This is a story of how, in complex systems, tiny individual choices can have big consequences.

Here's our system: these little cuties are 50% Triangles, 50% Squares, and 100% slightly shapist. But only slightly! In fact, every polygon actually prefers being in a diverse crowd:

The Squares on the left are fine with where they are, but look how much happier they are when they have some Triangle neighbors!

Here's how our little Parable of the Polygons works: you can only move them if they're unhappy with their immediate neighborhood. Once they're OK where they are, you can't move them unless they're unhappy with their neighbors again. To determine if they are happy or not, they have one, simple rule:

“I want to move if less than 1/3 of my neighbors are like me.”

Harmless, right? Every polygon would be happy with a mixed neighborhood. In fact, they would be happier with a mix than not! Surely their small preference to have some neighbors who look like them can't affect the larger shape of society, can it? Well...

And... our shape society becomes super segregated. Weird!

Sometimes a neighborhood just becomes square by chance, and suddenly no triangles seem to want to stick around. And a triangular neighborhood would welcome a square, but, because of their tiny little "1/3rd like me" rule, the squares aren't interested.

In this next bit, unhappy shapes automatically move to random empty spots. There's also a graph that tracks how much segregation there is over time.

What's up with that? These are good shapes, nice shapes. We're not even simulating racial redlining or any kind of exclusion or unfriendliness! And yet, though every individual only has a slight preference, the entire shape of society cracks and splits.

The result: in our "polyogon society" complex system, small individual bias can lead to large collective bias.

Well, what if we taught these shapes to have zero bias? (Or if you're feeling particularly nasty today, more bias?)

Notice how much more segregated things become, when you increase the bias beyond 33%. What if the threshold was at 50%? Seems reasonable for a shape to prefer not being in the minority...

So, isn't a solution just to turn everyone's bias down to zero? Sadly, no. The real world doesn't start anew with a random shuffling of citizens every day, so why should these polygons?

See what doesn't happen? No change. No mixing back together. The problem is that in this system, equality is an unstable equilibrium—a tiny bias can push the whole society past a tipping point, but once it's out of whack, there's nothing pushing it back. In other words: in a world where bias ever existed, being unbiased isn't enough!

We're gonna need active counter-measures. What if shapes wanted to seek out just a little more variety?

Woah. Even though each polygon would be okay with having up to 90% of their neighbors that are like them, they all eventually mix together! It's the same system-level effect as before, only in reverse! Let's see this play out on a larger scale.

All it takes is a change in the perception of what an acceptable environment looks like. These shapes liked diversity. But it wasn't until they acted when they encountered a lack of diversity than anything changed.

GET THEM ALL IN THE BOX OF F R I E N D S H I P
(hint: don't move them straight to the box; keep the pairs close together)

At first, going out on your own can be isolating... but by working together, step by step, we'll get there.

1. Small individual bias → Large collective bias.
When someone says a society is shapist, they're not saying the individuals in it are shapist. As we just showed, even when individuals are happier with diversity, a society may still contain emergent bias against diversity at the system level.

2. The past haunts the present.
Your bedroom floor doesn't stop being dirty just because you stopped dropping food all over the carpet. Creating equality is like being clean: keeping it that way takes continuous work.

3. Demand diversity near you.
If small biases created the mess we're in, small anti-biases might fix it. Look around you. Your friends, your colleagues, that conference you're attending. If you're all triangles, you're missing out on some amazing squares in your life - that's unfair to everyone. Reach out, beyond your immediate neighbors.