Pips do this:
In honor of the series, and because we have probably really figured it out by now, and because there is still confusion, here is Everything You Need to Know About Pip Planting.
Thanks for the discoveries and shares along the way @Coolthulhu, @abud, @snoozer, @shuuny, @Lurve, @Gurgel, @Promethien, @OxCD, @bzgzd, @suxkar, @vascoegertklei, @mathmanican @Tobruk @Ketmol and many people I missed.
1. Planting rules.
Pips will consider planting a seed in a tile under these conditions:
The tile has no more than 2 other plants in a square 6 left, 6 down, 5 right, 5 up from the tile.
It is either a "natural tile" of less than 150 hardness, a farm tile or a hydroponic farm.
The pip can navigate to the seed and the tile, and there must be no buildings obstructing the plant's location.
The atmospheric pressure is greater than 100g.
The atmospheric temperature is around ±50C to ±100C of the requirements of the plant.
If you can't figure out why your pip isn't planting, it is always rule #1.
2. Optimal Horizontal Spacing
The 3x3. Highest density pattern. This 15 tile span has 9 plants, or 60% density.
Start out as shown, then remove each ladder starting from the right, waiting for the plant to take its place.
The 1x1. This 15 tile span has 8 plants: 53% density. At long distances these two will be about even, but the 3x3 is nicer for placing buildings anyway.
The Tree One. (UK spelling: The 3-1) Place a 2 space gap every third tree.
This pattern allows for maximum branch density. The 4 middle ladders must be left there until all trees mature. This will ensure that the outer trees grow 4 branches on their exclusive spots, and the middle will be available for the middle tree to fill in. These spots are the outside 4.
If you mess it up, you can still prune (dig) the middle branches out and they will respawn until you get maximum density.
3. Vertical Spacing
For maximum density for normal plants go top to bottom to achieve a plant every 5th tile.
For hanging plants go from bottom to top, every 6th tile.
4. How to make "natural" tiles
As always, there are better and worse ways.
The better way.
Yup. You really just deconstruct a door. It needs all 7 tiles surrounding it. It also works when rotated and deconstructed from the right.
The other ways usually involves using vole puke or cooking algae or fertilizer into dirt.
For algae, you can construct/deconstruct storage bins to drop 1-10kg of algae into each location.
The Glass Forge.
Now with high efficiency thanks to @abud. Place 5kg algae per tile and set the valve to 2084 (25kg glass / 12).
Original recommendation in the spoiler.
You can cook it from below with an aquatuner or tricked tepidizer.
The Tricked Space Heater.
Cook it from all over.
Metal Refinery and Conveyers.
5. But why won't they plant!
It's always rule #1. Here are some examples of problems and how to identify them by applying rule #1.
Thanks for reading! Please share if you have found any exceptions or better methods.