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Preprint · Preprints.org · September 29, 2026

Hybrid Fractal–Parametric Modeling and NSGA-II Optimization of Material-Efficient Generative Architectural Façades

Golib Berdiev, Shahzoda Anarova, Navruz Khujakulov

Golib Berdiev
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Abstract

Fractal geometry provides a compact mathematical framework for generating and measuring multi-scale architectural form, but its integration with material-aware generative façade optimization remains limited. This study introduces a Hybrid Fractal–Parametric Model (HFPM) that combines recursively composed affine iterated-function-system transformations, parametric control, finite-scale box-counting, three-dimensional extrusion, and NSGA-II optimization in a reproducible Python–Blender workflow. The design vector P = (r, s, θ, d, t) controls recursion, scale, rotation, retained branch density, and thickness. Material volume is minimized while deviation from a baseline finite-scale box-counting dimension is minimized simultaneously. A balanced 300-configuration experiment characterized the design space before NSGA-II optimization with a population of 40 over 15 generations. The optimizer evaluated 603 unique non-baseline configurations; 602 passed all geometric and numerical validation checks, and 39 formed the final Pareto set. Relative to the baseline (Df = 1.9077; Vm = 0.9228 m³), material volume decreased by 34.9% within a 1% Df tolerance and by 44.6% within 2%. HFPM therefore exposes a reproducible material–complexity trade-off for early-stage fractal façade exploration without making unsupported structural-performance claims.

Architecture and Computational DesignArchitecture and Art History StudiesTopology Optimization in Engineeringfractal geometrygenerative designbuilding exteriors

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