Do cactus plants branch every 50 years?

No, cactus plants don't branch necessarily every 50 years. In fact, not all cactus plants branch. Not all of those that do branch have a life expectancy of 50 years. Those that do live 50 years and more can't count on regular intervals between branching. For example, environmental factors, such as extended drought, get in the way of any predictable pattern with the giant saguaro cactus [Carnegiea gigantea]. The saguaro has a life expectancy of 150+ years. It first branches at 40+ years. But subsequent branches can't be counted on to appear every 40-50 years. The desert can be counted on for predictably high levels of heat and light. But it can't be counted on for consistently adequate or regularly occurring amounts of moisture.