Hexagons have been a core part of MoteMancer’s design from day one. But knowing I wanted hexes and actually understanding all their nuances are two very different things. Today I want to share a little mathemagical discovery that totally blew my mind and shaped how a lot of MoteMancer works behind the scenes.
🧩 Rule Tiles and Hexes
Unity has a super powerful system called Rule Tiles: you can define how a tile should behave based on its neighbors. There are tons of resources for how to leverage this for square tiles, but very little for hexagons.
When I sat down to map out every possible neighbor combination for a hex tile, something uncanny happened: There are exactly 64 unique combinations.
Being an FX Artist for years, this was baffling. We often think in atlases and 4x4 or 8x8 grids, so for this to magically manifest as a perfect atlas set immediately made me think i did something wrong. It turns out there is a super well-established reason for this.
🔺 Pascal’s Triangle
Here’s how all the neighbor connections break down:
- 1 way to have no neighbors.
- 1 way to have all 6 neighbors.
- 6 ways to have exactly 1 or 5 neighbors.
- 15 ways to have exactly 2 or 4 neighbors (two sets of 6 plus the 3 straight sections).
- 20 ways to have exactly 3 neighbors (three sets of 6 plus the 2 perfect triangles).
And those values are a perfect match to the 6th row of Pascal’s Triangle.
That means the humble hex grid is hiding binomial coefficients under the hood, and likely has this pattern for any shape, which is a super fun random math fact that I would never have known. It also demonstrates how much more complex hexes are compared to squares for artistic considerations.
⚗️ Where it shows up
Every omni-directional visual in MoteMancer - Mana Roots, Ichor Slicks, Swiftstone, and more - is built on this foundation. Understanding that there’s an orderly backbone beneath the complexity plays a huge part in how to wield the rule tile system into something predictable and fun to work with.
I’ll dig deeper into the layered nuance that have been built atop this in a future musing, but for now I just wanted to share this little piece of hex-shaped serendipity. Next time you’re laying out your alchemical garden, take a moment to stop and bask in the bestagons.
Back to the lab,
~CyanAvatar