But it is more than that. Teenage women in Tehran now carry tiny pictures of Leonardo DiCaprio in their wallets, the American film star - playing the fictional Jack Dawson - being one of the Titanic's martyrs.
Even the government newspaper Iran was moved to carry a full-page story on the ship's sinking, headlined "The Greatest Maritime Tragedy of the Century".
True, the Titanic's fate embraces a lot of revolutionary Iran's favourite obsessions: mass death, self-sacrifice, the collapse of Western self- confidence and the corruption of wealth. Kate Winslet's fiance in the film employs a butler who spies on her and DiCaprio - like the Iranian morals police. And when the butler loses sight of them, they drink alcohol and make love. What a message for an Iranian audience.
But bootleg copies of the movie, illegally videotaped in cinemas, are now flooding the black market. And Iran's own film industry is blossoming. One of the stars of the Cannes festival was Samira Makhmalbaf, who plays the heroine of The Apple, an Iranian movie recording the story of two sisters whose mother was blind and whose father - fearful that they would be corrupted by the outside world - kept them in a cage until neighbours released them. What is more, their story is true.
Three of four years ago, such cinema-viewing would be inconceivable. So would the advent of a real, competitive, aggressive afternoon newspaper. But the new Jamiyah (Society) - circulation higher than 130,000 - campaigns for human rights, covers sport and Hollywood, and has even asked President Clinton for an interview. It has talked to former White House man Geoffrey Kemp on Iran (Mr Kemp is conservative to the point of dullness) and to the Iranian journalist Faraj Sarkuhi following his release from prison after being charged with denigrating the government.
When the Mayor of Tehran, Gholamhossein Kharbashi - a friend of President Mohamed Khatami - was jailed for corruption, Jamiyah cartooned the unfortunate civic leader chained to a flower-pot - an allusion to his dramatic creation of public parks and flower-beds in central Tehran.
Mr Kharbashi is secretary-general in the new Servants of Construction party, which has been set up as a political platform for Mr Khatami in an obvious attempt to provide democratic credentials to all those who oppose the conservative "Supreme Leader", Ali Khamenei. In the new party can be found the governor of the Iranian Central Bank, Mohsen Nourbakhsh, the bright and liberal Islamic Guidance minister, Ataollah Mohajerani, and Faizah Hashemi, daughter of the former president.
The new party was set up on the first anniversary of the election of the highly educated, German-speaking and even humorous Mohamed Khatami as president. The Servants of Construction mouth the same comfortable policies as Mr Khatami; civil society and "transparent" politics - the latter a clear insult to the highly untransparent politics of Ayatollah Khamenei and his supporters.
But the Supreme Leader has not lost his power. When Ayatollah Hossein Montazeri, a supporter of Mr Khatami, called a demonstration to show support for him at Friday prayers last week in Isfahan, where the unfortunate prelate is under house arrest, Ayatollah Khamenei denounced the protest as a conspiracy "by US arrogance and its Zionist elements." Mr Khatami's attempts to secure improved relations with Washington resulted in an exchange of wrestling teams; the Americans were welcomed as friends in Tehran - the Iranian team arrived in the United States to be photographed and finger- printed like criminals.
Old habits die hard. The Americans are prepared to talk to Iran if it abandons "terrorism" - a reference to the killing of Iranian dissidents abroad and Tehran's support for the Hizbollah guerrillas fighting Israeli occupation forces in Lebanon. Last week, Iran issued its own four conditions for talking to Washington: an end to American "interference" in Iran and the return of Iranian assets frozen when the Shah was overthrown, a halt to support of opponents of the Tehran regime and to accusations of "terrorism", because "America itself supports terrorism, including Israeli state terrorism."
Although Europe appears to have softened the Helms-Burton sanctions against foreign companies doing business with Iran, the US Senate has imposed a sanctions Bill against firms which sell military technology to Iran, claiming Russia is advancing an Iranian missile programme. Moscow says it is merely completing a 1,000-megawatt nuclear power station at Bushehr - "no secrets, no hidden agreements," according to President Yeltsin's spokesman.
An Iranian delegation led by Gholamreza Aghazadeh was in Russia last week to discuss delays in the Bushehr construction, which Ukraine refused to honour; Mr Aghazadeh is likely to visit Peking next month to discuss nuclear co-operation with China. American suspicions will not have been softened by the theft in Isfahan of a truck carrying parts from the Bushehr plant.
At the same time, Kamal Kharrazi, the Iranian Foreign Minister, has been visiting the Arab Gulf to continue building relations between Tehran and the kings and emirs of Britain's former protectorates.
Iran's claim to three islands in the United Arab Emirates - in dispute since the early 1970s and memorably called Abu Moussa and the Greater and Lesser Tunbs - continues to stifle trust between Arabs and Iranians. Iranian mediation in Afghanistan has meanwhile failed to unite two factions opposed to the "Black Taliban" Islamic militia supported by Saudi Arabia.
The 1994 bombing of a Jewish community centre in Buenos Aires - for which the Argentines fingered an Iranian diplomat called Mohsen Rabbani - has led to the recall of most of Argentina's diplomats in Tehran and a demand from Buenos Aires that Iran reduces its embassy in Argentina to a single envoy. "Baseless," Mr Kharrazi responded to the claims, which were, he said, "based on the antagonistic patterns of the ... propaganda machinery of the Zionist regime".
Routine rhetoric, perhaps, but not particularly upsetting to the people of Tehran who, amid their Kharbashi-installed public gardens and new shopping malls and cinemas, care little about accusations of terrorism or even about Salman Rushdie. The economy - which is quite another story - will perhaps be President Khatami's greatest challenge; some call it, too, a Titanic. But Iran itself shows every sign of becoming - horror of horrors for the United States - a normal country.