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This article describes an algorithm to generate a triangulation of an implicit surface. The generated triangles are close to equilateral and the triangle edge lengths vary with local surface curvature (the user may choose the ratio of edge length to surface curvature). The output of this algorithm is useful for applications that require high-quality triangulations, such as medical imaging, molecular modeling, computer aided design, and finite element analysis. Triangles are "grown" on the surface outward from a seed triangle. After the growing stops, the remaining gap in the triangulation is filled by a set of heuristics. Experiments show that the algorithm consistently builds high-quality triangulations, which compare favorably to those produced by cell-based and particle-based algorithms.