Wolfram’s 4 colour theorem | Relationship mapping?

I was listening to Ray Otus’s podcast (which I like). He was talking about Wolfram’s Four colour theorem, which states (perhaps paraphrased as):

“Any map in a plane can be colored using four-colors in such a way that regions sharing a common boundary (other than a single point) do not share the same color”

I wondered if this could be used to map out relationships where each colour represents a certain intensity in that relationship from high to low. The idea being to design a relationship map that is random, but with some “design” to it.

Let’s try it out …

Example 1 – D&D starting characters – using Wolfram’s Four colour theorem

Maybe this design concept could be applied to D&D stats, where certain stats tend to go together … :

Rules:

  1. Populate a 7 hex Hex Flower with each stat and one for wealth, so STR, INT, WIS, DEX, CON, CHAR & wealth
  2. Using up to 4 pencils colour/outline the Hexes using Wolfram’s Four colour theorem, starting from the middle
  3. Randomly assign each colour a different value from 1 to 4 using a D4 where: 

1 = low (6-9),
2 = medium-low (9-12),
3= medium-high (12-15)
4 = high (15-18):

Let’s try two examples:

Step 0 – Blank Hex Flower

W1

Step 1 – populate the Hex Flower with the 6 stats and wealth:

W2

Step 2 – colour according to Wolfram’s Four colour theorem (in this case using all 4 colours)

w3

Step 3 – randomly assign each colour a different value from 1 to 4:

Red                     2  (- ) e.g. 5 days’ living wage 
Orange              4 (++) i.e. 15-18
Green                1 (- -) i.e. 6-9
Blue                   3 (+) i.e. 12-15

So the result is:

w4

So the new PC is strong and tough (15-18), quite wise and personable (12-15), clumsy and dumb (6-9) and has modest wealth. So perhaps an fighter then from a poor background.

Let’s try it again (using the same stat placement), but with fewer colours more of a-go-for-broke min-max arrangement) and re-rolling:

Red                     3 (+) e.g. 3 months’ living wage
Orange              1 (- -) i.e. 6-9
Blue                   4 (++) i.e. 15-19
(no green)

             w4a

So the new PC is very smart, wise, personable (15-18), but very weak, fragile and clumsy (6-9). But quite wealthy. Hrmmm, perhaps a Magic-user then for an affluent family.  

If this sort of min-max 3-colour-option option does not appeal, then you could get rid of the central hex (and get rid of wealth slot) and insist that all four colours are used.

Example 2 – Random NPC’s personality

Rules:

  1. Populate a 7 hex Hex Flower with a personality trait, one from each group (you can make your own traits)
  2. Using up to 4 pencils colour/outline the Hexes using Wolfram’s Four colour theorem, starting from the middle
  3. Randomly assign each colour a different value from 1 to 4 using a D4 where:

1 = low (- -)
2 = medium-low (-)
3= medium-high (+)
4 = high (+ +)

7 NPC Traits:

  1. wealth, resources, influence
  2. status, reputation, level
  3. cynical, duplicity, prejudice
  4. Personable, warmth, empathic
  5. wit, intelligent, charming
  6. greed, selfish, evil
  7. desperate, needs, desire

Let try two examples:

Step 0 – Blank Hex Flower

W1

Step 1 – populate the Hex Flower with the 7 traits:

w5

Step 2 – colour according to Wolfram’s Four colour theorem (in this case using all 4 colours)

w6

Step 3 – randomly assign each colour a different value from 1 to 4:

Red                     4  (++)
Orange              3 (+)
Green                1 (- -)
Blue                   2 (-)

So the result is:

w7

So, they really desire something from the PCs, they are quite wealthy and greedy, they are not especially smart or personable, they are of low social status but at least not very treacherous.  A quest giver, perhaps a merchant, who desperately wants something to (further) enrich themselves and is happy to pay the PCs to get it. 

What happens if we had coloured the hex’s differently, using just 3 colours e.g.:

  w7a

Now they would have some desire to get something from the PCs, they would be smart, greedy and treacherous with no money, status and quite cold. Doesn’t sound like a nice chap. Perhaps a street thief full of animal cunning and wants the PCs’ coin. 

Again, three colours gives a more polarized outcome. 

Some initial conclusions – I think you can try and set this up so coloured pairs go together, perhaps wealth & status, greed & duplicity and wit & warmth.

That said, I wonder if we should scrap the middle hex and insist that 4 colours must be used to introduce less homogeneity. Perhaps.  

Is this useful (?)– not sure, just brainstorming here. Perhaps if you planning a session and want some inspiration about an NPC, or have a bunch of templates ready to pull out of a hat??

More
Clearly, these are not just the two ways this idea could be used. 

– – –

Me on DriveThruRPG

2 thoughts on “Wolfram’s 4 colour theorem | Relationship mapping?

  1. Max

    I’d have to play around with it a bit to decide whether it’s actually “useful” in the strictest sense, but regardless, this is a really interesting idea. I always appreciate these simple experimental mechanics you develop based on known mathematical principles, it’s just a cool thing to see and whether they’re all winners or not, it seems like by its nature a more fruitful way to bring in new ideas to game mechanics.

    Like

    Reply

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