Motivation: Recurrent substructures in RNA, known as 3D motifs, consist of networks of base pair interactions and are critical to understanding the relationship between structure and function. Their structure is naturally expressed as a graph which has led to many graph-based algorithms to automatically catalog identical motifs found in 3D structures. Yet, due to the complexity of the problem, state-of-the-art methods are often optimized to find exact matches, limiting the search to a subset of potential solutions, or do not allow explicit control over the desired variability. Results: We developed FuzzTree, a method able to efficiently sample subgraphs in an RNA structure that lie in a close neighborhood of a requested motif. It is the first method that allows explicit control over (1) the admissible geometric variability in the interactions, (2) the number of missing edges, and (3) introduction of discontinuities in the backbone given close distances in the 3D structure. Our tool relies on a multidimensional Boltzmann sampling procedure with complexity parameterized by the treewidth of the requested motif. We applied our method to the well-known internal loop Kink-Turn motif, which can be divided into 12 subgroups. Given only the graph representing the main Kink-Turn subgroup, FuzzTree retrieved over 3/4 of all kink-turns. We also highlight two occurrences of new sampled patterns. Our tool is available as free software and can be customized for different parameters and types of graphs.