## Archive for the ‘Game Design’ Category

### 4D Toys: a box of four-dimensional toys

Friday, June 2nd, 2017

So I have been working on Miegakure for a long time now, and I have created and accumulated many cool 4D things of all sorts. I think it’s about time that I share some of them, so…

Surprise! Today I am releasing something!

### The History of 4D Toys

Near the very beginning of Miegakure’s development, someone joked I should do a “4D physics engine.” Then a year or so later I had gathered enough knowledge (especially in geometric algebra) that it was a possibility. So I made one for fun, and kept working on it on the side. It evolved into a 4D physics-based toy box that you can get right now, for iOS (Multitouch & Accelerometer) and Steam (both VR (Vive) and Mouse/Keyboard).

Basically it turns out the rules of how objects bounce, slide, fall, spin and roll around can be generalized to any number of dimensions, and this toy lets you experience what that would look like.

My initial goal in making this was to have a ton of fun inventing the math for it. At first I was skeptical it was going to be possible at all, but in the end the mathematics fit together so well.

I was only planning to use 4D physics a little bit for Miegakure as a purely aesthetic component, since dynamic physics is a bit too unpredictable to make good puzzles with. But then I started thinking about making a stand-alone iOS toy to play with 4D objects, to take full advantage of the physics. At first it was very simple and based around the idea that in 4D you can have interesting new dice shapes like a perfectly symmetrical 600-sided die, or a 4D hypercube die with 8 faces (each of them a cube). But I kept adding new shapes like hyperspheres, etc… and it got out of hand, so the dice theme didn’t fit anymore, and I named it simply “4D Toys.”

## More details about the design of 4D Toys

### Undirected 4D Play

4D Toys doesn’t take you through carefully-constructed successively harder challenges the way Miegakure does. It’s just 4D shapes, as if you were a very young kid again and given a box of wooden toys. Since the toys are 4D, that’s sort of true: you have no experience playing with 4D shapes.

Play is undirected and we don’t expect a child to come up with verbal realizations of what they are doing. They can learn about making stacks, and gravity, and fitting shapes into holes, and that could form the foundation for future, verbal, learning. Alternatively, one can just look at how pretty it is, like the waves rolling down the ocean, or the intricate swirling patterns in a fire.

It’s so exciting to me to see a pile of hypercubes or a rolling 120-cell. Most representations of a fourth dimension are so abstract (a spinning bundle of lines) and my work has been to get away from that. It’s the first time anyone has seen these objects as physical objects that bounce and roll and can be grabbed!

### Side project

4D Toys was a very fun side project. It uses the same engine as Miegakure, and many improvements I made to it have hugely benefited Miegakure. For example, I built a lot of the complex 4D collision detection code used in Miegakure for 4D Toys. I also came up with many ideas for Miegakure levels and scenes while playing with 4D Toys.

### Designing how to present 4D Toys

After I made it, I had to come up with a metaphor for what it was. Miegakure players know it is a puzzle-platforming game, so if they’ve played one before it sets a frame for the interaction, and the game can spend less time explaining everything and focus on the new stuff. They know how the game teaches things.

But 4D toys cannot rely on this well-known format. My goal was to strongly imply that it is not supposed to teach you in the way a puzzle-platformer like Miegakure does, but instead that it may only teach in an intuitive way. I came up with the idea of a box of toys, so the “menu” could be toys laid out on the floor, and you pick one and play with it, then come back to the menu.

However unlike a real toy box I have to first teach players how to manipulate the shapes a little bit. So I made a short tutorial that you have to play initially. The only thing that players really need to know besides the basic interactions is how to get back to the 4D shapes if they loose them into the fourth dimension. It’s fascinating to me that the tutorial teaches exactly that, even if a player has no idea what they are doing. Once the tutorial is complete almost all the shapes are available to play with.

I also wanted to explain, non-verbally, this idea of a 4D toy box, so we also put a small comic strip that shows how someone might end up with such a toy box. I like how subtly this idea is communicated. By the way, Kellan Jett (who is doing concept art for Miegakure) did the amazing art for it.

(By the way, for the VR version it is recommended to be on floor when playing!)

### Adding an optional verbal explanation

I wanted to stop there and just give out a mysterious box of toys with barely any instructions, but playtesting revealed that some people really wanted to know more about how the shapes and how the fourth dimension worked and what they were seeing.

I think that while kids are fine playing with toys without fully understanding them, as we get old enough we start to ask “why?” when we discover something new… and as much as I like non-verbal learning, I didn’t want to leave these “why?” questions hanging in the air. If I manage to make you interested, why wouldn’t I try to answer these questions if I can? So I decided to add an optional interactive “Interactive Explanation” that takes you step by step through what the fourth dimension is, how a 2D being would experience the third dimension, and by analogy how a 3D being would experience the fourth dimension. This provides the beginning of an answer, and the toys become even more beautiful if you understand just a tiny bit more. There are also optional questions marks in certain scenes you can click on to get more info.

The interactive explanation could stand and be interesting on its own. It is very verbal, as opposed to the toy itself, which is totally non-verbal and freeform. While I wanted to get away from verbal learning because it is so often done poorly and takes you away from the experience, it is interesting to think about when verbal communication is appropriate and when it isn’t. In this case I think it is good that the explanation stands next to the experience itself and can be ignored. Interestingly, Miegakure sits sort of in-between these two extremes: it is goal-oriented and directed and has words, but it very intentionally never verbally teaches you about the fourth dimension or how to solve its puzzles.

### Interaction method

Like I mentioned before, a problem that comes up when you are a 3D being playing with 4D toys is that they tend to disappear into the fourth dimension. A friend intuitively suggested a scrollbar to move along the 4D, and that seemed like the simplest way to solve the problem. Also this way we can display the extent of each shape in the fourth dimension and that allows players to very quickly find shapes when they lose them. Note that this is different from Miegakure’s mechanic of rotating the player’s slice. Miegakure’s rotation mechanic is necessary since the avatar would hit invisible walls if they could move in a direction they can’t see: 4D Toys does not have this problem since there is no physical avatar. Aside from the fact that both Miegakure and 4D Toys are 4D, the experience of playing each is completely different and complementary!

### Final words

It is out now for iOS and Steam (both VR (Vive) and Mouse/Keyboard).

I am excited to release something, anything (!) and see how it goes and learn from the process. While I plan to add things to it when I feel like it, my focus is on Miegakure’s development. Please enjoy!

### The World of Miegakure (+Concept Art!)

Wednesday, April 26th, 2017

When I first started making Miegakure, my goal was for each puzzle to be about a cool consequence of being able to move in 4D. For example, entering a temple that is closed from all sides but not from the fourth dimension, going around a wall in 4D, appearing on top of hill too steep to normally climb, etc…

But it was also clear to me that there should be regular characters that also live in the same world. These characters provide a normal human’s perspective on the 4D miracles the player is accomplishing. For example they might be astonished at how the main character managed to appear on top of the hill. They also make the game much more alive because it’s not just about the pure puzzles themselves.

If characters live in each level, there should be a consistent world they live in. So the temple might be located in the outskirts of a village the player explored previously. The player might meet a few characters from that village multiple times, etc.. A bit like an RPG, except without fighting but deeper puzzles, and split into levels.

It’s possible to think of a 4D world as a bunch of parallel 3D worlds (just like it’s possible to think of the 3D world as a bunch of parallel 2D worlds, see the trailer for more). I use this fact to make the levels easier to understand, so a level might have a “desert world” and a “grass world.” (Actually there are infinitely many worlds, but they are grouped together so worlds next to each other in the fourth dimension look very similar)

So if I use this fact in the levels, I should use it in the world building as well. And hence the world of Miegakure contains a bunch of parallel universes, some of which containing their own civilization. The world the main character is from is a bit like our own, with a Japanese/European medieval theme. But there are others. For example here is some concept art of a windmill from a civilization that is wealthy, extravagant, but also a bit dark, with strange beliefs and customs…

Art by the amazing Kellan Jett (He may post concepts that are in-progress ideas and not representative of things that will actually be in the game).

### Talk: Exploring and Presenting a Game’s Consequence-Space

Saturday, January 9th, 2016

I gave a talk at the PRACTICE game design conference at the NYU Game Center a couple months ago:

Slides are here

I had meant to update the talk I gave at Indiecade in 2011, and talk more in depth about how I used these ideas for Miegakure, but in the end because of the half hour format I do not cover the first half (designing mechanics to generate an interesting possibility space) and only cover the second half (how to explore the space the mechanics create). I also talk about a bunch of game design problems that are especially interesting in the case of Miegakure. I also cut the intro a bit, but posted it Here.

### Abstraction Design

Sunday, December 6th, 2015

The Introduction to a talk I gave recently…

### Abstractions

Creating an abstraction means to take a phenomenon or concept and reduce it to a simpler version by ignoring certain factors. We can then use an abstraction to predict things about the more complex phenomenon or concept.
For example, we can predict the motions of entire planets just using a few simple equations, despite the fact that planets are extremely complicated, by reducing planets to points with mass.

When building abstraction with the goal of predicting something the goal is to simplify as much as possible, but not too much so that we don’t lose the ability to predict what we want to predict. An abstractions that is more detailed (ignores less effects) can potentially predict more about the world, but at the cost of being more complicated.
In some sense that is what we have evolved to do as humans, is to learn to ignore the parts of the chaos of our universe that are not necessary for our survival.

### Instantiation

If we take a model/abstraction and look at a particular case, we get a prediction.
If we are doing a thought experiment we can imagine what the future state might be.
Or if we have an equation that models some part of the world we can plug in some numbers into it and it will output predictions of what the state of the object will be in the future, for example.
But it recently got very interesting because computers have made this step much easier to do.

For example to produce images of a 3D scene a computer uses abstractions of how light bounces around in the world before it reaches our eyes to produce the images we see, and computes this 30 or 60 times per second.
In some way, by instancing abstractions computers turn them back into “realities” because they can feel surprising, interactive, etc…

### Generalization

There is another thing we can do an abstraction. We can take any abstraction and generalize it without concern for whether it has a physical representation in our universe. You could say this is what pure mathematics is about.
For example, we can add a fourth number to space (x,y,z,w) and see what that would be like.

Any game does this and in a sense games are a natural part of a process to understand the universe, a universe in a more general sense including its generalizations.
For example, Sim City is based on a model (i.e. is an instance of an abstraction) of a city created by Jay Wright Forrester. Adding Godzilla to Sim City is a generalization.

### Designing Abstractions

When you look at the world to design an abstraction, ideally if you are a physicists the abstraction might contain surprising results because it might encode more about the world than what you based in on when you designed it.

For example one of the things that made Einstein famous is that his theory of relativity predicted that light’s path would get bent by heavy objects, and in 1919 during a solar eclipse, it was confirmed by looking at starlight as stars passed behind the sun.

When you are making a Video Game, you have to decide what the abstraction level for each component is going to be.

The highest abstraction (i.e. the less detailed) might be “if statements,” for example: if (main character does this) then { react like this } else { react like that }.

For more detail we could use an equation for example to compute the path of a projectile. The equation might become more detailed: we could consider air friction, etc…

An equation might return something that the designer of the equation didn’t expect. That’s interesting because it means that systems that are at a more detailed level of abstraction are more interesting to explore since the designers themselves more often do not know everything that could happen with them. This effect is what I care about a lot as a designer.

If statements are essentially step functions, which also create discontinuities that are often a source of problems in models. It is possible to combine lots of step functions to make a smooth-looking curve, but it takes a lot more effort.

By the way, I am not saying that all if statements are bad, just that as a designer we chose to focus on a region to explore, and where we explore it is better to use more detailed abstractions. For example, in Miegakure there are characters that walk around using simple state machines. I choose to not explore their internal state very much, as just their change in position is interesting enough with respect to the core of the game.