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The smaller one goes like this:
A > AB
B > AB > ABCD
C > CD > ABCD
D > CD
Then in the middle it joins and splits the first AB and the last CD and it is already pretty much balanced at that point already but the splitters at the end make it more solid for all of those times where one or more of the lanes are not moving.
Since splitters are pretty much perfect 50% as long as nothing is clogged you really don't need more.
The main difference between the two solution is that the "normal" small one shares the splitters (they all have 2 inputs and 2 outputs) while yours is working off a more basic understanding of how they work.
And neither solution balances the lanes, so if you have belts that have one side being more filled or clogges it won't be solved.
There are many approaches to balancers, some people don't even bother with proper balancers and use cascading splitters to mostly balance things after branching out a line off a main bus for example.
For example, splitters have two inputs but your top example uses just one input so obviously you will need twice as many splitters to achieve the same result.
1) 100% throughput under full load.
2) Any arbitrary amount of input belts should be able to go to any arbitrary amount of output belts.
Because I know the average input of every belt, I coul'd use the specific 7-3 splitter and then just use the 3-3 balancer. Or 4-4 balancer for balancing only 3 belts. But according to factorio forum, there are problems with splitter timings those may cause the limited throughput.
I've read about Beneš network and all the stuff in factorio wiki and forum. Just this is still some rocket science for me.
I thought that will do:
1st belt: AAAA->ABAB
2nd belt: BBBB->BABA
But is is doing:
AAAA->AAAA
BBBB->BBBB
It is still behaving properly though: It takes an item from an input belt then places it onto an output belt, then takes from the other input belt & places on the other output belt, repeat.
If the belts are fully compressed (as in your example), there will be no interruptions to the regular perfectly-repeating pattern of in-out. A tiny gap in one belt could cause an interruption to the pattern & so flip the outputs around.
Due to this predictable behaviour, some funky stuff can be done, such as logic gates made out of belts & splitters.
Trivia: Prior to 0.16.16, different item types were tracked separately by the splitters for the in-out, so some really cool "black magic" belt-based item sorters were possible. (0.17 added filters to splitters, making this double-obsolete, but worth a look if you are curious about Factorios belt mechanics / cool applications.)
If true, using simple maths, it appears the small balancer is perfect (25% on each of the 4 final outputs)
I didn't check the big one, I assume that's the goal.
(I'm a beginner, am I wrong?)
The whole point of a balancer (and splitters in the majority of their uses) is to work with belts that have the same items on all inputs and outputs, so when the belts are already balanced
AAAA
BBBB
Is the exact same as
ABAB
BABA
If you are using a balancer with different items as input and want it to perfectly mix and distribute them to all outputs you definitely need to use a different approach, but that's because what you are trying to do is not what the smaller version was made to handle.
try this.
https://gist.github.com/Bilka2/aeec4ff7123ff5544cb9a80cf1046a06
Not that there is anything wrong with trying to make your own, factorio is all about designing your own solution to problems you find, and sometimes the generally accepted way (like those compact balancers) has a flaw for your own specific use so knowing how to do it yourself isn't exactly a bad thing.