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 | s8 wavelet Energy, slope, r^2 | s10 wavelet Energy, slope, r^2 | s12 wavelet Energy, slope, r^2 |
| Fungus DTheor=1.600 Ritz et al. | 20. 5.576e+003 -1.3462 0.9190 21. 3.382e+003 -1.3542 0.9249 22. 1.730e+003 -1.3674 0.9300 23. 7.465e+002 -1.3874 0.9336 24. 2.444e+002 -1.4173 0.9343 25. 5.306e+001 -1.4612 0.9296 26. 3.965e+000 -1.5318 0.9107 Mean: D=1.583 | 20. 5.538e+003 -1.3480 0.9180 21. 3.447e+003 -1.3554 0.9240 22. 1.849e+003 -1.3672 0.9292 23. 8.353e+002 -1.3853 0.9331 24. 2.963e+002 -1.4123 0.9347 25. 7.120e+001 -1.4522 0.9316 26. 1.029e+000 -1.5099 0.9203 Mean: D=1.588 | 20. 5.631e+003 -1.3482 0.9186 21. 3.411e+003 -1.3557 0.9246 22. 1.883e+003 -1.3671 0.9298 23. 9.168e+002 -1.3837 0.9339 24. 3.171e+002 -1.4097 0.9356 25. 8.053e+001 -1.4480 0.9331 26. 1.451e+001 -1.5011 0.9239 Mean: D=1.590 |
| Neurite DTheor=1.210 | 15. 2.880e+003 -1.6183 0.9102 16. 1.480e+003 -1.6460 0.9198 17. 7.466e+002 -1.6750 0.9271 18. 3.103e+002 -1.7093 0.9322 19. 1.194e+002 -1.7489 0.9352 20. 3.236e+001 -1.7993 0.9349 21. 3.708e+000 -1.8739 0.9263 Mean: D=1.806 | 15. 2.954e+003 -1.6330 0.9027 16. 1.676e+003 -1.6572 0.9134 17. 7.382e+002 -1.6870 0.9214 18. 3.310e+002 -1.7200 0.9273 19. 1.165e+002 -1.7605 0.9307 20. 3.444e+001 -1.8099 0.9313 21. 5.849e+001 -1.8762 0.9265 Mean: D=1.190 | 16. 1.692e+003 -1.6443 0.9188 17. 9.587e+002 -1.6676 0.9266 18. 4.081e+002 -1.6970 0.9323 19. 1.464e+002 -1.7344 0.9356 20. 4.700e+001 -1.7796 0.9364 21. 1.280e+001 -1.8337 0.9343 22. 1.675e+000 -1.9075 0.9256 Mean: D=1.220 |
| Vicsek Snowflake DTheor=1.465 | 19. 2.364e+003 -1.4915 0.9329 20. 1.256e+003 -1.5079 0.9379 21. 6.341e+002 -1.5278 0.9417 22. 2.863e+002 -1.5525 0.9442 23. 1.124e+002 -1.5831 0.9449 24. 2.865e+001 -1.6252 0.9420 25. 2.995e+000 -1.6899 0.9297 Mean: D=1.417 | 20. 1.413e+002 -1.5033 0.9377 21. 7.324e+002 -1.5212 0.9417 22. 3.150e+002 -1.5450 0.9443 23. 1.118e+002 -1.5766 0.9448 24. 3.386e+001 -1.6168 0.9425 25. 5.414e+001 -1.6736 0.9339 Mean: D=1.423 | 19. 2.347e+003 -1.4944 0.9328 20. 1.354e+003 -1.5089 0.9379 21. 7.384e+002 -1.5259 0.9420 22. 3.417e+002 -1.5476 0.9449 23. 1.399e+002 -1.5751 0.9463 24. 4.242e+001 -1.6118 0.9449 25. 9.003e+000 -1.6612 0.9391 Mean: D=1.425 |
| 2-D Structure | s8 wavelet Energy, slope, r^2 | s10 wavelet Energy, slope, r^2 | s12 wavelet Energy, slope, r^2 |
| Snowflake DTheor=1.850 | 25. 5.730e+003 -1.1786 0.9521 26. 3.766e+003 -1.1820 0.9550 27. 2.161e+003 -1.1889 0.9575 28. 1.033e+003 -1.2013 0.9590 29. 3.163e+002 -1.2239 0.9572 30. 3.831e+001 -1.2663 0.9443 Mean: D=1.799 | 25. 5.994e+003 -1.1814 0.9570 26. 3.913e+003 -1.1839 0.9596 27. 2.237e+003 -1.1902 0.9619 28. 1.053e+003 -1.2021 0.9631 29. 3.472e+002 -1.2234 0.9615 30. 4.795e+001 -1.2631 0.9500 Mean: D=1.798 | 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 | 22. 2.800e+003 -1.3237
0.9604 23. 1.574e+003 -1.3384 0.9622 24. 7.880e+002 -1.3572 0.9622 25. 3.825e+002 -1.3796 0.9624 26. 1.563e+002 -1.4074 0.9603 27. 4.172e+001 -1.4454 0.9541 28. 5.423e+000 -1.5014 0.9389 Mean: D=1.620 | 22. 2.622e+003 -1.3280 0.9623 23. 1.666e+003 -1.3407 0.9642 24. 9.073e+002 -1.3564 0.9653 25. 4.225e+002 -1.3768 0.9652 26. 1.571e+002 -1.4043 0.9629 27. 4.703e+001 -1.4404 0.9573 28. 8.546e+000 -1.4903 0.9453 Mean: D=1.623 | 21. 4.273e+003 -1.3151 0.9579 22. 2.613e+003 -1.3277 0.9603 23. 1.505e+003 -1.3427 0.9620 24. 8.352e+002 -1.3599 0.9631 25. 4.021e+002 -1.3812 0.9630 26. 1.701e+002 -1.4075 0.9613 27. 5.041e+001 -1.4427 0.9563 Mean: D=1.619 |
| Kock curve DTheor=1.500 | 21. 3.324e+003 -1.3118 0.9601 22. 1.632e+003 -1.3312 0.9612 23. 7.722e+002 -1.3550 0.9609 24. 3.186e+002 -1.3845 0.9587 25. 1.030e+002 -1.4222 0.9534 26. 2.369e+001 -1.4713 0.9431 27. 1.860e+000 -1.5446 0.9192 Mean: D=1.455
| 22. 2.424e+003 -1.3370 0.9653 23. 1.130e+003 -1.3540 0.9663 24. 4.386e+002 -1.3788 0.9651 25. 1.675e+002 -1.4099 0.9617 26. 4.540e+001 -1.4510 0.9543 27. 6.190e+000 -1.5090 0.9380 Mean: D=1.491 | 22. 3.481e+003 -1.3199 0.9634 23. 1.780e+003 -1.3371 0.9647 24. 9.996e+002 -1.3562 0.9653 25. 1.304e+002 -1.4161 0.9594 26. 3.410e+001 -1.4607 0.9505 27. 5.772e+000 -1.5195 0.9351 28. 2.342e-001 -1.6088 0.9014 Mean: D=1.520 |
| Real Fractal aggregate: Pycnoporus cinnabarinus DTheor=1.691 | 22. 4.526e+003 -1.2808 0.9427 23. 2.624e+003 -1.2905 0.9464 24. 1.270e+003 -1.3057 0.949 25. 2.022e+002 -1.3283 0.9496 26. 1.366e+002 -1.3624 0.9459 27. 1.855e+001 -1.4153 0.9324 Mean: D=1.672 | 22. 4.520e+003 -1.2931 0.9463 23. 2.730e+003 -1.2916 0.9498 24. 1.395e+003 -1.3049 0.9524 25. 6.033e+002 -1.3246 0.9535 26. 1.770e+002 -1.3551 0.9508 27. 3.103e+001 -1.4014 0.9406 28. 1.710e+000 -1.4761 0.9123 Mean: D=1.675 | 22. 4.514e+003 -1.2829 0.9427 23. 2.646e+003 -1.2921 0.9464 24. 1.434e+003 -1.3051 0.9493 25. 6.085e+002 -1.3249 0.9506 26. 1.750e+002 -1.3556 0.9481 27. 3.261e+001 -1.4014 0.9386 28. 2.260e+000 -1.4726 0.9136 Mean: D=1.675 |