{
  "abstract": "This study develops a hybrid fractal–parametric modeling (HFPM) workflow integrating recursive affine iterated-function systems, finite-scale box-counting, fixed-thickness prism extrusion, and NSGA-II to explore trade-offs between geometric material volume and geometric complexity in generative architectural façades. A common 729 × 729 raster and four box-counting scales (3, 9, 27, and 81) are applied to both investigated recursion depths (r = 3 and r = 4). Across five independent NSGA-II runs, the pooled final non-dominated reference set yielded geometric material-volume reductions of 34.58% and 44.57% within 1% and 2% deviations, respectively, from the baseline finite-scale fractal dimension (Df). Mean hypervolume was 0.26182 ± 0.00113, evaluated in the original objective space against a common reference point (1.000000, 0.323566); mean inverted generational distance was 0.01732 ± 0.00244, evaluated using range-normalized distances to the empirical pooled reference front. Independent fixed-recursion optimization, simple branch-pruning controls, and density-seed, grid-origin, raster-resolution, and scale-window sensitivity tests further delimit these findings. Branch removal contributes substantially to the volume reductions, while the measured trade-offs and tolerance-feasible solutions depend on the chosen box-counting window. The results therefore establish a computational, protocol-dependent geometric trade-off for the investigated fixed-thickness prefactal prisms, not structural efficiency, equivalent façade functionality, fabrication feasibility, cost savings, or environmental benefits.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Information Technologies, University of Information Technologies and Management, Karshi 180100, Uzbekistan",
    "Department of Digital Technologies Convergence, Tashkent University of Information Technologies Named After Muhammad al-Khwarizmi, Tashkent 100084, Uzbekistan",
    "Department of Software and Hardware Support of Computer Systems, Karshi State Technical University, Karshi 180100, Uzbekistan"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Golib Berdiev",
      "orcid": "0000-0003-0075-5414"
    },
    {
      "affs": [
        1
      ],
      "name": "Shahzoda Anarova"
    },
    {
      "affs": [
        2
      ],
      "name": "Navruz Khujakulov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9tvyy31dgbrfk.bib",
  "cited_by": 0,
  "doi": "10.3390/fractalfract10110771",
  "fulltext_url": null,
  "id": "9tvyy31dgbrfk",
  "issns": [
    "2504-3110"
  ],
  "landing_url": "https://www.mdpi.com/2504-3110/10/11/771",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/9tvyy31dgbrfk.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T12:20:48Z",
      "native_id": "10.3390/fractalfract10110771",
      "source": "crossref",
      "url": "https://www.mdpi.com/2504-3110/10/11/771"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "issn:2504-3110",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Hybrid Fractal–Parametric Modeling and NSGA-II Optimization of Geometric Material-Volume Reduction in Generative Architectural Façades",
  "title_text": "Hybrid Fractal–Parametric Modeling and NSGA-II Optimization of Geometric Material-Volume Reduction in Generative Architectural Façades",
  "type": "peer-reviewed",
  "updated_at": "2026-11-07T00:21:05Z",
  "url": "https://research.draconitic.com/paper/9tvyy31dgbrfk",
  "venue": "Fractal and Fractional",
  "versions": []
}