Programming chaotic centers for shaping light branching in topological nematic vortices.

Chaotic behaviors, epitomized by the butterfly effect where small causes have outsized consequences, are ubiquitous in light-matter interactions yet remain challenging to localize and even harder to engineer. Here, we demonstrate and model the direct light interacting with a programmable chaotic center-the core of photopatterning liquid-crystal topological vortices-where chaos reshapes into symmetry-protected light branching. Via confocal polarizing microscopy and Landau-de Gennes free-energy simulations, we observe the core splitting in-plane while spanning out-of-plane. This splitting pattern and peripherical director field dictate the branches number, while defect-induced refractive index variations with core-sensitive nonlinear dynamics yield distinct, spatially mapped Lorenz-like attractors. Applying a low-voltage field further allows us to reconfigure the splitting pattern and dynamically redirect the branching pathways. These findings potentially establish a versatile platform for on-chip topological photonics while serving as a laboratory analog for light scattering in extreme cosmological environments, such as near black holes.