Hybrid Fractal–Parametric Modeling and NSGA-II Optimization of Geometric Material-Volume Reduction in Generative Architectural Façades

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.

The authors' abstract, as published at the source. Fractal and Fractional, 2026 · DOI ↗