In the "silicate garden" reaction, crystals of a metal salt are placed in sodium silicate solution. The crystals become coated with a semipermeable membrane of metal silicate reaction product, from which hollow tubes of metal silicate rise convectively upward, against gravity. Ln the absence of gravity, and free of convective influences, the reaction might be expected to reveal more fundamental organizing principles. accordingly, we have grown silicate gardens in microgravity, from salts of calcium, cobalt, and magnesium with added nickel. Even in these isotropic conditions, complex structures developed. They included tubes and hollow spheroids, and also novel dendritic '"fingers'" which grew by continuous plastic deformation. This new mode of growth is favored by the slow, diffusion-limited rate of reaction in microgravity, which greatly reduces the rate of hardening of the reaction products. The magnesium-nickel garden grew almost entirely as a fluid interfacial instability between the metal salt solution inside and the silicate solution outside, by deformation of the semipermeable fluid membrane between them. The resulting shape had similarities to that of a solid front advancing through a supercooled melt. The morphology of such a solid is determined by the diffusion of released latent heat away from it, according to the Laplacian diffusion equation. We suggest that Laplacian-growth morphology arises in a microgravity silicate garden when its development is controlled by the analogous diffusion of dissolved ions away from it.