Fascinating patterns may be observed when performing chemical garden experiments, which occur when metal salts come into contact with solutions such as sodium silicate. Hele-Shaw cells, quasi-two-dimensional micro reactors, can be used to reduce the complexity of the system: osmosis is removed when performed with injection, and buoyancy if placed horizontally; the results are thus only dependent on the relationship between flow and chemical reaction. Firstly, we analyse the behaviour of horizontal filaments, one of the main patterns of confined chemical gardens. We model their erratic motion by considering the diffusive supply of ions to the tip, and the spreading of product as the filament advances. We show that these effects lead to an oscillation of the concentration of product at the tip and its internal pressure, causing the filament tip to periodically change direction. We also demonstrate from statistical mechanics that the filament tips grow with a self-organized dispersion mechanism. Effective diffusivities as high as 10−5 m2 s-1 are measured, an efficient transport four orders of magnitude larger than molecular diffusion in a liquid, ensuring widespread contact and exchange between fluids in the chemical garden structure and its surrounding environment. In a second study, experiments were carried out with a vertical Hele-Shaw cell, introducing the effect of buoyancy into the system. The expanded model shows good agreement with the results, while also suggesting that the concentration of the host solution of sodium silicate also plays a role in the growth of the structures despite being in stoichiometric excess. In a third study, novel patterns are described, which grow at flow rates below the threshold for the formation of filaments. We describe and model the evolution of a thin filament wrapping around an expanding “candy floss” structure, forming a new pattern resembling an Archimedean spiral. The effective density of the precipitate as well as the permeability of the membrane were estimated from the results. Finally, in a fourth study, these findings were applied to geological fluid and venting systems of methane. The precipitate filaments grown in the laboratory are used as a theoretical analogue of the spreading of methane hydrates under the seabed. We discuss how this methane venting leads to the formation of marine authigenic carbonate rocks, and for confirmation, we analyse two field samples from the Gulf of Cadiz for composition and mineralogy of the precipitates. We note the implications of this work for hydrate melting and methane escape from the seabed.