Mellosaurio

I wasn’t completely happy with the previous formula, it was messy and imprecise. So i followed my previous reasoning of dividing everything py power of the level, and with the cube i got a nice little parabolic function (Figure 1), which i fitted using ↑Figure 1: Breath divided by the level cubed Of course, some of the values don’t fit very well, and with the final formula, those are the farthest of the original values. Then i multiplied the previous formula by x³ and got And i with this i fitted the original values (Figure 2) ↑Figure 2: BioChromatic Breath vs Heightening level, fitted and with this i got The predicted breath for each heightening is: And for an 11th: (120623 ± 9.576) Conclusion I believe this Formula is a LOT better than the last i got, and much more precise.

Reading Warbreaker and the amount of breath for each heightening, I noticed that the amount of breath followed some kind of exponential function. So I tried to find the math law that they follow I started by plotting the amount of breath versus the level (Figure 1) taking into account an error of 1% for each level. This is because it is written that the amount for each level is not exact, so I assume a value that increases as the level does. ↑Figure 1: BioChromatic Breath for each Heightening Then I tried different basic functions, but I found that it doesn’t follow those. Eventually I divided every amount by 50 (Figure 2) and by the level squared (Figure 3). ↑Figure 2: Figure 1 divided by 50 ↑Figure 3: Figure 2 divided by Level Squared With this i started to try again with this formula () and found values for A, B and C that approximated the curve. then i expanded the formula so the results approximated Figure 1, i got Eq. (1) Using OriginLab I plotted Figure 1, and fitted using Eq. (1). And i got Figure 4: ↑Figure 4: Figure 1 fitted using Eq. (1) The values for this formula are: Replacing the level we got this values: This aren’t very accurate, but they are very near, and may be the real values that are approximated in the books. Be aware that there is an unknown error to this values, they could be less or more Conclusion The most probable thing is that Brandon picked random values for each level, but it still was fun to try and find out this law. Replacing for an 11th heightening we get around 120000 breaths for it. If in the future there are more levels, and they follow this formula i would be very happy. Keep in mind they will most probably not follow this.