# Keçeci Fractals: Keçeci Fraktals
Keçeci Circle Fractal: Keçeci-style circle fractal.
[](https://badge.fury.io/py/kececifractals)
[](https://opensource.org/licenses/MIT)
[](https://doi.org/10.5281/zenodo.15392518)
[](https://doi.org/10.5281/zenodo.15392773)
[](https://doi.org/10.5281/zenodo.15396198)
[](https://doi.org/10.48546/workflowhub.datafile.16.3)
[](https://doi.org/10.22541/au.175131225.56823239/v1)
[](https://anaconda.org/bilgi/kececifractals)
[](https://anaconda.org/bilgi/kececifractals)
[](https://anaconda.org/bilgi/kececifractals)
[](https://anaconda.org/bilgi/kececifractals)
[](https://opensource.org/)
[](https://kececifractals.readthedocs.io/en/latest)
[](https://www.bestpractices.dev/projects/)
[](https://github.com/WhiteSymmetry/kececifractals/actions/workflows/python_ci.yml)
[](https://codecov.io/gh/WhiteSymmetry/kececifractals)
[](https://kececifractals.readthedocs.io/en/latest/)
[](https://terrarium.evidencepub.io/v2/gh/WhiteSymmetry/kececifractals/HEAD)
[](https://badge.fury.io/py/kececifractals)
[](https://pepy.tech/projects/kececifractals)
[](CODE_OF_CONDUCT.md)
[](https://github.com/astral-sh/ruff)
---
<p align="left">
<table>
<tr>
<td style="text-align: center;">PyPI</td>
<td style="text-align: center;">
<a href="https://pypi.org/project/kececifractals/">
<img src="https://badge.fury.io/py/kececifractals.svg" alt="PyPI version" height="18"/>
</a>
</td>
</tr>
<tr>
<td style="text-align: center;">Conda</td>
<td style="text-align: center;">
<a href="https://anaconda.org/bilgi/kececifractals">
<img src="https://anaconda.org/bilgi/kececifractals/badges/version.svg" alt="conda-forge version" height="18"/>
</a>
</td>
</tr>
<tr>
<td style="text-align: center;">DOI</td>
<td style="text-align: center;">
<a href="https://doi.org/10.5281/zenodo.15392518">
<img src="https://zenodo.org/badge/DOI/10.5281/zenodo.15392518.svg" alt="DOI" height="18"/>
</a>
</td>
</tr>
<tr>
<td style="text-align: center;">License: MIT</td>
<td style="text-align: center;">
<a href="https://opensource.org/licenses/MIT">
<img src="https://img.shields.io/badge/License-MIT-yellow.svg" alt="License" height="18"/>
</a>
</td>
</tr>
</table>
</p>
---
## Description / Açıklama
**Keçeci Circle Fractal: Keçeci-style circle fractal.**:
This module provides two primary functionalities for generating Keçeci Fractals:
1. kececifractals_circle(): Generates general-purpose, aesthetic, and randomly
colored circular fractals.
2. visualize_qec_fractal(): Generates fractals customized for modeling the (version >= 0.1.1)
concept of Quantum Error Correction (QEC) codes.
3. Stratum Model Visualization (version >= 0.1.2)
Many systems encountered in nature and engineering exhibit complex and hierarchical geometric structures. Fractal geometry provides a powerful tool for understanding and modeling these structures. However, existing deterministic circle packing fractals, such as the Apollonian gasket, often adhere to fixed geometric rules and may fall short in accurately reflecting the diversity of observed structures. Addressing the need for greater flexibility in modeling physical and mathematical systems, this paper introduces the Keçeci Circle Fractal (KCF), a novel deterministic fractal. The KCF is generated through a recursive algorithm where a parent circle contains child circles scaled down by a specific `scale_factor` and whose number (`initial_children`, `recursive_children`) is controllable. These parameters allow for the tuning of the fractal's morphological characteristics (e.g., density, void distribution, boundary complexity) over a wide range. The primary advantage of the KCF lies in its tunable geometry, enabling more realistic modeling of diverse systems with varying structural parameters, such as porous media (for fluid flow simulations), granular material packings, foam structures, or potentially biological aggregations. Furthermore, the controllable structure of the KCF provides an ideal testbed for investigating structure-dependent physical phenomena like wave scattering, heat transfer, or electrical conductivity. Mathematically, it offers opportunities to study variations in fractal dimension and packing efficiency for different parameter values. In conclusion, the Keçeci Circle Fractal emerges as a valuable and versatile tool for generating geometries with controlled complexity and investigating structure-property relationships across multidisciplinary fields.
Doğada ve mühendislik uygulamalarında karşılaşılan birçok sistem, karmaşık ve hiyerarşik geometrik yapılar sergiler. Bu yapıları anlamak ve modellemek için fraktal geometri güçlü bir araç sunar. Ancak, Apollon contası gibi mevcut deterministik dairesel paketleme fraktalları genellikle sabit geometrik kurallara bağlıdır ve gözlemlenen yapıların çeşitliliğini tam olarak yansıtmakta yetersiz kalabilir. Bu çalışmada, fiziksel ve matematiksel sistemlerin modellenmesinde daha fazla esneklik sağlama ihtiyacından doğan yeni bir deterministik fraktal olan Keçeci Dairesel Fraktalı (KDF) tanıtılmaktadır. KDF, özyinelemeli bir algoritma ile üretilir; burada bir ana daire, belirli bir ölçek faktörü (`scale_factor`) ile küçültülmüş ve sayısı (`initial_children`, `recursive_children`) kontrol edilebilen çocuk daireleri içerir. Bu parametreler, fraktalın morfolojik özelliklerinin (yoğunluk, boşluk dağılımı, sınır karmaşıklığı vb.) geniş bir aralıkta ayarlanmasına olanak tanır. KDF'nin temel avantajı, bu ayarlanabilir geometrisi sayesinde, gözenekli ortamlar (akışkan simülasyonları için), granüler malzeme paketlemeleri, köpük yapıları veya potansiyel olarak biyolojik kümeleşmeler gibi yapısal parametreleri farklılık gösteren çeşitli sistemleri daha gerçekçi bir şekilde modelleyebilmesidir. Ayrıca, KDF'nin kontrol edilebilir yapısı, dalga saçılması, ısı transferi veya elektriksel iletkenlik gibi yapıya bağlı fiziksel olayların incelenmesi için ideal bir test ortamı sunar. Matematiksel olarak, farklı parametre değerleri için fraktal boyut değişimlerini ve paketleme verimliliğini inceleme imkanı sunar. Sonuç olarak, Keçeci Dairesel Fraktalı, kontrollü karmaşıklığa sahip geometriler üretmek ve çok disiplinli alanlarda yapı-özellik ilişkilerini araştırmak için değerli ve çok yönlü bir araç olarak öne çıkmaktadır.
---
## Installation / Kurulum
```bash
conda install bilgi::kececifractals -y
pip install kececifractals
```
https://anaconda.org/bilgi/kececifractals
https://pypi.org/project/kececifractals/
https://github.com/WhiteSymmetry/kececifractals
https://zenodo.org/records/
https://zenodo.org/records/
---
## Usage / Kullanım
### Example
```python
import kececifractals as kf
import importlib # Useful if you modify the .py file and want to reload it
# --- Example 1: Show the fractal inline ---
print("Generating fractal to show inline...")
kf.kececifractals_circle(
initial_children=5,
recursive_children=5,
text="Keçeci Circle Fractal: Keçeci Dairesel Fraktalı",
max_level=4,
scale_factor=0.5,
min_size_factor=0.001,
output_mode='show' # This will display the plot below the cell
)
print("Inline display finished.")
# --- Example 2: Save the fractal as an SVG file ---
print("\nGenerating fractal to save as SVG...")
kf.kececifractals_circle(
initial_children=7,
recursive_children=3,
text="Keçeci Circle Fractal: Keçeci Dairesel Fraktalı",
max_level=5,
scale_factor=0.5,
min_size_factor=0.001,
base_radius=4.5,
background_color=(0.95, 0.9, 0.85), # Light beige
initial_circle_color=(0.3, 0.1, 0.1), # Dark brown
output_mode='svg',
filename="kececi_fractal_svg-1" # Will be saved in the notebook's directory
)
print("SVG saving finished.")
# --- Example 3: Save as PNG with high DPI ---
print("\nGenerating fractal to save as PNG...")
kf.kececifractals_circle(
initial_children=4,
recursive_children=6,
text="Keçeci Circle Fractal: Keçeci Dairesel Fraktalı",
max_level=6, # Deeper recursion
scale_factor=0.5,
min_size_factor=0.001, # Smaller details
output_mode='png',
filename="kececi_fractal_png-1",
dpi=400 # High resolution
)
print("PNG saving finished.")
print("\nGenerating fractal and saving as JPG...")
kf.kececifractals_circle(
initial_children=5,
recursive_children=7,
text="Keçeci Circle Fractal: Keçeci Dairesel Fraktalı",
max_level=5,
scale_factor=0.5,
min_size_factor=0.001,
output_mode='jpg', # Save as JPG
filename="kececifractal_jpg-1",
dpi=300 # Medium resolution JPG
)
print("JPG saving finished.")
# --- If you modify kececifractals.py and want to reload it ---
# Without restarting the Jupyter kernel:
print("\nReloading the module...")
importlib.reload(kf)
print("Module reloaded. Now you can run the commands again with the updated code.")
kf.kececifractals_circle(output_mode='show', text="Keçeci Circle Fractal: Keçeci Dairesel Fraktalı")
```
---
---
---
---
## License / Lisans
This project is licensed under the MIT License. See the `LICENSE` file for details.
## Citation
If this library was useful to you in your research, please cite us. Following the [GitHub citation standards](https://docs.github.com/en/github/creating-cloning-and-archiving-repositories/creating-a-repository-on-github/about-citation-files), here is the recommended citation.
### BibTeX
```bibtex
@misc{kececi_2025_15392518,
author = {Keçeci, Mehmet},
title = {kececifractals},
month = may,
year = 2025,
publisher = {GitHub, PyPI, Anaconda, Zenodo},
version = {0.1.0},
doi = {10.5281/zenodo.15392518},
url = {https://doi.org/10.5281/zenodo.15392518},
}
@misc{kececi_2025_15396198,
author = {Keçeci, Mehmet},
title = {Scalable Complexity: Mathematical Analysis and
Potential for Physical Applications of the Keçeci
Circle Fractal
},
month = may,
year = 2025,
publisher = {Zenodo},
doi = {10.5281/zenodo.15396198},
url = {https://doi.org/10.5281/zenodo.15396198},
}
```
### APA
```
Keçeci, M. (2025). Scalable Complexity in Fractal Geometry: The Keçeci Fractal Approach. Authorea. June, 2025. https://doi.org/10.22541/au.175131225.56823239/v1
Keçeci, M. (2025). kececifractals [Data set]. WorkflowHub. https://doi.org/10.48546/workflowhub.datafile.16.3
Keçeci, M. (2025). kececifractals. Zenodo. https://doi.org/10.5281/zenodo.15392518
Keçeci, M. (2025). Scalable Complexity: Mathematical Analysis and Potential for Physical Applications of the Keçeci Circle Fractal. https://doi.org/10.5281/zenodo.15396198
```
### Chicago
```
Keçeci, Mehmet. Scalable Complexity in Fractal Geometry: The Keçeci Fractal Approach. Authorea. June, 2025. https://doi.org/10.22541/au.175131225.56823239/v1
Keçeci, Mehmet. "kececifractals" [Data set]. WorkflowHub, 2025. https://doi.org/10.48546/workflowhub.datafile.16.3
Keçeci, Mehmet. "kececifractals". Zenodo, 01 May 2025. https://doi.org/10.5281/zenodo.15392518
Keçeci, Mehmet. "Scalable Complexity: Mathematical Analysis and Potential for Physical Applications of the Keçeci Circle Fractal", 13 Mayıs 2025. https://doi.org/10.5281/zenodo.15396198.
```
Raw data
{
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"name": "kececifractals",
"maintainer": "Mehmet Ke\u00e7eci",
"docs_url": null,
"requires_python": ">=3.9",
"maintainer_email": "bilginomi@yaani.com",
"keywords": null,
"author": "Mehmet Ke\u00e7eci",
"author_email": "bilginomi@yaani.com",
"download_url": "https://files.pythonhosted.org/packages/13/4b/c7c8a2fb74bb92bcce8c15b968540f49ec5b01560175c1a9cea2ac13f4d6/kececifractals-0.1.3.tar.gz",
"platform": null,
"description": "\n# Ke\u00e7eci Fractals: Ke\u00e7eci Fraktals\n\nKe\u00e7eci Circle Fractal: Ke\u00e7eci-style circle fractal.\n\n[](https://badge.fury.io/py/kececifractals)\n[](https://opensource.org/licenses/MIT)\n\n[](https://doi.org/10.5281/zenodo.15392518)\n[](https://doi.org/10.5281/zenodo.15392773)\n[](https://doi.org/10.5281/zenodo.15396198)\n\n[](https://doi.org/10.48546/workflowhub.datafile.16.3)\n\n[](https://doi.org/10.22541/au.175131225.56823239/v1)\n\n[](https://anaconda.org/bilgi/kececifractals)\n[](https://anaconda.org/bilgi/kececifractals)\n[](https://anaconda.org/bilgi/kececifractals)\n[](https://anaconda.org/bilgi/kececifractals)\n\n[](https://opensource.org/)\n[](https://kececifractals.readthedocs.io/en/latest)\n\n[](https://www.bestpractices.dev/projects/)\n\n[](https://github.com/WhiteSymmetry/kececifractals/actions/workflows/python_ci.yml)\n[](https://codecov.io/gh/WhiteSymmetry/kececifractals)\n[](https://kececifractals.readthedocs.io/en/latest/)\n[](https://terrarium.evidencepub.io/v2/gh/WhiteSymmetry/kececifractals/HEAD)\n[](https://badge.fury.io/py/kececifractals)\n[](https://pepy.tech/projects/kececifractals)\n[](CODE_OF_CONDUCT.md)\n[](https://github.com/astral-sh/ruff)\n\n---\n\n<p align=\"left\">\n <table>\n <tr>\n <td style=\"text-align: center;\">PyPI</td>\n <td style=\"text-align: center;\">\n <a href=\"https://pypi.org/project/kececifractals/\">\n <img src=\"https://badge.fury.io/py/kececifractals.svg\" alt=\"PyPI version\" height=\"18\"/>\n </a>\n </td>\n </tr>\n <tr>\n <td style=\"text-align: center;\">Conda</td>\n <td style=\"text-align: center;\">\n <a href=\"https://anaconda.org/bilgi/kececifractals\">\n <img src=\"https://anaconda.org/bilgi/kececifractals/badges/version.svg\" alt=\"conda-forge version\" height=\"18\"/>\n </a>\n </td>\n </tr>\n <tr>\n <td style=\"text-align: center;\">DOI</td>\n <td style=\"text-align: center;\">\n <a href=\"https://doi.org/10.5281/zenodo.15392518\">\n <img src=\"https://zenodo.org/badge/DOI/10.5281/zenodo.15392518.svg\" alt=\"DOI\" height=\"18\"/>\n </a>\n </td>\n </tr>\n <tr>\n <td style=\"text-align: center;\">License: MIT</td>\n <td style=\"text-align: center;\">\n <a href=\"https://opensource.org/licenses/MIT\">\n <img src=\"https://img.shields.io/badge/License-MIT-yellow.svg\" alt=\"License\" height=\"18\"/>\n </a>\n </td>\n </tr>\n </table>\n</p>\n\n---\n\n## Description / A\u00e7\u0131klama\n\n**Ke\u00e7eci Circle Fractal: Ke\u00e7eci-style circle fractal.**: \n\nThis module provides two primary functionalities for generating Ke\u00e7eci Fractals:\n1. kececifractals_circle(): Generates general-purpose, aesthetic, and randomly\n colored circular fractals.\n2. visualize_qec_fractal(): Generates fractals customized for modeling the (version >= 0.1.1)\n concept of Quantum Error Correction (QEC) codes.\n3. Stratum Model Visualization (version >= 0.1.2)\n\nMany systems encountered in nature and engineering exhibit complex and hierarchical geometric structures. Fractal geometry provides a powerful tool for understanding and modeling these structures. However, existing deterministic circle packing fractals, such as the Apollonian gasket, often adhere to fixed geometric rules and may fall short in accurately reflecting the diversity of observed structures. Addressing the need for greater flexibility in modeling physical and mathematical systems, this paper introduces the Ke\u00e7eci Circle Fractal (KCF), a novel deterministic fractal. The KCF is generated through a recursive algorithm where a parent circle contains child circles scaled down by a specific `scale_factor` and whose number (`initial_children`, `recursive_children`) is controllable. These parameters allow for the tuning of the fractal's morphological characteristics (e.g., density, void distribution, boundary complexity) over a wide range. The primary advantage of the KCF lies in its tunable geometry, enabling more realistic modeling of diverse systems with varying structural parameters, such as porous media (for fluid flow simulations), granular material packings, foam structures, or potentially biological aggregations. Furthermore, the controllable structure of the KCF provides an ideal testbed for investigating structure-dependent physical phenomena like wave scattering, heat transfer, or electrical conductivity. Mathematically, it offers opportunities to study variations in fractal dimension and packing efficiency for different parameter values. In conclusion, the Ke\u00e7eci Circle Fractal emerges as a valuable and versatile tool for generating geometries with controlled complexity and investigating structure-property relationships across multidisciplinary fields.\n\nDo\u011fada ve m\u00fchendislik uygulamalar\u0131nda kar\u015f\u0131la\u015f\u0131lan bir\u00e7ok sistem, karma\u015f\u0131k ve hiyerar\u015fik geometrik yap\u0131lar sergiler. Bu yap\u0131lar\u0131 anlamak ve modellemek i\u00e7in fraktal geometri g\u00fc\u00e7l\u00fc bir ara\u00e7 sunar. Ancak, Apollon contas\u0131 gibi mevcut deterministik dairesel paketleme fraktallar\u0131 genellikle sabit geometrik kurallara ba\u011fl\u0131d\u0131r ve g\u00f6zlemlenen yap\u0131lar\u0131n \u00e7e\u015fitlili\u011fini tam olarak yans\u0131tmakta yetersiz kalabilir. Bu \u00e7al\u0131\u015fmada, fiziksel ve matematiksel sistemlerin modellenmesinde daha fazla esneklik sa\u011flama ihtiyac\u0131ndan do\u011fan yeni bir deterministik fraktal olan Ke\u00e7eci Dairesel Fraktal\u0131 (KDF) tan\u0131t\u0131lmaktad\u0131r. KDF, \u00f6zyinelemeli bir algoritma ile \u00fcretilir; burada bir ana daire, belirli bir \u00f6l\u00e7ek fakt\u00f6r\u00fc (`scale_factor`) ile k\u00fc\u00e7\u00fclt\u00fclm\u00fc\u015f ve say\u0131s\u0131 (`initial_children`, `recursive_children`) kontrol edilebilen \u00e7ocuk daireleri i\u00e7erir. Bu parametreler, fraktal\u0131n morfolojik \u00f6zelliklerinin (yo\u011funluk, bo\u015fluk da\u011f\u0131l\u0131m\u0131, s\u0131n\u0131r karma\u015f\u0131kl\u0131\u011f\u0131 vb.) geni\u015f bir aral\u0131kta ayarlanmas\u0131na olanak tan\u0131r. KDF'nin temel avantaj\u0131, bu ayarlanabilir geometrisi sayesinde, g\u00f6zenekli ortamlar (ak\u0131\u015fkan sim\u00fclasyonlar\u0131 i\u00e7in), gran\u00fcler malzeme paketlemeleri, k\u00f6p\u00fck yap\u0131lar\u0131 veya potansiyel olarak biyolojik k\u00fcmele\u015fmeler gibi yap\u0131sal parametreleri farkl\u0131l\u0131k g\u00f6steren \u00e7e\u015fitli sistemleri daha ger\u00e7ek\u00e7i bir \u015fekilde modelleyebilmesidir. Ayr\u0131ca, KDF'nin kontrol edilebilir yap\u0131s\u0131, dalga sa\u00e7\u0131lmas\u0131, \u0131s\u0131 transferi veya elektriksel iletkenlik gibi yap\u0131ya ba\u011fl\u0131 fiziksel olaylar\u0131n incelenmesi i\u00e7in ideal bir test ortam\u0131 sunar. Matematiksel olarak, farkl\u0131 parametre de\u011ferleri i\u00e7in fraktal boyut de\u011fi\u015fimlerini ve paketleme verimlili\u011fini inceleme imkan\u0131 sunar. Sonu\u00e7 olarak, Ke\u00e7eci Dairesel Fraktal\u0131, kontroll\u00fc karma\u015f\u0131kl\u0131\u011fa sahip geometriler \u00fcretmek ve \u00e7ok disiplinli alanlarda yap\u0131-\u00f6zellik ili\u015fkilerini ara\u015ft\u0131rmak i\u00e7in de\u011ferli ve \u00e7ok y\u00f6nl\u00fc bir ara\u00e7 olarak \u00f6ne \u00e7\u0131kmaktad\u0131r.\n\n---\n\n## Installation / Kurulum\n\n```bash\nconda install bilgi::kececifractals -y\n\npip install kececifractals\n```\nhttps://anaconda.org/bilgi/kececifractals\n\nhttps://pypi.org/project/kececifractals/\n\nhttps://github.com/WhiteSymmetry/kececifractals\n\nhttps://zenodo.org/records/\n\nhttps://zenodo.org/records/\n\n---\n\n## Usage / Kullan\u0131m\n\n### Example\n\n```python\nimport kececifractals as kf\nimport importlib # Useful if you modify the .py file and want to reload it\n\n# --- Example 1: Show the fractal inline ---\nprint(\"Generating fractal to show inline...\")\nkf.kececifractals_circle(\n initial_children=5,\n recursive_children=5,\n text=\"Ke\u00e7eci Circle Fractal: Ke\u00e7eci Dairesel Fraktal\u0131\",\n max_level=4,\n scale_factor=0.5,\n min_size_factor=0.001,\n output_mode='show' # This will display the plot below the cell\n)\nprint(\"Inline display finished.\")\n\n# --- Example 2: Save the fractal as an SVG file ---\nprint(\"\\nGenerating fractal to save as SVG...\")\nkf.kececifractals_circle(\n initial_children=7,\n recursive_children=3,\n text=\"Ke\u00e7eci Circle Fractal: Ke\u00e7eci Dairesel Fraktal\u0131\",\n max_level=5,\n scale_factor=0.5,\n min_size_factor=0.001,\n base_radius=4.5,\n background_color=(0.95, 0.9, 0.85), # Light beige\n initial_circle_color=(0.3, 0.1, 0.1), # Dark brown\n output_mode='svg',\n filename=\"kececi_fractal_svg-1\" # Will be saved in the notebook's directory\n)\nprint(\"SVG saving finished.\")\n\n# --- Example 3: Save as PNG with high DPI ---\nprint(\"\\nGenerating fractal to save as PNG...\")\nkf.kececifractals_circle(\n initial_children=4,\n recursive_children=6,\n text=\"Ke\u00e7eci Circle Fractal: Ke\u00e7eci Dairesel Fraktal\u0131\",\n max_level=6, # Deeper recursion\n scale_factor=0.5,\n min_size_factor=0.001, # Smaller details\n output_mode='png',\n filename=\"kececi_fractal_png-1\",\n dpi=400 # High resolution\n)\nprint(\"PNG saving finished.\")\n\nprint(\"\\nGenerating fractal and saving as JPG...\")\nkf.kececifractals_circle(\n initial_children=5,\n recursive_children=7,\n text=\"Ke\u00e7eci Circle Fractal: Ke\u00e7eci Dairesel Fraktal\u0131\",\n max_level=5,\n scale_factor=0.5,\n min_size_factor=0.001,\n output_mode='jpg', # Save as JPG\n filename=\"kececifractal_jpg-1\",\n dpi=300 # Medium resolution JPG\n)\nprint(\"JPG saving finished.\")\n\n# --- If you modify kececifractals.py and want to reload it ---\n# Without restarting the Jupyter kernel:\nprint(\"\\nReloading the module...\")\nimportlib.reload(kf)\nprint(\"Module reloaded. Now you can run the commands again with the updated code.\")\nkf.kececifractals_circle(output_mode='show', text=\"Ke\u00e7eci Circle Fractal: Ke\u00e7eci Dairesel Fraktal\u0131\")\n```\n---\n\n\n---\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n---\n\n\n---\n\n## License / Lisans\n\nThis project is licensed under the MIT License. See the `LICENSE` file for details.\n\n## Citation\n\nIf this library was useful to you in your research, please cite us. Following the [GitHub citation standards](https://docs.github.com/en/github/creating-cloning-and-archiving-repositories/creating-a-repository-on-github/about-citation-files), here is the recommended citation.\n\n### BibTeX\n\n```bibtex\n@misc{kececi_2025_15392518,\n author = {Ke\u00e7eci, Mehmet},\n title = {kececifractals},\n month = may,\n year = 2025,\n publisher = {GitHub, PyPI, Anaconda, Zenodo},\n version = {0.1.0},\n doi = {10.5281/zenodo.15392518},\n url = {https://doi.org/10.5281/zenodo.15392518},\n}\n\n@misc{kececi_2025_15396198,\n author = {Ke\u00e7eci, Mehmet},\n title = {Scalable Complexity: Mathematical Analysis and\n Potential for Physical Applications of the Ke\u00e7eci\n Circle Fractal\n },\n month = may,\n year = 2025,\n publisher = {Zenodo},\n doi = {10.5281/zenodo.15396198},\n url = {https://doi.org/10.5281/zenodo.15396198},\n}\n```\n\n### APA\n\n```\nKe\u00e7eci, M. (2025). Scalable Complexity in Fractal Geometry: The Ke\u00e7eci Fractal Approach. Authorea. June, 2025. https://doi.org/10.22541/au.175131225.56823239/v1\n\nKe\u00e7eci, M. (2025). kececifractals [Data set]. WorkflowHub. https://doi.org/10.48546/workflowhub.datafile.16.3\n\nKe\u00e7eci, M. (2025). kececifractals. Zenodo. https://doi.org/10.5281/zenodo.15392518\n\nKe\u00e7eci, M. (2025). Scalable Complexity: Mathematical Analysis and Potential for Physical Applications of the Ke\u00e7eci Circle Fractal. https://doi.org/10.5281/zenodo.15396198\n\n\n```\n\n### Chicago\n```\nKe\u00e7eci, Mehmet. Scalable Complexity in Fractal Geometry: The Ke\u00e7eci Fractal Approach. Authorea. June, 2025. https://doi.org/10.22541/au.175131225.56823239/v1\n\nKe\u00e7eci, Mehmet. \"kececifractals\" [Data set]. WorkflowHub, 2025. https://doi.org/10.48546/workflowhub.datafile.16.3\n\nKe\u00e7eci, Mehmet. \"kececifractals\". Zenodo, 01 May 2025. https://doi.org/10.5281/zenodo.15392518\n\nKe\u00e7eci, Mehmet. \"Scalable Complexity: Mathematical Analysis and Potential for Physical Applications of the Ke\u00e7eci Circle Fractal\", 13 May\u0131s 2025. https://doi.org/10.5281/zenodo.15396198.\n\n```\n",
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