Tulip permutations


A recent facebook post on tulips revealed some interesting information. (Read the comments)

There are eight base colours. Each can be mixed with the others at eight gradients. Maths. Stuff. Number. Coffee! Stat!.. - milla

So how many possible tulip colors are there?

This is fairly simple to work out.

Take one color, say blue. If there are 8 base colors, then there are 7 different colors that it can be mixed with, and since each color can be mixed with 8 different ways, there are 56 (that is, 7*8) possible color combinations when mixed. Add one for the “pure” color, and there are 57 possible combinations for each base color.

This results in a total of 57*8 = 456 variations. That’s a lot of possible colors!

It is somewhat unclear if this means there are 456 possible “solid” colors, or 456 total. If there are 456 “solid” colors, then there are WAY more colors. Since the “order” matters (base vs tip) this is a simple permutation equation. P(456, 2) = 207480 possible tulip variations.

To help you put that number into perspective, if you planted a different color tulip on each block (column) in a 16x world, you would cover ~79% of the world before you finished.

Tulip sharing! 🌷
How U Make These Tulips?
Complete guide to Tulip Breeding
Tulip lovers thread
Recruiting Tulip Planting Master
What to do after endgame?
Anyone would like to give me tulip
Tuilips and dodos

Hmm, I’m gonna need a bigger garden. And a LOT more coffee. LOL


I was with you until:

Then my head went :boom:


Thanks Bib for the detailed calculations. Just as well I do have a 16x server to accommodate all these colours should we eventually get them all (ie from breeding/collecting/trading) :stuck_out_tongue:

Might have to build a few more tulip depositories too.

Black-base hybrids:

White-base hybrids:


That is a pretty good amount of tulips breeded right there. I have a question about tulip permutation. If a color looks a lot like another color, but is slightly like lighter than the previous one, is it considered tulip mutation, or just the same color?


I would consider it as a different colour if using the Blockheads camera to view them and they clearly show variation of colour even in the slightest. As a reference, you may wish to check the colour gradient of the colour wheel to see how the colours transitions gradually.

Having said that I could be wrong, so do feel free to correct me :stuck_out_tongue_winking_eye:


So it’s possible to see more difference between your eyes on the blockheads screen(tablet) and the blockheads camera? That’s something interesting. I think you might be right about the variation of the color if it changes a slight bit.


Explained in a bit more detail:

If we assume that there are 456 possible solid colored tulips (base and tip are the same color), then each of these 456 colors can be combined with any of the other 455 colors to create a new hybrid. You can then apply the same logic as before, 456 “base” colors, with 455 ways to combine it with a different color, multiply these 455*456, and we get the same number as before, 207480.

Or, remember back to your days in algebra, and just use the permutation formula. It’s well explained on Khan Academy (though apparently some people put this under precalculus).

This formula is the following (reminder: ! is the factorial symbol. 5! = 5 * 4 * 3 * 2 * 1):

n! / (n - r)!

Where n is the number of objects (base colors) and r is the sample size (2, we have the base color, and tip color), which results in the following:

456! / (456 - 2)!

Now let’s write out just a bit to make this easier to see.

456 * 455 * (454 * 453 * ... * 1) / (454 * 453 * ... * 1)

As you can see, we have two sets of (454 * 453 * ... * 1) which lets us cancel this, resulting in the same equation we figured out before, 456 * 455!

Hopefully that helps :slight_smile:

Humm… Maybe I should consider teaching math, that was fun!

I agree with Asyc. I consider this a different mutation, assuming that you have the exact same lighting.

It is easier to compare tulips with a camera because you can zoom in so that one pixel on a tulip will take up more pixels on your device. Personally, I like screen mirroring with a mac and using a color picker to get the exact RGB values.

Also make sure to compare the same pixel between tulips since they vary a bit!


Ok and here I was thinking all my tulip breeding was over. And then POOF this post shows up. How many years did it take to get all those tulip colours and combinations by the way? It took me a week to get 1 hybrid. A WHOLE WEEK. Im bad at this stuff :confused:


I understand 456*455 The algebra is the equivalent of hearing blah blah blah :scream:

I know I did some algebra and I’ve been able,to,help,my children with homework when they needed it but I don’t think I ever did anything as complicated as that equation. As for finding it fun??? You definitely need to teach maths, or have a job that relies heavily on it!


@Bibliophile do you know where I can buy a new brain? Also you Should teach maths your amazing!


I started a tulip farm thing. In the first few minutes i got a hybrid
Then i kept getting more and more hybrids every cycle ( i got 2 every cycle).
So i reset the two that kept growing as a red tip - yellow base hybrid tulip back to its original color, yellow. And the “problem” stopped


Why is getting a hybrid a problem??? Most of us would love to be as lucky as you have been!


Much later, I’ve done more digging into tulips, specifically, how their colors are stored.

I’ve come to realize that there must be some inconsistency between what Milla said and what I extrapolated from the results.

Tulip colors are stored as an (unsigned?) short. This means that colors are stored as a number ranging from 0 to 65,535. This is clearly much less than my calculated 207480 possible colors. Much less, but still a TON of colors to procure!


That’s good to know. I think we have maybe 1000 unique hybrid combo sorted so far. Still in the process of decoding tulip genes…


does anyone know if the rarity level of the tulip colour has a direct correlation to its gene’s dominance in hybrids?