User blog:Zonnyrov/Breeding List and Mathematical Monsters

So I know that everyone here loves My Singing Monsters, or else why would you be here? But I don't know if I am the only one who also loves math, and has noticed that monsters and math have a lot in common. So I put together this list of the natural monsters that has a few interesting properties (ignore the binary for now):

The first cool thing about this list is that it can be used as an effective breeding guide. For example, if you want to breed Spunge + Noggin and you don't know what the result will be, you can just add the numbers together and get your result. 21 + 8 = 29 (Shellbeat). So Spunge + Noggin = Shellbeat. Try more if you want, and if they are valid combinations, it will always work. But be warned that this does not work in the case that the two monsters have overlapping elements (e.g. Oaktopus (5) and Fwog (9) both have water, add the two numbers and you get 14 (Clamble), and Oaktopus + Fwog is definitely is not Clamble). If you are satisfied, you may stop reading here.

The reason that this list works for valid combinations (and doesn't for invalid ones) is because it is based on converting the monsters into their elements, and then into binary (base 2). Let me explain. Binary is made up of 0's and 1's, which really just mean on and off, or yes and no, and so on. The 1's represent on or yes, and the 0's represent off or no. Now that you understand this, don't be intimidated when you see numbers like 10110 or 11001.

In binary, there are place values just like in our number system (base 10). Except instead of representing powers of 10 (1, 10, 100, etc), they represent powers of 2 (1, 2, 4, 8, etc). The rightmost digit represents the 1's place the second rightmost represents the 2's place, the third rightmost represents the 4's place, and so on. For example, if you saw the number 110, you would have one 4, one 2, and zero 1's. 4 + 2 is 6, so 110 is 6.

So how does all this relate to monsters, you ask? Well, I made the 1's place represent the water element, 2's place represent the cold element, 4 represent plant, 8 represent earth, and 16 represent air. What does this mean? It simply means that if a monster has the water element, I put a 1 in the 1's place, or else I put a 0; if a monster has the cold element, I put a 1 in the 2's place, or else I put a zero, and so on. For example, take the Scups, it has Air, Earth, and Water elements. So I put a 1 in the 16's place (air), a 1 in the 8's place (earth), a 0 in the 4's place (because it doesn't have plant), a 0 in the 2's place (no cold), and a 1 in the 1's place (water). This makes the number 11001. We can convert this back to base 10 by adding the place values together: 16 + 8 + 1 = 25, and voilà, 25 is Scups. You can try to go through this process with any other monster, which actually isn't that complicated even though it may seem like it.

The reason why valid combinations work is very simple. If we add them in binary, we just get the result in binary. Let's try Oaktopus + Drumpler. Oaktopus has plant and water, which we can convert to 00101. Drumpler has earth and cold, which we can convert to 01010. Then we can add the two numbers together in the same way we would normally add two numbers in base 10. Our result is 01111. The elements it represents is earth, plant, cold, and water. We know that the monster with those elements is Entbrat, so Oaktoups + Drumpler = Entbrat. If you notice, we didn't have to regroup.

The reason why it doesn't work for invalid combinations is because if you try to breed two monsters with overlapping elements, regrouping is necessary. For example, if we try to breed T-Rox + Clamble, we convert the equation to 01011 + 01110. When we add it all up, there are ones in both of their 8's place and both of their 2's place. This is because they both have earth and cold. The reason this doesn't work is because in binary, we can't simply place a 2 in those columns, because the only digits are 0 and 1. So we have to regroup. The final regrouped result is 11001, which is Scups, and T-rox + Clamble is certainly not Scups. The regrouping makes elements appear where they shouldn't, and we see that the air element has worked its way into our equation.

One other thing I want to show you about this list. If you examine the binary forms for each monster, you can tell which island(s) the monster is on. A zero in the 16's place means the monster is on Plant island, a one in 16's place means it is not. A zero in 8's place means the monster is on Cold island, a one in the 8's place means it is not. And so on from left to right continuing with all five natural islands. For example, Pango's binary number is 10010. We can derive that it is on Cold, Air, and Earth islands (zero in 8's place, 4's place, and 1's place).

This works because I set up the table in this way. You may have been wondering why I chose each element to represent a certain place value. I chose them in that specific order because from left to right, the elements that represent each place value are the ones that aren't on the island that the 0 would represent. For example, Earth element isn't on Cold island, and since Cold island is the second island, I put Earth element in the second place from left to right. Why does this work? Because if it doesn't have the earth element, it's on cold island. If it doesn't have the earth element, there is a 0 in the 8's place. If there is a 0 in the 8's place, it's on cold island.

So there you go. Sorry for the math lecture, but I hope you enjoyed it anyway.

Happy monstering!