Flexi Says: They include binary fission, fragmentation, and budding. Binary fission occurs when a parent cell splits into two identical daughter cells of the same size. Fragmentation occurs when a parent organism breaks into fragments, or pieces, and each fragment develops into a new organism. Starfish, like the one in Figure below, reproduce this way. A new starfish can develop from a single ray, or arm. Starfish, however, are also capable of sexual reproduction. Budding occurs when a parent cell forms a bubble-like bud. The bud stays attached to the parent cell while it grows and develops. When the bud is fully developed, it breaks away from the parent cell and forms a new organism.