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<p>The Sierpinski Triangle, one of the most widely recognized fractal geometries, is not only a fascinating mathematical construct but also a powerful tool in engineering applications. In RF and microwave engineering, its unique self-similar structure has been successfully exploited to enhance the performance of antennas, waveguides, and filters by improving bandwidth, achieving miniaturization, and enabling multi-band operation. Despite these advantages, manually creating such fractal geometries in electromagnetic simulation tools like HFSS can be tedious, error-prone, and time-consuming, especially as the iteration level increases and the number of sub-triangles grows exponentially. To address these challenges, this work proposes a Python-based automation methodology for the generation of Sierpinski Gasket fractals within HFSS. This approach allows engineers to efficiently adjust key parameters, such as the iteration level, and instantly generate accurate models of complex fractal structures. The results show that the number of sub-triangles grows exponentially with each iteration (N(n)=<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\:{3}^{n+1}\)</EquationSource> </InlineEquation>), leading to longer execution times—e.g., from about 1&#xa0;s at <i>n</i>=1 to roughly 7&#xa0;min at <i>n</i>=5—but still representing a significant improvement over manual design. By streamlining the workflow, this method reduces human error, improves precision, and enables efficient exploration of complex fractal configurations, providing a scalable solution for high-frequency component development.</p>

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Enhancing HFSS design efficiency through python-based automation: a case study of Sierpinski triangle fractal

  • 期刊论文

  • 发表日期：

    2026年6月3日

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  • Mariem Abdi,
  • Taoufik Aguili

摘要

The Sierpinski Triangle, one of the most widely recognized fractal geometries, is not only a fascinating mathematical construct but also a powerful tool in engineering applications. In RF and microwave engineering, its unique self-similar structure has been successfully exploited to enhance the performance of antennas, waveguides, and filters by improving bandwidth, achieving miniaturization, and enabling multi-band operation. Despite these advantages, manually creating such fractal geometries in electromagnetic simulation tools like HFSS can be tedious, error-prone, and time-consuming, especially as the iteration level increases and the number of sub-triangles grows exponentially. To address these challenges, this work proposes a Python-based automation methodology for the generation of Sierpinski Gasket fractals within HFSS. This approach allows engineers to efficiently adjust key parameters, such as the iteration level, and instantly generate accurate models of complex fractal structures. The results show that the number of sub-triangles grows exponentially with each iteration (N(n)= \(\:{3}^{n+1}\) ), leading to longer execution times—e.g., from about 1 s at n=1 to roughly 7 min at n=5—but still representing a significant improvement over manual design. By streamlining the workflow, this method reduces human error, improves precision, and enables efficient exploration of complex fractal configurations, providing a scalable solution for high-frequency component development.