How does the horsetail life cycle show alternation of generations?

Horsetails (Equisetum) exhibit alternation of generations, a life cycle characterized by two distinct, alternating phases: the asexual sporophyte and the sexual gametophyte.1

• Sporophyte Generation: This is the familiar, perennial horsetail plant. It produces strobili (cones) containing sporangia, where spores are formed through meiosis. These spores are released and dispersed into the environment.21
• Gametophyte Generation: When spores germinate, they develop into small, independent, green, pincushion-like gametophytes. These plants produce sex organs: antheridia (which produce sperm) and archegonia (which produce eggs).2134
• Fertilization: Sperm swim through a film of water to reach the archegonia, where they fertilize the egg. This fusion creates a diploid zygote, which develops into a new embryo and eventually grows into a mature sporophyte, completing the cycle.431

While most horsetails are homosporous, some species exhibit functional heterospory, producing physiologically distinct male or female gametophytes.3