A cool technique I’ve wanted to write up for a while is “Fractal Coordinates” described in a paper by Peter Mawhorter. Don’t be scared by the name, it’s essentially a variant on quadtrees that covers the entire 2d plane. Fractal coordinates have some interesting properties that are useful for procedural generation.
Suppose you wanted to code a simple chess game. One key bit of game logic is to describe what are legal moves for each piece. There’s only 6 types of piece (pawn, knight, bishop, rook, queen, king) so this isn’t exactly a hard task. You can write rules such as:
def canRookMove(from, to):
# Ignores questions about colliding with other pieces
return (from.x == to.x or from.y == to.y) and from is not to
But these days, I’ve been thinking a lot about grids, and the above approach just doesn’t generalize. What if you wanted to play chess on a stranger grid?
What would it mean to play chess on the grid above, or a hexagonal grid, and so on? You’d have to write a whole new set of rules, and they could get very complicated depending on the grid in question. What I want is a language that describes how pieces move, which generalizes to any board. And I think I’ve found it, using regular expressions.
For many years I was a hobbyist programmer. I’d try out small projects, experiment, then move on to the next thing. This was a great way to learn a lot, but I’ve got almost nothing tangible to show from that era. Despite the best of intentions, every project reached a point where it started to drag, and I’d get bored and move on.
It was only a problem for the projects I worked on myself. Working for others, I never really found the same problems. It was a problem of motivation and focus.
More recently, it is different. Now when I start hobby projects, there’s a good chance I’ll cross that finish line, and have something I’m ready to share with the world. What changed? Well in part it is increased experience and maturity, things I cannot teach. But also, I have found some strategies and thought processes helpful, and other, very tempting ones, not so much.
In short, I’ve learned to finish, which is a real skill you can learn over time. I thought I’d share with you what has worked for me. Maybe it’ll work for you too. I make software, but I think this advice is generally true for any other spare time activities. There’s three sections – scope, motivation and distractions.
Graphs are a data structure we’ve already talked a lot. Today we’re looking at extension of them which is both obvious and common, but I think is rarely actually discussed. Normal graphs are just a collection of nodes and edges, and contain no spatial information. We’re going to introduce rotation graphs (aka rotation maps) that contain just enough information to allow a concept of turning left or right – i.e. rotation.
As a side-project of a side-project, I’ve made a little painting program. It’s like a normal paint program, only you paint on a tile grid instead of pixels. You can create mosaic and stained-glass style images.
I’ve usually referred to this technique as “editable WFC“. It’s a combination of autotiling and WFC, and contains the best of both:
Being an autotiler, it allows users to easily and interactively make changes to an existing level.
Being constraint based, it automatically ensures that those changes are consistent with the predefined rules of the constraints, potentially making further changes to the level to make it fit
This is different from most other autotilers, which either require manual configuration of patterns used to enforce good behaviour, hidden layers, or come with more stringent requirements on what tiles are available.