When Mr. Lin arrived onstage, the audience members applauded, shouted and held up banners proclaiming their love. At the end of the show, they waved their phones, creating a sea of lights.

Cloud Gate, which will now be run by Cheng Tsung-lung, the director of the company’s junior troupe, has long been an established presence on the international dance scene. “Lin Hwai-min is the name card of Taiwan in the performing arts, one of the most important representatives of our culture,” said Chang Hui-chin, the director general of Arts Development at the Ministry of Culture, who was attending the outdoor performance. “He has connected us to the world.”

Lin Yatin (no relation to Mr. Lin), an associate professor of dance at the Taipei National University of the Arts, said there was no professional contemporary dance troupe in the Chinese-speaking world when Mr. Lin founded Cloud Gate in 1973. That was a moment when Taiwan was seeking its own cultural identity following 50 years of Japanese rule (1895-1945), after which it was ceded back to China. In 1949, China’s nationalist government lost control of mainland China and fled to Taiwan, establishing martial law.

“They made my parents’ generation Japanese, and they tried to make us Chinese,” Mr. Lin said in an interview before the concert. “I didn’t set out to reflect Taiwanese society, but when I started choreographing, I knew I wanted it to be something of our own.”