I started by making a perfect 13 radius circle in the ground found on this page.
http://donatstudios.com/PixelCircleGenerator
The end result:
576 farmable tiles used for 576 carrots.
I'll list the things I did confirm and if I don't explain it here if anyone else posts anything about it I'll give more detailed explanation about that part.
Confirmed:
1. Beehives produce wax when crops change stage.
2. When planting a new crop in the ground it behaves like a stage change.
3. Last stage change in a crop (growing to the last stage) doesn't produce wax or honey.
4. Beehives can produce wax, honey or both at the same time.
5. Beehives quality of wax and honey can go above 100Q.
Listed above are the most common knowledge facts about beehives and most people know this already. The list below was found through the experiments done.
6. Beehives produce wax or honey every 20 real life minutes, it does not produce wax or honey at random times. The server must send an update to update all beehives every 20 min. The crops on the ground can change stage at any time and is not related to when the beehive gets its update.
7. The beehive will produce wax or honey depending on how much crop stage changes have acquired between the beehive updates. To many updates and it only produces the maximum amount. To little crop updates and it produces the minimum. More on this later.
8. Beehive can get crop stage changes even when lifted in the air by a player.
9. The beehive quality will not reset if its lower then 100 quality but it will reset if its higher. By reset it means you either leave the area and have that area unload (this means items on ground disappears, wildlife disappears and beehive resets). It also resets to 100Q if the beehive is placed inside a boat and is then instantly taken out. By reset it means that your beehive can have a internal quality of 217Q and its instantly reset to a default 100Q. It does not reset to 100Q if its for example 77Q.
10. The crop stage changes directly affect the quality of the beehive. The beehive increases in quality depending to the average quality of the crops changing stage around it. The quality levels out at the same exact quality level as the average surrounding crops that have changed stage.
11. The first plantation reduces the quality of the beehive. It was never confirmed what exact quality it was but pointed towards half the crops quality. If ones trying to farm high quality wax this must be avoided. Later on about this.
12. The beehive have an internal quality and its this quality that determines the quality of the products coming out.
The first thing I want to add is that I used a script to keep a character logged in at all times to keep the beehive from resetting. The script also printed out quality of products at the time of them being made by the beehive showing a timestamps and counting the amount of crops that have changed stage sense the last time it produced any product. By some standards this is unacceptable and it clearly shows that beehives are a clear broken game mechanic that needs fixing. Its clear that its only possible to farm high quality wax by game abuse and bots. Added to the end of this post is some but not all of the printouts during the experiment.
These are some of my hypotheses and might not be overly accurate.
The beehive will produce different amounts of materials depending on how many crop stage changes it has gotten between the updates.
0-25: updates seams to not produce anything.
25-40: produces 0.1 L of honey.
40-60: 1 wax or 0.1L honey.
60-90: both 1 wax and 0.1 L honey
90+: 0.2 L honey and 1 wax.
I chose carrots for 4 main reasons.
1. Its the crop that had the highest quality besides beetroots in my base.
2. Its the fastest growing crop in the game and because of this wax is produced quicker in a compressed time while you have your character logged in.
3. It can be replanted at stage 3 with carrot seeds as stage 4(the last stage) is useless in wax production as it gives no wax or honey.
4. I didn't choose beetroots because carrots have 4 stage in there growth cycle and beetroots have only 3. This means more crop stage changes and more wax / honey production from farming carrots compared to beetroots.
One thing that was very difficult to confirm was if the beehive remembered the updates from the previous update cycle. Meaning if it got 20 crop stage changes on the previous update it would produce 1 wax if 20 more crops changed stage on the current update cycle 20+20 = 40. Or if each update reset the amount of crop stage changes it needed before producing any product. It was clear that it reset the counter each time it produced any product though. This meant that if it detected 90 crop stage changes it would produce the maximum product output or if it detected 200. It showed that it was not wise to update all crops at the same time when farming wax on a larger field. It also showed that trying to produce the maximum amount of wax with the minimum amount of crops the plantation cycle would have to happen between the update cycles to get as many crop stage changes between the updates for guaranteed wax output.
One other thing to note was that I lifted the beehive up and moved far enough away from the crops when replanting them to not receive updates on the beehive. If this was not done the beehive was heavily influenced by the crop updates negatively reducing the products coming out of the beehive until all crops was turned over. The quality of the products coming out of the beehive was heavily reduced during the replantation. One interesting side affect was the way the quality of the products behaved over time. They were coming out in a buffered manner meaning that they went down as more crops got replanted and stop when all the crops had been replanted. Later it increased as crops changed stage. It behaved as if the beehive was receiving quality updates from the crops directly into its buffer with something similar to this equation.
beehive quality = ( old beehive quality + (average crops update quality * 2) ) / 3
Note that its just a guesstimate and might not be accurate. It is hinting towards this equation though. I also guess that a crop update takes the delta of the cropQ and is semi confirming why the first crop plantation has such a drastically negative affect on the beehive. Something similar to this
crop update quality = old crop quality + next crop quality / 2
This would mean that the first stage would have half the quality of the crops usual quality update. 0+max/2. All the successive crop updates gave the same quality as the crop quality planted.
Things I didn't get to test was.
1. Confirm the quality level of beehive when replanting crops. If this behaves as the equation above it might be possible to get Q0 wax.
2. How exactly does beehive share crop updates. Are crops only connecting to the first beehive that updates making one dominant or if its always tied up to the closest beehive.
3. Does all beehives in the same area update at the same time or does each beehive have its own update timer.
I hope this helps clarify some of the myths surrounding beehives and get you to try making some Q wax as I did.