First and foremost, I want to stress that a friend and I did all of this by hand: The map was cleared with Snowman Cannons, all of the materials used in building the farm were gathered by us, and every block, actuator, and wire was placed manually. It was a long and tedious process, but the rewards have been well worth it. The farm yields 10-15 Strange Plants per hour, and still works well as of 1.3.0.4.
Do you want to have a Strange Plant dye storage chest like this one?
Of course you do!
I'll be using a map viewer (experimental release of TEdit) in order to show you the farm's layout. Firstly, my friend and I created a new Small world and cleared out an approximately 1600ft x 750ft area with Snowman Cannons, starting from 0 height, due to the fact that Strange Plants cannot spawn within 700ft of any other dye plant or Strange Plant. (This may have changed since 1.3.0.4; we built the farm the day before the patch).
Note that we had originally planned to make the farm twice as tall as shown, but that would have been almost twice as much work, and it yields plenty of dye anyway. As of 1.3.0.4, you may not need to dig as far as we did, but if you want to be sure....
This is the farm in macro showing the area that we cleared:
So, what is the farm, exactly? It's 204ft wide, including the glass side walls. Most of it is 47 tiers of empty air, dirt, and glass. The first layer of dirt is at the "Level Surface" height on a Depth Meter, and very close to the center of the world horizontally. The last layer of dirt ends just before "Space" begins on a Depth Meter. You need three blocks of air for the Strange Plants to spawn, a layer of dirt for them to spawn on of course, and glass beneath just in case Orange Bloodroots might spawn and reduce the farm's efficiency.
In this screenshot you can see the basic form of the farm, as well as the ceiling we added above the 47th tier. The empty shaft in the middle is for maintenance purposes, but otherwise serves no purpose and you can feel free to fill it in:
But that's all just dirt and air. What makes the farm tick are two wiring devices that I designed (although, I doubt I'm the first to do so).
Here's the bottom of the farm:
That group of switches on the far bottom-left is a pair of 10-second timer arrays, and they're the most important part of the farm. 10-second timer arrays are made by wiring one 5-second timer and two 3-second timers together in a certain way, such that the final 3-second timer activates once every 10 seconds. With a pair of 10-second timer arrays wired to actuated blocks with two different colors of wire, you can automatically set the timers to "pulse" actuated blocks off and on occasionally by clicking each of the 5-second timers. If you click the 5-second timers half a second apart, the wired blocks will be solid for 9.5 seconds, and unsolid for .5 seconds, every ten seconds, harvesting Strange Plants and allowing them to drop down.
This is important, because the dirt needs to be solid most of the time in order to give Strange Plants plenty of time to spawn. However, we don't want the Strange Plants to just sit there preventing more Strange Plants from spawning, so we need to harvest them every ten seconds. We also need them to drop down to us.
Here's the wiring. Just copy what I've done if you don't understand it:
All of the dirt and glass blocks—except for the glass sides, ceiling, and floor—must be wired with blue wire, red wire, and actuators.
You may have noticed all those timers and teleporters at the bottom, underneath the farm. They automatically move your character west and easy endlessly, so that you can collect Strange Plants automatically if you wish, while AFK. This is fairly optional, since you shouldn't surpass 400 loot entities unless you leave the farm running for a very long time.
This is the wiring, and note that you must use 3-second timers. They're what makes it work properly.
Flick the switch to spawn a bird from the statue, which hits all those pressure plates in succession, activating the timers for the teleporter array. The dart trap at the end kills it, or you can be nice and leave that block open so that the bird can escape. You then simply step onto the first teleporter, and you'll move back and forth endlessly.
The solid glass will keep pirate invasions out of the teleporter corridor, if in Hardmode. At night, Wraiths will kill you if you don't use summons or wear higher-tier armor that damages enemies, although even if you die, chances are you can just walk over and pick up the Strange Plants that have accumulated. I imagine Solar Eclipses will also kill you regardless of summons or armor, but again, it doesn't really matter.
Final summary: Once the farm is built, flick the switch to activate the bird statue, which activates the teleporters. Then, press the two 5-second timers half a second apart in order to start the farm pulsing off and on. Then step onto the first teleporter, and enjoy your dyes! World file download is attached to this post, creatively named "World 8."
Video of the farm in action:
IMPORTANT NOTE:
Strange Plants behave oddly on servers of any kind, often requiring a restart in order to "refresh" themselves. No one's quite sure just what the issue is. It's important to use single-player mode if you intend to farm AFK.
There is a way to force Terraria to run in the background during single-player mode. First, set the game to windowed mode; then, instead of ALT-tabbing or clicking on another window to change focus, click the taskbar icon three times (for some reason, the first try won't stick) in order to minimize the game.