RASH-HIT Fractal Analysis

RASH-HIT Fractal Analysis is a research-grade, zero-rasterization computational geometry engine engineered for exact vector box-counting, spatial occupancy profiling (fill vs. empty void ratio), and fractal dimension ($D_B$) analysis directly from Scalable Vector Graphics (SVG) vector motifs, architectural drawings, textile patterns, and graphic compositions.

---

🔬 Scientific Foundation & The Exact Vector Paradigm

For over three decades, computational fractal analysis in design and morphology has relied on raster image-processing tools (e.g., ImageJ FracLac, HarFA, Benoit). These conventional tools force vector artwork to be rasterized into fixed-resolution pixel grids (PNG/JPEG/TIFF), introducing three severe classes of mathematical error:

1. Resolution & DPI Inconsistency: Measured fractal dimensions vary artificially depending on the arbitrary export resolution, canvas size, or DPI chosen.
2. Anti-Aliasing & Fringing Distortion: Vector curves produce semi-transparent grayscale boundary pixels during rasterization, forcing arbitrary binarization thresholds that corrupt fine geometric boundaries.
3. Discretization Corner Clipping: Fine ornamental strokes, sharp corner vertices, and sub-pixel details smaller than pixel dimensions are merged, blurred, or obliterated.

The RASH-HIT Solution

RASH-HIT Fractal Analysis completely eliminates rasterization artifacts. It operates natively on continuous vector path geometry: SVG shapes are flattened to exact line segments and measured as supercover cell sets on a fixed-point integer lattice (pure NumPy engine, geometric-contact semantics). Grid cell occupancy is evaluated via exact Liang-Barsky closed-box segment intersection (touch_counts boundary policy: interior, edge, and corner contacts all count), guaranteeing 100% mathematical determinism, zero discretization error, and publication-grade reproducibility — with zero Shapely/GEOS dependency.

---

🏛️ Comprehensive Application Domains

RASH-HIT Fractal Analysis serves as a bridge between pure computational geometry and creative design disciplines:

1. 🧵 Textile, Fashion & Pattern Design

• Jacquard & Woven Structure Porosity: Quantify the exact spatial density and void-to-fill distribution of woven structures, knitwear repeats, and lace filigree.
• Carpet & Kilim Motif Analysis: Mathematically profile traditional Anatolian, Persian, Caucasian, and Oriental carpet motifs, quantifying the transition of motif density from central medallions to borders.
• Fashion Print Scaling & Repeat Balance: Evaluate self-similarity across different scale factors in surface pattern design and all-over textile prints.

2. 🏺 Cultural Heritage, Islamic Geometry & Visual Ornamentation

• Historic Ornament Morphology: Analyze ornamental styles across cultural eras (Seljuk, Ottoman, Celtic, Gothic, Baroque, Islamic Geometric Star Patterns, Muqarnas, Tezhip, Ebru, Marbling).
• Cultural Motif Classification: Provide objective numerical metrics ($D_B$, $R^2$, level-by-level fill ratios) for digital humanities, archaeological pattern classification, and museum heritage preservation.
• Geometric Complexity Indexing: Distinguish between Euclidean symmetry and true fractal self-similarity in traditional craftsmanship.

3. 🎨 Graphic Design, Typography & Visual Branding

• Logo Visual Weight & Balance: Quantify positive vs. negative space distribution and visual occupancy ratios across branding assets.
• Typographic Complexity: Measure the structural complexity, stroke density, and spatial coverage of diverse typefaces and calligraphic scripts.
• Generative & Algorithmic Vector Art: Benchmark procedural vector patterns, cellular automata graphics, and L-system fractals.

4. 🏢 Architectural & Urban Morphology

• Facade Articulation & Porosity: Analyze architectural screens (e.g., Mashrabiya, Brise-soleil, perforated metal panels) for light filtration and structural complexity.
• Floor Plan Spatial Hierarchy: Quantify structural enclosure, wall-to-void density, and circulation complexity in architectural layouts.
• Urban Footprint Scaling: Evaluate the fractal scaling behavior of street networks, historical urban perimeters, and building layouts.

5. ⚙️ Industrial, Surface & Parametric Product Design

• Laser-Cutting & CNC Path Optimization: Assess vector distribution and material removal ratios prior to fabrication.
• Biomimetic Textures & Metamaterials: Measure geometric scale hierarchies in biologically-inspired lattice structures and textured functional surfaces.

---

📊 Analytical Comparison: Exact Vector vs. Raster Box-Counting

Metric / Capability	Conventional Raster Tools (ImageJ/FracLac)	RASH-HIT Fractal Analysis (Exact Vector)
Input Representation	Discrete Bitmap Pixels (PNG/JPG/TIFF)	Continuous Double-Precision Floating Point (SVG)
Geometry Evaluation	Pixel counting (Binary 0/1 threshold)	Exact supercover cell sets on a fixed-point int64 lattice (pure NumPy, Liang-Barsky)
DPI / Resolution Dependency	⚠️ High (Results shift with image size/DPI)	🟢 Zero (Scale-invariant exact lattice anchored at the viewBox origin)
Anti-Aliasing Artifacts	⚠️ Severe (Blurred edges distort boundary counts)	🟢 None (Evaluated as true continuous boundaries)
Stroke Width Accuracy	⚠️ Subject to pixel round-off error	🟢 Exact (Centerline contact measured directly on the lattice)
Aspect Ratio Handling	Often square-padded, distorting non-square ratios	🟢 Adaptive (Aspect-ratio-aware grid planning)
Execution Performance	Slower on large images (O(N*M) pixel scan)	🟢 Ultra-fast (vectorized NumPy; L9 in ~5 ms, scales cleanly to L11)
Reproducibility	Depends on export settings and binarizer threshold	🟢 100% Deterministic & Scientifically Exact

---

⚡ Core Architecture & Engineering

• Single Pure NumPy Engine (v1.2.0): The supercover segment engine measures the contacted line geometry of an SVG — every boundary the renderer draws — as exact supercover cell sets on a FIXED_ORIGIN integer lattice (fixed-point int64 coordinates), with exact Liang-Barsky closed-box intersection (touch_counts boundary policy: interior, edge, and corner contacts all count). Validated against hand-derived ground-truth cell sets; zero Shapely/GEOS dependency (v1.x's GEOS area engine was removed after L9 benchmarking showed the pure NumPy engine 203x faster at deep levels with identical exactness).
• Aspect-Ratio-Aware Multi-Level Grid Planning: Automatically adapts grid cell dimensions to arbitrary SVG viewbox dimensions ($AR = W/H$) with power-of-two resolution doubling across levels ($L_1 \dots L_N$).
• Vectorized Deep-Level Scaling: Fixed-point int64 lattice arithmetic keeps deep levels (L9–L11) in milliseconds where per-cell predicate engines spend seconds.
• Comprehensive SVG Specification Support:
  • Standard shapes: <rect>, <circle>, <ellipse>, <line>, <polyline>, <polygon>, and <path> (Cubic/Quadratic Bézier curves, elliptical arcs).
  • 2D affine transformation matrices: matrix(), translate(), scale(), rotate(), skewX(), skewY().
  • CSS style hierarchy: Inline style="...", presentation attributes, and <style> blocks (via tinycss2).
  • Per-channel alpha and visibility resolution: Filters non-rendered, hidden, or zero-opacity geometries.
• Ordinary Least Squares (OLS) Regression: Evaluates Box-Counting Fractal Dimension ($D_B$) and coefficient of determination ($R^2$) from: $$\log N(\epsilon) = D_B \cdot \log(1/\epsilon) + C$$
• Zero Disk Footprint: Generates clean, publication-ready ASCII framed summary tables directly to stdout.

---

📦 Installation & Setup

Method 1: Instant Execution via NPX (Zero Setup)

# Run immediately without manual dependency installation
npx rash-hit-fractal-analysis --input motif.svg --levels 7

# Or install globally
npm install -g rash-hit-fractal-analysis
rash-hit-fractal --input motif.svg --levels 7

(All required Python core libraries such as NumPy, defusedxml, and tinycss2 are automatically detected and installed on first run).

Method 2: Install via PyPI

pip install rash-hit-fractal-analysis

Method 3: Install from Source

git clone https://github.com/rasitnarcicek/RASH-HIT-Fractal-Analysis.git
cd RASH-HIT-Fractal-Analysis
pip install -e .

---

🚀 Usage & Examples

When installed via pip or npm, the rash-hit-fractal command is available system-wide:

1. Analyze a Single SVG Motif

rash-hit-fractal --input input_svgs/test.svg --levels 7

The single engine measures the contacted line geometry (supercover cell sets on a fixed integer lattice, touch_counts boundary policy) with only numpy as the numerical dependency:

Measures	Engine	Dependencies
Line segments (fill boundaries + stroke centerlines) as supercover cell sets on a fixed integer lattice	Pure NumPy (fixed-point int64, Liang-Barsky)	numpy (+ defusedxml/tinycss2 for loader security)

Terminal Output:

+------------------------------------------------------------------------------+
|               RASH-HIT FRACTAL ANALYSIS - ANALYSIS REPORT                |
+------------------------------------------------------------------------------+
  Motif Loaded       : test (100.00 x 200.00)
  Geometries         : 4 vector elements
  Analysis Engine    : cpu
  Selected Engine    : RASH-HIT Fractal Analysis Engine
+------------------------------------------------------------------------------+
| Level | Grid     | Total Cells | Filled Cells | Empty Cells | Occupancy % | Time ms  |
+-------+----------+-------------+--------------+-------------+-------------+----------+
|  L01  | 4x8      |          32 |           20 |          12 |      62.50% |     0.00 |
|  L02  | 8x16     |         128 |           44 |          84 |      34.38% |     0.00 |
|  L03  | 16x32    |         512 |           84 |         428 |      16.41% |     0.00 |
|  L04  | 32x64    |       2,048 |          164 |       1,884 |       8.01% |     0.00 |
|  L05  | 64x128   |       8,192 |          332 |       7,860 |       4.05% |     0.00 |
|  L06  | 128x256  |      32,768 |          668 |      32,100 |       2.04% |     0.00 |
|  L07  | 256x512  |     131,072 |        1,332 |     129,740 |       1.02% |     0.00 |
+-------+----------+-------------+--------------+-------------+-------------+----------+
  [RESULT] Box-Counting Fractal Dimension Db = 0.9997
  [RESULT] Linear Regression Fit R2           = 0.9998
  [RESULT] Total Execution Time               = 21.10 ms
+------------------------------------------------------------------------------+

2. Batch Process an Entire Directory of Motifs

rash-hit-fractal --dir ./input_svgs --levels 5

---

🎓 Academic Citation

If you use RASH-HIT Fractal Analysis in your research, thesis, journal articles, or architectural/textile studies, please cite the software using the persistent DOIs below:

• Concept DOI: 10.5281/zenodo.22069152
• Version DOI (v1.0.1): 10.5281/zenodo.22069941 — v1.1.0 DOI will be minted on release (concept DOI always resolves to the latest version)
• Author ORCID: 0009-0005-3423-255X

BibTeX

@software{Narcicek_RASH_HIT_Fractal_Analysis_2026,
  author    = {Nar{\c{c}}i{\c{c}}ek, Mehmet Ra{\s}it},
  title     = {RASH-HIT Fractal Analysis},
  year      = {2026},
  version   = {1.0.1},
  publisher = {GitHub},
  doi       = {10.5281/zenodo.22069941},
  url       = {https://doi.org/10.5281/zenodo.22069941},
  orcid     = {https://orcid.org/0009-0005-3423-255X},
  license   = {Apache-2.0}
}

APA

Narçiçek, M. R. (2026). RASH-HIT Fractal Analysis (Version 1.0.1) [Computer software]. GitHub. https://doi.org/10.5281/zenodo.22069941

RIS

TY  - COMP
AU  - Narçiçek, Mehmet Raşit
TI  - RASH-HIT Fractal Analysis
PY  - 2026
ET  - 1.0.1
PB  - GitHub
DO  - 10.5281/zenodo.22069941
UR  - https://doi.org/10.5281/zenodo.22069941
ER  - 

---

📜 License & Authorship

Licensed under the Apache License, Version 2.0.
Copyright (c) 2026 Mehmet Raşit Narçiçek. All rights reserved.