MUD ISLAND. Mud Island lies eighteen miles east of Angleton between West Bay, Bastrop Bay, and Christmas Bay in extreme east central Brazoria County (at 29°05' N, 95°09' W). The island is a mile wide and more than two miles long. It is divided from Moody's Island by the Titlum-Tatlum Bayou and from the mainland by the Guyton Cut. The island terrain consists of brackish to saltwater marsh, where mud and sand support rushes and other grasses.