Terraforms: Engineering Self-emergent Natural Structures

What is the ultimate determinant of strikingly diverse patterns? Can we find a reflection of empirically fabricated patterns into ecological patterns? Can we use these fabricated patterns to inquire about the ontogeny and optimality of nature’s forms and engineer optimal eco-restoration and environmental applications that leverage materials? In this paper, we propose a simple yet powerful uniform pressure-stress response model where the heterogeneous triphasic mixture’s proportions are the leading control determining networked patterns (Terraforms) from uniform to random topologies with fine-scale hybrid motifs. The clay proportion – as the foundational material bonded by water – is the leading factor determining the topology of the patterns, while the ratio of water and binder (mimicking ecological interactions) is the second-order factor determining patterns’ motifs. Scale-free patterns arise from log-normal materials’ proportions, where the systemic stress and hygroscopy are the minimum and maximum for a universal water/binder ratio equal to the Pacioli golden ratio.