Multifractal Art-Texture Pipeline
User Guide & Reference Manual

The core measurement engine. For every image: computes a sparse gradient-magnitude binary mask and box-counts it for D₀; builds a normalised gradient-magnitude measure and runs the partition-function / Legendre-transform pipeline for D₁, D₂, spectrum width, α₀, and asymmetry. Also produces a first-pass box/pairplot/heatmap figure set and prints Kruskal–Wallis and pairwise Mann–Whitney results to the console.

OUTPUT (in the working directory):
  multifractal_stable_results.csv     ← the file every other script needs
  multifractal_summary.csv            (groupby-describe per category)
  multifractal_stable_boxplots.png
  multifractal_stable_pairplot.png
  multifractal_stable_heatmap.png

OUTPUT (inside dataset_root/<category>/preprocessed_images/, if SAVE_PREPROCESSED=True):
  <file>_01_original.png
  <file>_02_gradient_magnitude.png
  <file>_03_sparse_binary_D0.png
  <file>_04_probability_measure.png

Edit main(r"G:\Fractals\dataset") at the bottom of the file to point at your dataset. Runtime scales with image count and NUM_SCALES; the box-counting and partition-function loops are pure Python/NumPy, not vectorised across images.

Independent of the engine above (it recomputes its own gradient measure and its own D₁/D₂/spectrum, using the same maths but a slightly different scale range, MIN_BOX_DQ only, not MIN_BOX_D0). Its purpose is visual: a full, fine-grained f(α) singularity spectrum curve per image, not just the six summary numbers.

OUTPUT (in multifractal_spectra/):
  <category>/<file>_f_alpha.png       (one high-res plot per image)
  <category>_composite_spectra.png    (all images of a category, overlaid)
  master_composite_spectra.png        (mean ± s.d. curve per category)
  f_alpha_curves.csv                  (raw α, f(α) points for every image)

Per-category kernel density estimate of spectrum width, an enhanced version with a normal-distribution overlay, and Q–Q plots for a quick-look normality check ahead of the formal test in 06_shapiro_analysis.py.

OUTPUT in 02_extract_spectrum_width_distribution_output/:
  spectrum_width_distribution.png
  spectrum_width_distribution_enhanced.png
  spectrum_width_distribution_enhanced_per_artist.png
  spectrum_width_qq_plots.png

The full 4×4 scatter matrix across D₀, D₁, D₂, spectrum width with per-category colour and marker coding, a focused subplot isolating spectrum width against each dimension, and per-category correlation heatmaps.

OUTPUT in 03_generate_pairplot_enhanced_output/:
  multifractal_stable_pairplot.png     (4×4 scatter matrix, 600 DPI)
  spectrum_width_vs_dimensions.png
  correlation_heatmaps.png

Publication-style spectrum-width figures: a boxplot with significance-ready layout, a violin+strip alternative, and a combined 2×2 panel of all four core metrics.

OUTPUT in 04_generate_spectrum_width_plot_output/:
  spectrum_width_boxplot.png
  spectrum_width_violin_plot.png
  all_metrics_combined.png
  spectrum_width_summary.csv

The full descriptive + inferential statistics table for spectrum width: N, mean, s.d., SEM, 95% CI, median, min/max, quartiles, IQR, coefficient of variation, and Shapiro–Wilk p, plus a Bonferroni-corrected pairwise Mann–Whitney report. Console output is mirrored to a text file via a small Tee class.

OUTPUT in 05_spectrum_width_statistics_output/:
  spectrum_width_statistics.csv
  spectrum_width_statistics_report.txt   (full console transcript)

The script prints step-by-step instructions for pasting the CSV into Word via Excel — useful if the table is going straight into a manuscript.

Shapiro–Wilk normality test for all six metrics (D₀, D₁, D₂, spectrum width, α₀, asymmetry), grouped by category, with a colour-coded pivot table and an explicit parametric-vs-non-parametric recommendation based on the results. The only script in the package with no functions and no output folder — it runs top to bottom and writes to the working directory.

OUTPUT (in the working directory):
  shapiro_wilk_results.csv

Standardises category-mean metric vectors (z-scores), then builds a hierarchical clustering dendrogram (Ward linkage), a pairwise distance heatmap, a standardised-feature heatmap, a silhouette analysis to suggest a cluster count, and a metrics bar chart with error bars.

OUTPUT in hierarchical_clustering_output/:
  dendrogram.png
  distance_heatmap.png
  feature_heatmap.png
  silhouette_analysis.png
  metrics_barplot.png
  distance_matrix.csv
  standardised_means.csv