The Institute of Statistical Mathematics, 4-6-7, Minami-Azabu, Minato-ku, Tokyo 106-8569, Japan
(Received March 31, 1993; Accepted June 14, 1994)
Keywords: Adjustment Models of Type I and Type II, Lexell's Circle, Packing Density, Radiolarian, Spherical Cap, Spherical Trigonometry, Voronoi Tessellation
Abstract. This paper is concerned with the spatial patterns on the sphere which include a certain randomness. At first, the random sequential packing on the sphere is discussed and some results of its computer experiment are shown for several spherical radii of spherical caps. Secondly, the networks based on the spherical Voronoi tessellation are considered and the models for pattern formation of tessellation network are presented. Application to real data is also discussed. Finally, a consideration of the optimal spherical network is given as the application of the pattern formation model presented in the text.