The orientator is a new technique for the estimation of length and surface density and other stereological parameters using isotropic sections. It is an unbiased, design-based approach to the quantitative study of anisotropic structures such as muscle, myocardium, bone and cartilage. A simple method for the practical generation of such isotropic planes in biological specimens is described. No special technical equipment is necessary. Knowledge of an axis of anisotropy can be exploited to optimize the efficiency. To randomize directions in space, points are selected with uniform probability in a square using various combinations of simple random, stratified random, and systematic random sampling. The point patterns thus produced are mapped onto the surface of a hemisphere. The mapped points define directions of sectional planes in space. The mapping algorithm ensures that these planes are isotropic, hence unbiased estimates of surface and length density can be obtained via the classical stereological formulae. Various implementations of the orientator are outlined: the prototype version, the orientator-generated ortrip, two systematic versions, and the smooth version. Orientator sections can be generated without difficulty in large specimens; we investigated human skeletal muscle, myocardium, placenta, and gut tissue. Slight practical modifications extend the applicability of the method to smaller organs like rat hearts. At the ultrastructural level, a correction procedure for the loss of anisotropic mitochondrial membranes due to oblique orientation relative to the electron beam is suggested. Other potential applications of the orientator in anisotropic structures include the estimation of individual particle surface area with isotropic nucleators, the determination of the connectivity of branching networks with isotropic disectors, and generation of isotropic sections for second-order stereology (three-dimensional pattern analysis).