How do I multiply Lava and water?

Solution 1:

The liquid physics in Terraria are not completely precise. You can abuse it to duplicate them. Good thing, too, since transporting a decent amount of lava/water anywhere is a huge pain.

1. Infinite container: If you make a liquid container large enough, the amount that drains each frame is rounded down to nothing, for some reason. For example, a 49×25 liquid container with a 1 block hole will create an infinite amount of liquid (video example of this). This will break if liquids are settled (via the server console or when saving and loading the map).
2. Liquid splitting: When a liquid falls onto a single block and could flow down both the left and right edge, it will. Somehow, this leaves you with more liquid in total than you started with.
3. Bucket weirdness: Buckets create 1 block of liquid when they're emptied, but filling them seems to require less. If you place a block, let some of it flow and then quickly pick it up again, you will have a full bucket, but some of the liquid will remain.

Applying #2 and #3, this is a very simple liquid duping setup:

The lava is placed on the edge, where it flows into both the container and the 1-block "basin" on the right side. Both "portions" are enough to be picked up by a bucket again (though in this case, the first scoop will be spread too thinly in the container).

Solution 2:

Due to the way fluids are coded, both water and magma seem to 'multiply' when they flow down a series of blocks. Though I don't know why this happens (look to someone who has poked through the Terraria code, for instance) I can show you how to do this.

Here is what I call my Lava Accelerator. It is a series of downward steps with a large pit at the bottom to collect the resulting fluid.

To begin, you grab some lava from the trough here, and put it on the lip of the lava trough. The lava will pour both left and right, with the left going back into the lava trough, and the right heading into the lava acceelerator proper.

At the bottom, the lava has collected. After falling down these stairs, one bucket of lava...

...has turned into more than four.

If you do this repeatedly, you can quickly fill even the large tank (which I've hooked up to an obsidian generator).

I don't know the particulars of fluid splitting, so I may not have the most efficient of infinite fluid splitting, but hopefully this explains the principle well enough.