It particularly shows the lines of the material continuity within a design space, and they may derive from the classical Michell structural optimization of truss structures [47; 48]. One of the main issues which can be faced is the appropriateness and the fabricability of PSLs in AM. Prior research works have successfully addressed the topology design method based on PSLs for AM of two-dimensional structures [43; 49]. According to [PERSON] and [PERSON] [50], PSLs do not depend on the scaling of the material stiffness and the applied load but rather on the design boundaries, the location and the degree of the force, and the boundary conditions. Moreover, PSLs represent a continuous field in which they can either cross multiple design boundaries or be fully periodic. These mechanical and geometric properties prove the usefulness of PSLs as AM printing paths [51]. Based on the aforementioned statements and the literature, PSLs can serve as guidelines or paths for material growth and distribution inside a structure. A similar strategy was developed by [PERSON] et al. [52] and [PERSON] et al. [53] to enhance structural performance of additively manufactured objects through build orientation and gradient paths. Plant growth algorithms and theories developed by [PERSON] and [PERSON] are widely known as L-systems [54]. From a geometric point of view, L-systems are a formalism to model the development of growing linear and branching structures, from basal filamentous organisms to trees to entire plant ecosystems [55; 56]. Efforts in this research area are mainly focused on their graphical representation and computation [57,58]. However, interesting studies showed root system models using L-systems and proved their effectiveness in estimating the shear strength of root-soil composites [59,60]. Such systems have provided promising results when coupled with topology optimization algorithms. For instance, [PERSON] et al. [61] proposed a genetic algorithm that encodes design variables and governs the development of the structure. An interpreter is required to translate genomic information into structural topologies, therefore leading to adaptive structures capable of achieving multiple design objectives in light weight and increasing stiffness. L-systems have also been combined with cellular automaton to generate mechanical structures for multiple mechanical conditions [62]. Tree-like systems or fractals have also inspired engineers to develop heat exchangers and cooling systems. A review of fractal heat exchangers has demonstrated their big advantages in lowering the pressure drop and in maintaining a uniform temperature [63]. Then, the generalization of L-systems within a structure for objectives of light weight is a challenge. The utility of integrating L-systems inside mechanical structures can be validated via numerical simulations using different FEA software such as ANSYS Workbench and COMSOL Multiphysics. Indeed, numerical simulations of bioinspired mechanical structures and composites have proven the effectiveness of emulating nature in its aspects and shapes [64,65,66]. Despite all the research works based on L-systems in the aforementioned domains, there is still a lack in the application for biomimetic lightweight structures with high stiffness in AM. To address this challenge, this paper proposes a novel computational design method based on L-systems generated and distributed along the PSLs' directions. By considering a rough design space, multiple load cases and boundary conditions are investigated. The resulting tree-like structures are studied through numerical simulations followed by a design of experiments (DOE). The latter scheme of parametric optimization utilized the branches' thicknesses as two design variables for the models using the first and second PSLs directions separately. This method aims to find the optimal structure after conducting a series of simulations and sensitivity studies [67].