Fractal Geometry: Surface Characterization of Printing Paper
Abstract
1. Introduction
2. Materials and Methods
2.1. Materials
2.2. Surface Characterization
2.2.1. Surface Roughness Characterization
2.2.2. Surface Friction Characterization
2.3. Fractal Geometry Dimension Analysis of Surface Roughness Profiles
3. Results and Discussion
3.1. Surface Roughness of Printing Paper
3.2. Surface Friction of Printing Paper
3.3. Surface Friction vs. Surface Roughness
3.4. FD Analysis of Surface Roughness of Printing Paper
3.5. Application of Fractal Geometry to Surface Characterization
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
FD | Fractal Dimension |
PSD | Power Spectral Density |
Ra | Average of Surface Roughness |
COF | Coefficient of Friction |
MIU | Average of Coefficient of Friction |
MAD | Mean Absolute Deviation |
RMAD | Mean Absolute Deviation of Surface Roughness |
FMAD | Mean Absolute Deviation of Surface Friction |
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Sample | Basis Weight, g/m2 | Thickness, mm | Density, g/cm3 |
---|---|---|---|
P&W1 | 86.9 | 0.11 | 0.78 |
P&W2 | 76.0 | 0.10 | 0.74 |
P&W3 | 74.1 | 0.10 | 0.72 |
P&W4 | 81.7 | 0.11 | 0.74 |
P&W5 | 84.4 | 0.11 | 0.77 |
P&W6 | 83.6 | 0.11 | 0.76 |
P&W7 | 80.9 | 0.11 | 0.74 |
P&W8 | 80.9 | 0.11 | 0.75 |
P&W9 | 72.5 | 0.11 | 0.66 |
P&W10 | 79.5 | 0.10 | 0.75 |
P&W11 | 89.2 | 0.11 | 0.82 |
P&W12. | 89.4 | 0.11 | 0.81 |
Sample | Ra, μm | Rq, μm | RMAD, μm | |||
---|---|---|---|---|---|---|
Mean | COV | Mean | COV | Mean | COV | |
P&W1 | 1.40 | 15.4% | 1.46 | 15.4% | 0.32 | 9.5% |
P&W2 | 2.09 | 14.6% | 2.19 | 14.4% | 0.50 | 5.1% |
P&W3 | 1.88 | 13.6% | 2.05 | 16.1% | 0.45 | 5.8% |
P&W4 | 1.27 | 7.5% | 1.30 | 6.5% | 0.30 | 5.7% |
P&W5 | 1.80 | 8.4% | 1.95 | 11.5% | 0.44 | 5.6% |
P&W6 | 1.25 | 12.4% | 1.32 | 13.0% | 0.30 | 6.8% |
P&W7 | 2.32 | 10.5% | 2.37 | 10.3% | 0.53 | 6.4% |
P&W8 | 1.95 | 16.6% | 2.20 | 19.9% | 0.49 | 9.2% |
P&W9 | 1.96 | 17.2% | 2.10 | 19.7% | 0.51 | 7.6% |
P&W10 | 2.17 | 7.5% | 2.55 | 24.8% | 0.51 | 3.6% |
P&W11 | 1.87 | 9.4% | 2.03 | 14.9% | 0.42 | 6.9% |
P&W12 | 1.54 | 13.3% | 1.68 | 18.1% | 0.35 | 6.6% |
Sample | MIU | FMAD | ||
---|---|---|---|---|
Mean | COV | Mean | COV | |
P&W1 | 0.187 | 21.9% | 0.029 | 9.9% |
P&W2 | 0.230 | 21.4% | 0.039 | 17.0% |
P&W3 | 0.249 | 25.2% | 0.036 | 9.7% |
P&W4 | 0.162 | 18.8% | 0.027 | 13.9% |
P&W5 | 0.179 | 21.4% | 0.038 | 11.6% |
P&W6 | 0.119 | 15.8% | 0.025 | 12.4% |
P&W7 | 0.279 | 20.4% | 0.043 | 16.1% |
P&W8 | 0.272 | 16.0% | 0.037 | 13.5% |
P&W9 | 0.218 | 21.9% | 0.036 | 10.5% |
P&W10 | 0.144 | 9.0% | 0.034 | 8.2% |
P&W11 | 0.203 | 19.3% | 0.037 | 9.2% |
P&W12 | 0.250 | 17.3% | 0.031 | 15.1% |
Sample | RMAD, μm | MIU | FMAD | FD | ||||
---|---|---|---|---|---|---|---|---|
Mean | COV | Mean | COV | Mean | COV | Mean | COV | |
P&W1 | 0.32 | 9.5% | 0.187 | 21.9% | 0.029 | 9.9% | 1.27 | 3.6% |
P&W2 | 0.50 | 5.1% | 0.230 | 21.4% | 0.039 | 17.0% | 1.13 | 3.3% |
P&W3 | 0.45 | 5.8% | 0.249 | 25.2% | 0.036 | 9.7% | 1.13 | 3.5% |
P&W4 | 0.30 | 5.7% | 0.162 | 18.8% | 0.027 | 13.9% | 1.16 | 4.6% |
P&W5 | 0.44 | 5.6% | 0.179 | 21.4% | 0.038 | 11.6% | 1.21 | 4.3% |
P&W6 | 0.30 | 6.8% | 0.119 | 15.8% | 0.025 | 12.4% | 1.23 | 4.9% |
P&W7 | 0.53 | 6.4% | 0.279 | 20.4% | 0.043 | 16.1% | 1.19 | 5.6% |
P&W8 | 0.49 | 9.2% | 0.272 | 16.0% | 0.037 | 13.5% | 1.18 | 3.4% |
P&W9 | 0.51 | 7.6% | 0.218 | 21.9% | 0.036 | 10.5% | 1.18 | 2.8% |
P&W10 | 0.51 | 3.6% | 0.144 | 9.0% | 0.034 | 8.2% | 1.14 | 5.5% |
P&W11 | 0.42 | 6.9% | 0.203 | 19.3% | 0.037 | 9.2% | 1.19 | 5.3% |
P&W12 | 0.35 | 6.6% | 0.250 | 17.3% | 0.031 | 15.1% | 1.25 | 3.7% |
Sample | RMAD, μm | MIU | FMAD | FD |
---|---|---|---|---|
P&W11 | 0.42 | 0.203 | 0.037 | 1.19 |
P&W12 | 0.35 | 0.250 | 0.031 | 1.25 |
Change | −16.7% | 23% | −16.2% | 5% |
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Lee, Y.J.; Kim, G.-W.; Lee, T.-J.; Kim, H.J. Fractal Geometry: Surface Characterization of Printing Paper. Fractal Fract. 2025, 9, 123. https://doi.org/10.3390/fractalfract9020123
Lee YJ, Kim G-W, Lee T-J, Kim HJ. Fractal Geometry: Surface Characterization of Printing Paper. Fractal and Fractional. 2025; 9(2):123. https://doi.org/10.3390/fractalfract9020123
Chicago/Turabian StyleLee, Yong Ju, Geon-Woo Kim, Tai-Ju Lee, and Hyoung Jin Kim. 2025. "Fractal Geometry: Surface Characterization of Printing Paper" Fractal and Fractional 9, no. 2: 123. https://doi.org/10.3390/fractalfract9020123
APA StyleLee, Y. J., Kim, G.-W., Lee, T.-J., & Kim, H. J. (2025). Fractal Geometry: Surface Characterization of Printing Paper. Fractal and Fractional, 9(2), 123. https://doi.org/10.3390/fractalfract9020123