Vegetal Crossing

Spatial Diagrams

This application uses spatial diagrams to show the color of every variety of each flower species in Animal Crossing: New Horizons.

A variety's color is determined by its genes. Most flower species have three genes, so three dimensions are required to show all possible varieties. Those three dimensions are represented here as a stack of two-dimensional grids. Roses have four genes. To represent four dimensions, we use a series of three-dimensional stacks.

There are three possible values for each gene. This means each dimension is three tiles wide, deep, or high, and there are three stacks of rose varieties.

Varieties that are available as seeds from shops are marked with a seed icon. Varieties that were available as plants from mystery islands before Version 1.2.0 are marked with a Nook Miles Ticket icon.

Breeding

Choose a species, then click or tap a pair of varieties to select them as parents. The first parent will be labeled A, the second B. Their potential offspring will be highlighted, and the probability of each offspring will be shown as a fraction.

Click or tap the brown background to clear your selections.

Experiment with different combinations to get a feel for how flower breeding works. In general, when you breed varieties that are on edges or in corners, the results are more limited than when you include the more central varieties. Breeding the centermost variety with itself can yield offspring of any variety. Breeding a corner variety (e.g., the topmost, rightmost, frontmost variety) with itself can yield only copies of that variety.

The breeding rules are the same for every species, but the colors, seed starting points, and number of dimensions are different.

Advanced Breeding

Sometimes the question you want to answer isn't as simple as, "what happens when I breed variety A with variety B?" This can happen when you know the parents' colors but not their genotypes. For example, breeding red and yellow hyacinths from seeds gives you an orange variety that you can breed with a copy of itself to make purple. But that orange variety can also make more copies of itself―or, half as often, it can make a second orange variety that's better than its parents at making purple. If you want to know the average probability that a pair of unidentified orange offspring from the first orange variety will produce purple (or anything else), you can select both of the orange varieties as potential A parents in a two-to-one ratio and do the same for the B parents.

Just select a variety as an A parent, then hold the Ctrl key and select another variety. Each time you Ctrl-click a variety, that variety is added to the pool of possible A parents. To select the B parents, simply let go of Ctrl, click the first B parent, and then hold Ctrl and select more B parents as desired.

The parent pools can contain more than one copy of each variety, so you can increase the ratio of one variety to the others by adding it multiple times. The number of copies of each variety in the pool is shown in front of the A or B label. (The number is omitted if the pool only contains a single copy of a single variety.)

Breeding Modes

The behavior described above applies to the default breeding mode, × All Combos. In this mode, every A parent is bred with every B parent, and the diagram shows the overall probability of each offspring from all combinations of parents. This method of breeding is similar to ordinary matrix multiplication, so it's denoted by the × symbol on the Breeding button and in recipes.

In the other breeding mode, ⊙ Clones Only, there is only a single pool called C, and each parent is bred only with a copy of itself. This is for situations where you might want to take the offspring produced by a given pair and isolate each one, letting each offspring clone itself and then breeding each one only with its own clone. In matrix terms, the result produced is like a Hadamard product of two identical matrices, so it's denoted by the ⊙ symbol.

See also: Why Use ⊙ Clones Only Breeding?

Recipes

For each species, breeding recipes are shown beside or below the diagram. You can click a recipe to see its potential offspring on the diagram.

Some recipes use only seed varieties as parents, while some use offspring from other recipes. Any offspring that is used as a parent in another recipe is marked with an icon of an in-game item, such as a tree branch or stone.

For a given species and color, each icon represents either one specific variety or a mixture of varieties in a specific ratio. For example, in the tulip recipes, orange components marked with a tree branch always refer to the bottom-center orange variety, while black components marked with cherries always refer to a two-to-one mixture of the Nook Miles Ticket black variety and the other black variety. If you hover your cursor over a recipe component, the included varieties are shown on the diagram.

Recipes that use mixtures as parents are probabilistic. It is not assumed that you will identify the varieties before breeding them.

See Breeding Modes above for an explanation of the × and ⊙ symbols. An ellipsis (⋯) means the recipe produces other, less-useful offspring that are only shown on the diagram. A repeat symbol (♻) means that if you feed any offspring that are the same color as their parents back into this recipe as new parents, each generation will produce better results than the last.

Not all recipes shown here are optimal; some are shown only for comparison or because they are interesting.

Why Use ⊙ Clones Only Breeding?

Short Answer

When you breed an unknown flower with another of the same variety (i.e. its own clone), the offspring will be more homozygous, on average, than if you breed that flower with a different unknown variety. Blue roses have four homozygous genes, so increasing the probability of homozygous offspring is helpful.

Long Answer

Imagine a flower species with the following properties.

• It has three genes and 27 varieties, like most species.
• All seeds have genotype 111.
• All varieties are white (and indistinguishable) during most of the year.
• In December only, the seed variety is red, and the variety with genotype 222 is green.

You're planting seeds in January. How can you maximize the number of green flowers you'll see in December?

Flowers of the first generation all have genotype 111, so all of them will turn red in December. If you plant them without letting them breed, you'll have no green flowers. If you let the seed flowers breed with each other, the second generation will be distributed as shown, and only 1 in 64 (about 1.6%) will turn green. If you breed the second-generation flowers with each other, the third generation will have the same distribution as the second! Have you reached a dead end?

No! You can do better. If you instead clone each second-generation flower and breed each original with its own clone, you'll get a very different distribution. In this case, 27 in 512 third-generation flowers (about 5.3%) will turn green.

This hypothetical example is similar to the challenge of breeding blue roses. One way to get blue roses is to breed pairs of 1110 red roses, which have a 1 in 64 chance to make blue. Blindly cloning and breeding all of their offspring would mean 27 in 512 third-generation roses were blue (as with green in the example above), but that count includes the blue offspring from any blue roses in the second generation. It doesn't make sense to consider that case, because if you get a blue rose in the second generation, you're done. So instead, here's the third generation produced by all nonblue roses from the second generation: 19 in 504 (3.77%) are blue.

On the other hand, it's not necessary to blindly breed all of the nonblue second-generation roses, because it's impossible for any white, yellow, or purple offspring from a 1110 pair make blue. Eliminating these and breeding only the red, orange, and black offspring—which make up 47 in 64 (about 73%) of the offspring—improves your odds per breeding pair to 19 in 376, or about 5.1%. That means any red, orange, or black pair will be, on average, 81% as effective as a pair of 1210 orange roses, which have a 1 in 16 (6.25%) chance to make blue. And 1210 orange roses are difficult to make: with the Folklore Orange method, you need to make at least one 0120 purple first, and when you breed it with a 1100 orange, only 1 in 8 (12.5%) of their offspring are 1210 orange.

BackwardsN states that an average breeding pair in the red, orange, and black Super Turtle layout has a 2.2% chance of making blue, for comparison. This diagram showing randomly-mixed pairs of red, orange, and black roses agrees with that figure: 49 in 2209 is about 2.2%. Cloned pairs are about 2.3 times as likely to make blue as mixed pairs in the Super Turtle layout.

Simulations

The math looks promising, but how well does this work in practice? Simulations suggest it outperforms BackwardsN 4-Step.

Each simulation below starts with 64 seeds in an attempt to compare the methods fairly.

If you find any errors or omissions in these simulations, please let me know!