Chemical gardens are self-assembled structures with intricate plant-like morphologies and consist of mineralized membranes, which form spontaneously at interfaces between compartments with dissimilar chemical composition, most typically acidic metal salt and alkaline sodium silicate solutions. While this phenomenon is thought to occur in a number of practical settings, it has also proven to be valuable for investigating transport characteristics in distinct applied systems. For example, coupled diffusion and precipitation processes were monitored in silica gardens based on calcium and iron salts, considered to be models for cement hydration and steel corrosion, respectively. Here we extend these studies to the case of aluminum-based silica gardens, one of the so far less frequently investigated examples of silica gardens. To this end, single macroscopic tubes were prepared in a reproducible way by the controlled addition of sodium silicate solution to a pellet of pressed aluminum nitrate. Continued sampling of the volumes enclosed by and surrounding the formed membraneous structure allowed the time-dependent development of ion concentration gradients to be tracked over extended periods of time, while both the pH and electrochemical potential differences across the membrane were recorded online by immersed probes. The dynamic behavior revealed in this way was finally complemented by ex-situ analyses of the composition of the formed tubes. The collected data shows that the as-prepared tubular structures consist of sodium aluminosilicate phases with certain similarities to zeolites and geopolymers. The emerging tube wall was further found to be permeable to all ionic species present in the system, allowing significant electrochemical potential to be sustained over tens of hours until diffusion had eventually diminished the initially generated gradients. The findings of this work may have important implications for the geochemical fate of natural aluminosilicate sources, the use of such geopolymers in construction applications, and the synthesis and properties of zeolites.