In the mid-1600s the collapsing Ming Dynasty leadership fled to Taiwan and brought with them their great past and their slowly dying culture. This introduced new architecture, art, pottery, and a blossoming of the sciences. Since the dynasty was on verge of collapse though the cultural significance and sustainability of these introductions were limited. What it did do though was encourage larger immigration to the island from China, again altering the culture to match historic Chinese culture.
Numerous aspects of Chinese culture were brought to Taiwan as education and the sciences grew, Chinese foods, languages, philosophies, and dress were introduced as was the Chinese mentality. The people and culture became a well-disciplined society who honored respect and humility. Another important aspect of Chinese culture that was brought to Taiwan was their need to "save face," something that again came from honor and respect for others.
After the communists came to power in mainland China, the fleeing Nationalist government made their way to Taiwan. The people of Taiwan accepted this government, and again many people immigrated to the island with the government, leading to another wave of Chinese immigration and a further solidification of Chinese culture in Taiwan. As mainland China became a communist country, Taiwan became a democracy on paper, although in reality their government was quite authoritarian.
Life in Taiwan took on a different path than that in China; religion was still allowed and men meeting in temples to play games and gamble continued to be a common occurrence. Family continues to be the center of personal lives and couples are allowed to have more than one child as food is still the center of family and other social events as eating always seems to be on the mind of locals.
Despite delays in receiving many of the world's modern technological achievements, Taiwan today not only has most modern technology, but is also a huge center for foreign investment, meaning they make much of this technology. This has changed the culture as cars and public transportation are common and easily available as the people are more urbanized and living in houses or high rise apartment buildings. Cell phones and the internet, along with games are becoming a more substantial part of the culture annually and new forms of communication is making the country more social and connected, but at its core, Taiwanese culture is still rooted in Chinese traditions.