NFTs, Generative NFTs, Programming, Math

How to Calculate the Number of Possible Unique NFTs in a Generative NFT Set

Hint: It’s pretty simple math, but let’s take a look.

Photo by Raghav Modi on Unsplash

I get this question all the time: “I’m doing a generative set with 250 traits. How many possible combinations are there?” Thankfully, the answer is pretty straightforward, although we need a little more information than that question indicates.

Basically, we just need to know the number of PROPERTIES (aka ASSET CLASSES), and the number of individual TRAITS within each one. For example, let’s imagine a set of cats with the following stats:

  • PROPERTY 1: BACKGROUNDS; # of background TRAITS: 25
  • PROPERTY 2: BASE BODY; # of base body TRAITS: 30
  • PROPERTY 3: SHIRTS; # of shirt TRAITS: 40
  • PROPERTY 4: HAIR STYLE; # of hair style TRAITS: 30
  • PROPERTY 5: HATS; # of hat TRAITS: 30
  • PROPERTY 6: EYES; # of eye TRAITS: 25
  • PROPERTY 7: WHISKERS; # of whisker TRAITS: 20
  • PROPERTY 8: NECKLACE; # of necklace TRAITS: 20
  • PROPERTY 9: CAT TOYS; # of cat toy TRAITS: 30

Okay, as you can see, there are 250 traits spread out over 9 properties.

The formula here is actually pretty simple. You basically just (1) take the number of items in each property and (2) multiply them all together. In other words:

25 Backgrounds  X  30 Base Bodies  X  40 Shirts  X  30 Hair Styles 
X 30 Hats X 25 Eyes X 20 Whiskers X 20 Necklaces X 30 Cat Toys

or...

25 x 30 x 40 x 30 x 30 x 25 x 20 x 20 x 30

According to Google, that works out to 8.1e+12, or 8.1 x 10¹², which is 8,100,000,000,000 (or, in word form: eight trillion one hundred billion).

So, that’s clearly indicative of a set with a crazy amount of possible variety, which is a good thing.

Just keep in mind when designing generative sets that the number of properties really matters. For example, what if there were just TWO properties — backgrounds and cat bodies, each with 125 possibilities? In that case, the math would be just 125 X 125, or just 15,625 possibilities. What if there were THREE with, say, 83, 83, and 84? That’s 83 X 83 X 84, or 578,676 possible combinations.

So, it’s not just the # of traits, but the # of traits AND the number of properties. What I’ve shown above, with 9 individual properties, is fairly typical of what I see in working on sets (full-time for about a year and a half now). So if you’re just beginning to plan out your generative set artwork, the above setup would be a great starting point. :-)

Jim Dee is a prolific writer, developer, and multi-media creator from Portland. You can find him, his businesses, his books, and more at JPD3.com. Thanks for reading! Cat image here courtesy of Midjourney AI.

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