<p>Non-periodic architectures observed in biological materials have been studied for their outstanding mechanical properties, such as high stiffness-to-weight ratio, energy absorption, and capacity to redistribute applied stresses. Taking inspiration from these architectures to generate engineering materials is still an open challenge. Irregular structures are challenging to model and fabricate using conventional design methods, yet they offer unique opportunities for creating functional and efficient material systems. One emerging approach is the use of tile-based computational algorithms that simulate growth processes to more effectively capture the structural irregularity of these materials. In this work, we discuss biological irregular architectures and the recent developments in computational tiling algorithms, with a particular emphasis on algorithms of virtual growth. These algorithms rely on simple tiles and a set of modifiable connection rules to generate countless complex, non-periodic structures with precise control over their geometry and topology. Recent studies have shown that material systems synthesized using tile-based designs inspired by non-periodic biological architectures can exhibit favorable properties, including enhanced impact absorbance and stress modulation. Despite this progress, integration of structure and function remains limited, highlighting the need for hybrid approaches that incorporate performance-based feedback and optimization strategies. In this context, these tools are uniquely positioned not only as generators of designs of increasing structural complexity for advanced architected materials but also as promising models for investigating fundamental questions in developmental biology.</p>