Ayn Rand, the sternly individualistic author of such best-selling novels as "The Fountainhead" and "Atlas Shrugged," and the founder of a philosophy known as objectivism, died yesterday at her home in New York City. She was 77.

The Russian-born Miss Rand, an American citizen since 1931, was found in her apartment on Manhattan's East Side in the early afternoon. Death was attributed to natural causes, but no details were immediately available.

"The Fountainhead," published in 1943, was the work that established her reputation and appeared to embody her philosophy, which has been described as a sort of romantic selfishness.

An unconventional novel of ideas, the book has as its hero a brilliant, iconoclastic architect who demolishes one of his own buildings because scorned planners had corrupted the purity of its design.

"When I am questioned about myself," Miss Rand wrote in a letter to the readers of the book, "I am tempted to say, paraphrasing Roark: 'Don't ask me about my family, my childhood, my friends or my feelings. Ask me about the things I think.' "

Miss Rand asserted that it is the "content of a person's brain, not the accidental details of his life, that determines his character. My own character is in the pages of 'The Fountainhead' . . . "

"The Fountainhead," along with "Atlas Shrugged," which was published in 1957, and appeared to glorify capitalism, served as texts for the objectivist movement led by Miss Rand. Objectivists appeared to adhere and aspire to a form of rugged individualism that rejected the doctrines of present-day conservatives and liberals. Her fictional characters, such as the architect Howard Roark, as well as John Galt, the industrialist hero of "Atlas Shrugged," reflected Rand's concept of objectivism.

Born in 1905 in St. Petersburg, now Leningrad, into a prosperous Jewish mercantile family, she was determined and independent from the start. "I decided to be a writer at the age of nine," she once said. "It was a specific, conscious decision--I remember the day and the hour."

"I left home when I was quite young," she said, "and have been on my own ever since . . . My life has been 'single-tracked' or anything anyone wishes to call a life consciously devoted to a conscious purpose.

"I have no hobbies," she went on. "I have few friends. I do not like to 'go out,' " she added in the letter to the readers. "I am unbearable--to myself and others--when I stay too long away from my work."

She said nothing else ever mattered to her very much except her husband, Frank O'Connor, to whom "The Fountainhead" is dedicated. The book was later made into a film starring Gary Cooper and Patricia Neal.

She came to the United States in the 1920s after graduating from college in the Soviet Union. Although college educated, she said, she was never trained in literature or writing, and "whatever I learned I had to learn by myself and in my own way."

She said she did not attempt to write professionally until she felt sure of herself, then sold the first film story, the first stage play and the first novel she ever wrote. The film story was bought by Universal Pictures. The play was produced on Broadway in the 1935-36 season as "The Night of January 16th" and the novel was "We, The Living" (1936).

In calling for a return to the principles of the Founding Fathers, Miss Rand asserted that man's right to his own life, liberty and pursuit of happiness meant his "right to exist for his own sake, neither sacrificing himself to others nor sacrificing others to himself . . . "