Tracking Topology-Synergistic Adaptive Emergence in Non-equilibrium Silica Surface Growth on Liquid Metals

Abstract In out-of-equilibrium systems, the absence of reciprocity can induce unconventional states, phase transitions, and rich emergent behaviors with broad scientific and technological relevance. Here, we demonstrate a far-from-equilibrium surface-growth system that surpasses conventional fractal complexity and leads to unprecedented pattern complexity with diverse collective topological nonlinear excitations. By harnessing the self-driven SiO2 nanoparticles (NPs) on high-temperature liquid copper featuring extreme surface tension, we show that the complex coupling of giant Marangoni-driven hydrodynamics and reaction-diffusion processes allows the formation of singular SiO2 adaptive collective topological surface structures (ACTS), along with their highly adaptive emergent variants and even deterministic chaos. We identify two multiscale topology-synergistic excitation modes enabled by “macro-order and micro-bifurcation” causal mapping and show that continuous modulation of NP density and layer viscosity autonomously switches between regimes, generating gradient-dependent assembled ACTS with unprecedented complexity and adaptivity. Our results provide new insights for understanding and controlling of complex nonlinear dynamics for a non-trivial texture in surface growth, paving the way for the design of next-generation active-matter-inspired adaptive interfacial materials with topological protection.