I want to share the strategy that allowed me to win a culture victory on Deity. It's not as difficult as it may seem, as long as you stick to an Archipelago map.
Proof
http://steamcommunity.com/sharedfiles/filedetails/?id=162002661
http://steamcommunity.com/sharedfiles/filedetails/?id=162002787
Overview of the strategy
I use Brazil. France may work. I believe that religious civs are viable for a culture victory on Deity, but this strategy has not been made for them.
I do not focus on a religion at all. This may seem counterintuitive because achieving World Religion status gives +50% tourism to the respective holy city, and buying Great Musicians with faith is very helpful. However, I learned that founding a religion, building the key wonders, and setting the capital up for long-term success is simply too hard with this approach.
I do not found other cities. One city culture victory on Deity sounds crazy, but it works. More than one city would slow me down too much in the critical early phase of the game.
You do need a good starting position. Brazil tends to start near or in the jungle. This is often bad. It is important to have enough production available early on, and enough land to grow a large city later on.
A culture victory relies heavily on wonders. This strategy relies heavily on engineers to hurry production of these wonders. This means you have to plan ahead in order to have an engineer available at the right time.
A culture victory also relies heavily on maintaining open borders and trade relations with as many civs as possible. Try to earn diplomacy bonuses whenever you can. When an AI asks for a luxury or a sum of gold, give it to them. Always share intrigues. Help AIs with their resolutions in the World Congress. Try to avoid diplomancy penalties whenever you can, and trade with everyone. This also has the benefit of netting you many research agreements which you need.
Ancient and Classical era:
Start filling out the Tradition tree.
You want to build the Temple of Artemis so that you will have an engineer ready to hurry the production of the Sistine Chapel. The extra +10% growth is also nice. Then you want to build the Hanging Gardens to feed all the specialists that you'll be running. To do that, you should research Mining -> Archery -> and then the tech which unlocks the Hanging Gardens. You should build a monument, worker, then Temple of Artemis. Chop forests, build mines... your top priority is to get these two wonders. If you fail to get them, victory will be unlikely.
After unlocking the Hanging Gardens, unlock whatever tech you need to get your local luxury resource. Then beeline for the National College, Writer's Guild and research Theology.
I also recommend building a second worker after the Hanging Gardens.
Medieval era:
Finish the Tradition tree and start working on Aesthetics.
Get an University as soon as possible, and researching Acoustics right after.
It's highly likely that the AI will enter the Renaissance before you do. It usually doesn't enter via Acoustics, so don't panic.
Steal the techs that unlock the Workshop and Artist's guild. Build and assign specialists to both. Do not assign specialists to the University. It is not necessary to get a Workshop in the Medieval era but you should get it early. You will need a second Great Engineer by the time you unlock the Louvre. You should be careful which civ you steal techs from. A suitable civ is one that is culturally weak (check the culture victory menu), and likes you. This minimizes the probability of being unable to maintain open borders with that civ later on, and minimizes the damage that would result from this.
At this point it should also be safe to invest production into cargo ships because the AI should have killed off barb camps, or at least have enough control of the seas to allow for safe trading. Save the Oxford Library for later.
Renaissance era:
Continue with the Aestethics tree. Make sure you unlock Exploration tree early enough.
Hurry production of the Sistine Chapel with your Great Engineer. If you don't have a workshop yet, research it. Then research Architecture. While researching also build the Heroic Epic for the extra Great Work of Writing slot, an Opera House to unlock the Hermitage, a Musician's Guild (assign specialists imediately, the Ironworks, and of course the Hermitage and lastly, a Harbor for increased range on trade routes.
It is unlikely that you will be able to build the Uffizi because at this point you're really starting to fall behind. It is probably a better idea to focus on getting a great start into the Industrial era. The plan is to enter the Industrial era by researching Navigation after Architecture, and timing the construction of the Oxford Library so that you can jump right to Archeology.
It's also a good idea to start checking how many Great Writers you still need. You'll need a total of five, two of them from different eras and different civilizations.
In the world congress, try to ban luxuries that you do not have access, and are not provided by mercantile city states. You'll want to befriend the mercantile city states later for happiness, but make life a little bit more difficult for the AIs.
Once you unlock Astronomy, build or buy a Caravel to explore the world around you so that you don't have to search for archaelogy sites later.
Industrial era:
You should have unlocked the Exploration tree. Finish the Aesthetics tree and start working on the Rationalism tree.
Hurry production of the Louvre with your second Great Engineer and build five Archaelogists. Two artifacts will be for your museum, two for the Louvre, and one for your palace. It's a good idea to let your workers, and supplemental scouts bought just for this purpose, occupy archaelogy sites until your Archaelogists arrive.
After you're done with this, your next priorities are to get a Public School, a Factory and then to research Radio. Assign specialists to the factory to get your third Great Engineer ready by the time Broadway is unlocked.
Try to sign as many research agreements as you can, and to maintain a trading fleet to finance them. As your Tourism increases, it becomes more and more important to maintain open borders and trade routes with all civs.
Sometimes no AI picks Rationalism (check Global Politics overview). If this happens, build the Porcelain Tower.
It is also a good idea to start building some properly trained military units if you have the time, because once you adopt an ideology, you may find yourself in one or several wars very quickly.
By the way: to get the theming bonus of the Broadway, you will need three Great Works of Music from the same era and civ. Fortunately, the era of a Great Work is that in which it was created, not that in which the Great Writer/Musician/Artist was born. So it's easy to get the theming bonus by just having 1-2 Great Musicians on standby until Broadway, which gives you one more Great Musician, is actually built.
You should also start adding specialists to your science buildings, but without overriding your next Great Engineer.
Modern era:
You'll have to pick an ideology. Think very carefully what's best in your current situation. Order should be your default choice because it has good tenets and is popular with the AIs. Freedom has slightly better tenets but AIs tend to avoid it, so by choosing Freedom you tend to make many enemies. Freedom also gives a lot of culture which allows you to finish the Liberty tree for a free golden age and Great Musician. Order and Freedom both synergize well with Brazil's UA. The former gets a tenet for bonus tourism to civs with lower happiness, the latter longer golden ages. That said, autocracy with the Cult of Personality tenet may be the best choice if the hardest nuts to crack (ie. the AIs with the most culture) have chosen it.
Diplomats will give you a tourism bonus towards civ of different ideologies, but not towards civs of the same ideology.
Hurry production of Broadway (or the Eiffel Tower if the AI was faster). Check how many Great Musicians you still need. There's a chance that you might be able to build the Sydney Opera House later, but it's not needed, nor would I count on it.
Afterwards, research Refrigeration and build a Hotel as soon as possible, then research Plastics, then Radar. If you have a spare Great Engineer, hurry production of Christo Redentor and build a research lab as soon as possible.
Once again, as your Tourism increases, it becomes more and more important to maintain open borders and trade routes with all civs.
In my last game, I was also able to finish the Rationalism tree in the Modern era, and used the free tech pick on Penicillin bringing me into the Atomic era. Your goal is to research Radar though for the airport.
Around this time it's also a good idea to start befriending religious city states because you'll want 1000 faith for a Great Musician after you research the Internet.
Atomic and Information era:
You're starting the sprint towards the Internet. Research ecology and then Telecommunications. Hurry production of the Sydney Opera House if you can. You don't need to get it, it's just nice and denies culture to the AI. Keep making those research agreements. Pop, rather than settle, your Great Scientists. Save at least one Great Artist for a golden age on demand later on.
Consider what options you have to turn the situation in your favor. If you picked order, try to deny happiness to the AI so that your Dictatorship of the Proletariat tenet comes into play. Try to befriend cultural city states to deny culture to the competition. Try to bribe the AIs to fight each other while keeping a low profile.
After you have built the National Visitor Center and researched Internet, pop whatever golden ages you can, and rock the civ with the highest culture with some Great Musicians. If everything went according to plan, you should be in a good position to win.
If you don't manage to win, that's just Deity difficulty. It took me a few tries to win once I understood that this strategy was good enough to work.
Proof
http://steamcommunity.com/sharedfiles/filedetails/?id=162002661
http://steamcommunity.com/sharedfiles/filedetails/?id=162002787
Overview of the strategy
I use Brazil. France may work. I believe that religious civs are viable for a culture victory on Deity, but this strategy has not been made for them.
I do not focus on a religion at all. This may seem counterintuitive because achieving World Religion status gives +50% tourism to the respective holy city, and buying Great Musicians with faith is very helpful. However, I learned that founding a religion, building the key wonders, and setting the capital up for long-term success is simply too hard with this approach.
I do not found other cities. One city culture victory on Deity sounds crazy, but it works. More than one city would slow me down too much in the critical early phase of the game.
You do need a good starting position. Brazil tends to start near or in the jungle. This is often bad. It is important to have enough production available early on, and enough land to grow a large city later on.
A culture victory relies heavily on wonders. This strategy relies heavily on engineers to hurry production of these wonders. This means you have to plan ahead in order to have an engineer available at the right time.
A culture victory also relies heavily on maintaining open borders and trade relations with as many civs as possible. Try to earn diplomacy bonuses whenever you can. When an AI asks for a luxury or a sum of gold, give it to them. Always share intrigues. Help AIs with their resolutions in the World Congress. Try to avoid diplomancy penalties whenever you can, and trade with everyone. This also has the benefit of netting you many research agreements which you need.
Ancient and Classical era:
Start filling out the Tradition tree.
You want to build the Temple of Artemis so that you will have an engineer ready to hurry the production of the Sistine Chapel. The extra +10% growth is also nice. Then you want to build the Hanging Gardens to feed all the specialists that you'll be running. To do that, you should research Mining -> Archery -> and then the tech which unlocks the Hanging Gardens. You should build a monument, worker, then Temple of Artemis. Chop forests, build mines... your top priority is to get these two wonders. If you fail to get them, victory will be unlikely.
After unlocking the Hanging Gardens, unlock whatever tech you need to get your local luxury resource. Then beeline for the National College, Writer's Guild and research Theology.
I also recommend building a second worker after the Hanging Gardens.
Medieval era:
Finish the Tradition tree and start working on Aesthetics.
Get an University as soon as possible, and researching Acoustics right after.
It's highly likely that the AI will enter the Renaissance before you do. It usually doesn't enter via Acoustics, so don't panic.
Steal the techs that unlock the Workshop and Artist's guild. Build and assign specialists to both. Do not assign specialists to the University. It is not necessary to get a Workshop in the Medieval era but you should get it early. You will need a second Great Engineer by the time you unlock the Louvre. You should be careful which civ you steal techs from. A suitable civ is one that is culturally weak (check the culture victory menu), and likes you. This minimizes the probability of being unable to maintain open borders with that civ later on, and minimizes the damage that would result from this.
At this point it should also be safe to invest production into cargo ships because the AI should have killed off barb camps, or at least have enough control of the seas to allow for safe trading. Save the Oxford Library for later.
Renaissance era:
Continue with the Aestethics tree. Make sure you unlock Exploration tree early enough.
Hurry production of the Sistine Chapel with your Great Engineer. If you don't have a workshop yet, research it. Then research Architecture. While researching also build the Heroic Epic for the extra Great Work of Writing slot, an Opera House to unlock the Hermitage, a Musician's Guild (assign specialists imediately, the Ironworks, and of course the Hermitage and lastly, a Harbor for increased range on trade routes.
It is unlikely that you will be able to build the Uffizi because at this point you're really starting to fall behind. It is probably a better idea to focus on getting a great start into the Industrial era. The plan is to enter the Industrial era by researching Navigation after Architecture, and timing the construction of the Oxford Library so that you can jump right to Archeology.
It's also a good idea to start checking how many Great Writers you still need. You'll need a total of five, two of them from different eras and different civilizations.
In the world congress, try to ban luxuries that you do not have access, and are not provided by mercantile city states. You'll want to befriend the mercantile city states later for happiness, but make life a little bit more difficult for the AIs.
Once you unlock Astronomy, build or buy a Caravel to explore the world around you so that you don't have to search for archaelogy sites later.
Industrial era:
You should have unlocked the Exploration tree. Finish the Aesthetics tree and start working on the Rationalism tree.
Hurry production of the Louvre with your second Great Engineer and build five Archaelogists. Two artifacts will be for your museum, two for the Louvre, and one for your palace. It's a good idea to let your workers, and supplemental scouts bought just for this purpose, occupy archaelogy sites until your Archaelogists arrive.
After you're done with this, your next priorities are to get a Public School, a Factory and then to research Radio. Assign specialists to the factory to get your third Great Engineer ready by the time Broadway is unlocked.
Try to sign as many research agreements as you can, and to maintain a trading fleet to finance them. As your Tourism increases, it becomes more and more important to maintain open borders and trade routes with all civs.
Sometimes no AI picks Rationalism (check Global Politics overview). If this happens, build the Porcelain Tower.
It is also a good idea to start building some properly trained military units if you have the time, because once you adopt an ideology, you may find yourself in one or several wars very quickly.
By the way: to get the theming bonus of the Broadway, you will need three Great Works of Music from the same era and civ. Fortunately, the era of a Great Work is that in which it was created, not that in which the Great Writer/Musician/Artist was born. So it's easy to get the theming bonus by just having 1-2 Great Musicians on standby until Broadway, which gives you one more Great Musician, is actually built.
You should also start adding specialists to your science buildings, but without overriding your next Great Engineer.
Modern era:
You'll have to pick an ideology. Think very carefully what's best in your current situation. Order should be your default choice because it has good tenets and is popular with the AIs. Freedom has slightly better tenets but AIs tend to avoid it, so by choosing Freedom you tend to make many enemies. Freedom also gives a lot of culture which allows you to finish the Liberty tree for a free golden age and Great Musician. Order and Freedom both synergize well with Brazil's UA. The former gets a tenet for bonus tourism to civs with lower happiness, the latter longer golden ages. That said, autocracy with the Cult of Personality tenet may be the best choice if the hardest nuts to crack (ie. the AIs with the most culture) have chosen it.
Diplomats will give you a tourism bonus towards civ of different ideologies, but not towards civs of the same ideology.
Hurry production of Broadway (or the Eiffel Tower if the AI was faster). Check how many Great Musicians you still need. There's a chance that you might be able to build the Sydney Opera House later, but it's not needed, nor would I count on it.
Afterwards, research Refrigeration and build a Hotel as soon as possible, then research Plastics, then Radar. If you have a spare Great Engineer, hurry production of Christo Redentor and build a research lab as soon as possible.
Once again, as your Tourism increases, it becomes more and more important to maintain open borders and trade routes with all civs.
In my last game, I was also able to finish the Rationalism tree in the Modern era, and used the free tech pick on Penicillin bringing me into the Atomic era. Your goal is to research Radar though for the airport.
Around this time it's also a good idea to start befriending religious city states because you'll want 1000 faith for a Great Musician after you research the Internet.
Atomic and Information era:
You're starting the sprint towards the Internet. Research ecology and then Telecommunications. Hurry production of the Sydney Opera House if you can. You don't need to get it, it's just nice and denies culture to the AI. Keep making those research agreements. Pop, rather than settle, your Great Scientists. Save at least one Great Artist for a golden age on demand later on.
Consider what options you have to turn the situation in your favor. If you picked order, try to deny happiness to the AI so that your Dictatorship of the Proletariat tenet comes into play. Try to befriend cultural city states to deny culture to the competition. Try to bribe the AIs to fight each other while keeping a low profile.
After you have built the National Visitor Center and researched Internet, pop whatever golden ages you can, and rock the civ with the highest culture with some Great Musicians. If everything went according to plan, you should be in a good position to win.
If you don't manage to win, that's just Deity difficulty. It took me a few tries to win once I understood that this strategy was good enough to work.
