There's an entire social forum devoted to Terraria Engineering! You can find a huge number of contraptions, farms, arenas, and other engineering builds posted there. A lot of these builds have been compiled here:
http://forums.terraria.org/index.ph...ve-t-mec-list-of-resources-inspirations.6220/
I recommend building the following:
1) Money Farm
2) Truffle Farm
3) HM Boss Arena
4) Moon Arena
5) Multi-purpose mob grinder with a surface changer
Money farms can be simple Lucky Coin farms set up by the ocean, or much more elaborate (but still relatively easy to build) Ectoplasm-based autofarms.
Here's an example of a simple and effective Lucky Coin farm by ImDragos that's super fast to build:
http://www.reddit.com/r/Terraria/comments/32lwxk/new_improved_money_farm_using_arapaima_mob/
Here's a more elaborate version that produces what I believe to be the fastest platinum/hr rate (55plat/hr):
http://forums.terraria.org/index.ph...0-ectoplasm-hr-a-massive-55-platinum-hr.5199/
Truffle Worm farms that are easy to build and produce the highest yield can be found here:
http://forums.terraria.org/index.ph...oik-engine-powered-spawn-area-tutorial.10152/
http://forums.terraria.org/index.ph...n-afk-farming-truffle-worm-afk-farming.16609/
Both versions can produce 300+ worms/hr, which is higher than any other farm out there by a long shot. The version by ZeroGravitas is lighter on traps, while my version (which was inspired by Full Metal Kirby's pit idea) is a more basic flat surface approach and avoids the need for hoiking if a builder is not into hoiks.
For automatic Moon farming, there's a wide variety of possibilities. The easiest to build and most effective Pumpkin Moon semi-autofarm is hands down the cannon arena, which is one of the best night-based money grinders if you don't want to use a Lucky Coin approach:
http://forums.terraria.org/index.ph...-way-of-beating-the-event-without-traps.9085/
If you want a full AFK autofarm and are willing to invest a bit of time grinding temples for traps, consider the autofarm presented here:
http://forums.terraria.org/index.ph...n-and-frost-moon-events-using-autofarms.4850/
It'll take a while to build, but that AFK autofarm currently holds the record for both Pumpkin Moon and Frost Moon since it is nearly optimized to dish out as much damage as possible to event mobs and bosses.
One final semi-autofarm for Frost Moon can be found here:
http://forums.terraria.org/index.ph...cord-time-horsemans-blade-semi-autofarm.5903/
The Horseman's Blade approach is a record-setting approach to Frost Moon using a semi-autofarm. Thanks to to the work of Gandalf K and Unftf, who worked on optimizing the arena later in that thread, the record for the 20th wave is astonishingly below 12am!
For hardmode boss farming, I have recently put out a couple of videos explaining the theory behind autofarm construction and how to build both simple and complex but highly effective farms for Plantera, Duke Fishron, and the rest of the HM bosses:
http://forums.terraria.org/index.ph...n-afk-farming-truffle-worm-afk-farming.16609/
http://forums.terraria.org/index.ph...bonus-how-to-rapidly-farm-temple-traps.16437/
In the first thread there is some important info about how the "invincibility machine" works (most other videos in youtube-land get it wrong unfortunately), while the second thread/video explains how to create the strongest minions to speed up any autofarming and also shows how to quickly farm temple traps. There's also some important info in the second thread/video about spawning Plantera Bulbs, some of which is thanks to the research by Vazilin who posted a pretty incredible fully-AFK Plantera farm here:
http://forums.terraria.org/index.ph...ed-plantera-farm-4-5-planteras-per-hour.8942/
Finally, if you want to build mob farms, I recommend you look at the info here:
http://forums.terraria.org/index.php?threads/autofarming-guide-the-ultimate-chain-autofarm.3244/
It discusses how to optimize spawn rates and kill rates, and how to set up farms for various items. There are a lot of farms out there in youtube land that discuss how to farm for individual items, but why take that approach when you can build farms that can grind for multiple (rare) items simultaneously at very high rates? The thread gives a few examples of fairly elaborate surface grinders, but the grinders don't have to be so elaborate to work effectively.
These are my recommendations if you desire to build the fastest/most efficient autofarms and aren't afraid to invest a little time and effort (although some of the farms are pretty fast to build with a schematic). But hey, if you're going to build your own ultimate world, they why settle for anything other than the most efficient?
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