[0.6.0dev11] Alchemist's Pot 100% Chance Transmutation Harmony Method

Foreword

Thanks to Miyazakura Mikoto for the ideas, thanks to Rain_Flying for writing the alchemy cauldron mcmod page, and thanks to the laptop that didn't explode until I finished testing.

This chart is only applicable to the 0.6.0 dev11 preview version, not applicable to dev10 and earlier.

Advanced recipes refer to recipes with higher output rates, such as Stardust Bloom or Bloom Aether.

Recipes with blue names can always produce 100% output when harmonized；

Recipes with red names will run 100% successfully at first, and after several times, they will fall back to a 90% probability.

Could not find a harmonization recipe for Phantom Ionic Liquid(Unavailable in the image)If anyone finds it, please comment it or directly edit the article.

As long as you follow the harmonization method shown in the figure, starting from the initial cauldron, run the positioning recipes in order, and then run the target recipe, the probability will be 100%

Butthe Alchemical Construct cannot be used interchangeablyand cannot run other recipes, otherwise it is very likely that it will no longer be able to be reconciled, and can only be dismantled and reinstalled.

Principle

The Cauldron's State PWithin a cube from coordinates 0,0,0 to 20000,20000,20000, coordinates can only beintegersWhen calculating coordinates, round to the nearest integer.Initial State Pis 10000,10000,10000.

We can establish a coordinate system with (10000, 10000, 10000) as the origin Cand the cube will be divided into eight octants by the new coordinate system. (All subsequent descriptions are based on the new coordinate system)

Each recipe has a target location T.

When the Alchemical Chest runs a recipe, it will make the Alchemical Chest's state P move towards the target T by 34% (meaning the PT distance is shortened to 66% of the original) and then check:

1. Pwhether or notTFurther from the origin(Manhattan distance);

2. PandTIn the same quadrant;

3. PTVectors andCPIs the angle between the vectors less than7.08°, which is to checkC,T,PAre the three points roughly on a straight line?(It should be 10° in the code, but the pre-calculated value is cos(10°) instead of cos²(10°), resulting in a more stringent actual angle)

If the above three points are met, the probability is 100%, otherwise it depends on the Manhattan distance d of P and T.

d ≤ 5 has a 90% chance;

5 < d < 3000 is random probability;

3000 ≤ d has a fixed 0.01% chance.

The eight positioning recipe target points are located at the eight corners of a cube, and they can be used to pull state points, moving the state points onto or near the extension line of CT.

As long as it can be successfully moved within the range that meets the three requirements(a slender cone with a half apex angle of approximately 7.08°)the probability can be turned into 100%

Why do some recipes have a final probability of 90%?

Because the coordinates within this cube are discrete, coordinates can only take integer values. Whenstate Pandtarget Tget closer and closer, until finally the xyz coordinates differ by only 1, due to the limitations of rounding rules and movement rules, no matter which direction is approached from,state Pwill inevitably be unable to coincide withtarget T. At this time, thePTvector can only have 26 types(i.e., xyz coordinates are all ±1 or 0, excluding the case of (0,0,0)). This means that the angle between thePTvector and theCPvector may not be less than 0 in all 26 cases, meaning that no matter how it is operated, after continuously running the recipe, it will become a 90% probability.

The range that meets the three requirements is a slender cone with a semi-vertical angle of approximately 7.08°, so there is only 1 chance out of 26 that the requirements can be met. BecausePTthe coordinates are extremely close at this time, they can be approximatedCPasCTvectors. Findrecipes corresponding toCTvectors whose standardized xyz coordinates are all close to ±1 or 0, which are the recipes that can always run with a 100% success rate, and are the recipes marked in blue in the figure.(In layman's terms, the absolute values of the xyz coordinates are equal or 0)