |
| 2-D Structure | d4 wavelet Energy, slope, r^2 | d6 wavelet Energy, slope, r^2 | d8 wavelet Energy, slope, r^2 |
| Snowflake DTheor=1.850 | 24. 9.144e+003 -1.1689 0.9453 25. 6.344e+003 -1.1695 0.9485 26. 4.072e+003 -1.1726 0.9516 27. 2.435e+003 -1.1789 0.9544 28. 1.124e+003 -1.1911 0.9561 29. 3.448e+002 -1.2135 0.9546 30. 2.668e+001 -1.2614 0.9375 Mean: D=1.809 | 24. 8.627e+003 -1.1746 0.9486 25. 5.979e+003 -1.1756 0.9517 26. 3.911e+003 -1.1788 0.9546 27. 2.286e+003 -1.1854 0.9571 28. 1.099e+003 -1.1974 0.9587 29. 3.378e+002 -1.2195 0.9571 30. 3.484e+001 -1.2636 0.9429 Mean: D=1.803 | 24. 8.568e+003 -1.1817 0.9503 25. 6.063e+003 -1.1818 0.9532 26. 3.970e+003 -1.1842 0.9560 27. 2.284e+003 -1.1903 0.9585 28. 1.102e+003 -1.2017 0.9601 29. 3.799e+002 -1.2220 0.9591 30. 5.119e+001 -1.2611 0.9483 Mean: D=1.798 |
| Van Damm Plaster dissolution DTheor=1.600 | 21. 5.535e+003 -1.2886
0.9580 22. 3.443e+003 -1.2989 0.9606 23. 1.954e+003 -1.3122 0.9626 24. 9.610e+002 -1.3301 0.9633 25. 3.695e+002 -1.3554 0.9619 26. 9.210e+001 -1.3929 0.9554 27. 1.067e+001 -1.4510 0.9378 Mean: D=1.670 | 22. 2.951e+003 -1.3619 0.9600 23. 1.713e+003 -1.3309 0.9619 24. 9.520e+002 -1.3474 0.9631 25. 4.576e+002 -1.3631 0.9631 26. 1.679e+002 -1.3959 0.9608 27. 3.927e+001 -1.4359 0.9534 28. 3.479e+000 -1.4987 0.9334 Mean: D=1.637 | 22. 2.840e+003 -1.3227 0.9630 23. 1.816e+003 -1.3344 0.9650 24. 9.965e+002 -1.3491 0.9662 25. 4.665e+002 -1.3687 0.9662 26. 1.732e+002 -1.3954 0.9640 27. 5.317e+001 -1.4307 0.9586 28. 7.771e+000 -1.4827 0.9449 Mean: D=1.631 |
| Kock curve DTheor=1.500
| 21. 3.510e+003 -1.2989 0.9634 22. 1.881e+003 -1.3168 0.9645 23. 5.945e+002 -1.3462 0.9620 24. 1.351e+002 -1.3900 0.9531 25. 7.068e-002 -1.5374 0.8497 Mean: D=1.463 | 22. 1.836e+003 -1.3327 0.9639 23. 8.978e+002 -1.3544 0.9639 24. 2.513e+002 -1.3884 0.9596 25. 5.705e+001 -1.4352 0.9496 26. 7.369e+000 -1.5005 0.9300 27. 2.953e-003 -1.6610 0.8276 Mean: D=1.500 | 22. 2.758e+003 -1.3238 0.9647 23. 1.308e+003 -1.3394 0.9660 24. 4.810e+002 -1.3638 0.9648 25. 1.598e+002 -1.3968 0.9606 26. 3.783e+001 -1.4415 0.9512 27. 2.615e+000 -1.5129 0.9262 28. 1.426e-003 -1.6707 0.8270 Mean: D=1.487 |
| Real Fractal aggregate: Pycnoporus cinnabarinus DTheor=1.691 | 22. 5.688e+003 -1.2685 0.9432 23. 3.233e+003 -1.2757 0.9470 24. 1.321e+003 -1.2916 0.9491 25. 3.590e-002 -1.3206 0.9478 26. 2.075e+001 -1.3825 0.9270 27. 6.462e-027 -2.3118 0.2755 Mean: D=1.708 | 22. 4.685e+003 -1.2753 0.9418 23. 2.766e+003 -1.2846 0.9456 24. 1.461e+003 -1.2981 0.9485 25. 5.741e+002 -1.3195 0.9494 26. 1.152e+002 -1.3568 0.9441 27. 8.930e+000 -1.4205 0.9232 28. 2.066e-027 -2.3198 0.2843 Mean: D=1.681 | 22. 4.654e+003 -1.2895 0.9462 23. 2.761e+003 -1.2965 0.9497 24. 1.433e+003 -1.3084 0.9521 25. 6.197e+002 -1.3268 0.9539 26. 1.832e+002 -1.3560 0.9517 27. 2.504e+001 -1.4048 0.9399 Mean: D=1.673 |