Fractal and Lacunarity Analyses: Quantitative Characterization of Hierarchical Surface Topographies
Why this work is in the frame
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Bibliographic record
Abstract
Biomimetic hierarchical surface structures that exhibit features having multiple length scales have been used in many technological and engineering applications. Their surface topographies are most commonly analyzed using scanning electron microscopy (SEM), which only allows for qualitative visual assessments. Here we introduce fractal and lacunarity analyses as a method of characterizing the SEM images of hierarchical surface structures in a quantitative manner. Taking femtosecond laser-irradiated metals as an example, our results illustrate that, while the fractal dimension is a poor descriptor of surface complexity, lacunarity analysis can successfully quantify the spatial texture of an SEM image; this, in turn, provides a convenient means of reporting changes in surface topography with respect to changes in processing parameters. Furthermore, lacunarity plots are shown to be sensitive to the different length scales present within a hierarchical structure due to the reversal of lacunarity trends at specific magnifications where new features become resolvable. Finally, we have established a consistent method of detecting pattern sizes in an image from the oscillation of lacunarity plots. Therefore, we promote the adoption of lacunarity analysis as a powerful tool for quantitative characterization of, but not limited to, multi-scale hierarchical surface topographies.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it