A fully automatic method of synthesizing isotropic textures on subdivision surfaces is presented. The method is designed around a restriction to isotropic textures because only isotropic textures can be automatically generated on an arbitrary surface in the absence of a parameterization. Both Gaussian and Laplacian pyramid representations of the sample texture are constructed. A nonparametric sampling procedure is developed that employs a nearest neighbor search while preserving first order statistics and avoiding discontinuities. Texture synthesis proceeds coarse-to-fine, successively sampling each Gaussian level and returning both the Gaussian RGB values and the Laplacian RGB values of the next finer resolution level. Between each application of sampling, the synthetic Laplacian pyramid is incrementally inverted to generate a first approximation to the texture on increasingly fine resolution levels. Texture is generated directly on the subdivision surface. Within the domain of isotropic textures, the proposed method offers improvements in faithful reproduction of a sample's appearance over a wide range of scales. The proposed method is particularly good at mimicking the sample's quality of randomness. It has a weakness in reproducing isotropic textures are composed of meaningful elements--such as collection of small cogs. The method can be used to produce isotropic variants of anisotropic textures. Finally, while our sampling procedure prevents the use of standard methods for quickly searching high dimensional spaces, an acceleration method is proposed that uses the eigenvector transform and a set of dynamic Kd-trees.