More Miegakure Concept Art!

Here's more concept art for one of the realms in Miegakure. I also showed concept art and explained some of the ideas behind the different realms in this post.

The people who inhabit this realm live longer and are in general happier than humans, but it does not mean their society is perfect — it also has a darker side.

This piece was just selected for inclusion into the twenty-fifth volume of Spectrum, which selects "the finest in the fantasy, horror, science fiction and the surreal genres from around the world."

Three Arch Building Concept Art

[It's actually not the first time a piece done for one of my games got selected (previous selections included an illustration for 4D Toys, and previous concept art for Miegakure).]

Here's another piece I really like:

Aqueduct City Concept Art

We have so many more but I don't want to spoil the game too much!

Old Building Sketch Concept Art

The state of the Miegakure, Feb 2018

Hi! I forgot that I have to update this blog often enough or people will start to flood me with questions about how the development is going.

As I said before all the puzzles are done and you can play the game from start to finish and get to the ending, watch the credits, etc... I do still add a puzzle here and there sometimes, if it is really awesome.

After shipping 4D toys I went and inserted all the dialogue I had written into the game, so it feels almost done in that sense as well. The "story" of the game is very exciting to me. I would like to talk about it a lot more but not yet. I did talk about the very basics in this post.

Then these past few months I have mainly been taking the “Main Game Mechanics” and making them look finished. By Main Mechanics I mean things you interact with beyond the Basic Mechanics such as jumping, rotating your view in 4D, and pushing blocks. There are about six of these main mechanics, but it's approximate as they're sometimes more like big categories covering related concepts.

A few of these main mechanics were very simple looking, but clear enough that you could play and understand what was happening.

So I went into graphics programmer mode and made them look amazing. But also as usual with this game there were a lot of game design considerations to keep the game understandable. I am sometimes jealous of video games that have simpler gameplay that lets them build any sort of crazy-looking stuff they want, but on the other hand when a beautiful thing also has gameplay it becomes so much more awesome! It’s just much harder to make. This freaking game is hard to make but so worth it.

Anyway I am done with all of them except one, which I am working on now, and it should be done within a month or so. (Edit March 2018: Done!)

After that my programming tasks will be small things like fix collision bugs, and I will keep placing props in levels and program the occasional cool 4D thing. We still need a bunch of 3D modelling done.

For 4D Toys I added a bunch of shapes that people had suggested over time, with more stuff to come. The trailer has a almost a million views (and the channel hit 3.1 million views and 20K subscribers) and the top comment says "this is the best description of 4d I have ever come across on the Internet." So that's cool.

4D Toys: a box of four-dimensional toys

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.”

The website (4dtoys.com) has more info on it!

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

Anyway! It's a thing. You can get more info about it at 4dtoys.com.

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!)

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).

Progress Report, and Miegakure Videos viewed over 1.5 million times.

Hi!

Miegakure is coming along great. All the puzzles have been done for almost a year now. I have polished many parts of the game, in areas such as graphics and sound, but a few more remain.

As an example of polish, I recently improved the lighting, which was difficult because the game is so dynamic it is not possible to precompute in advance where the light bounces, as most games do. I came up with with a novel way to do it and looks amazing and I can't wait to show it soon.

The largest task for me personally now is to go through the remaining levels and place objects and generally make them look as pretty as the levels we have shown so far. I get to make more cool 4D objects too, which I also can't wait to show. I have a few videos planned on them and other things.

By the way, I recently noticed the Miegakure videos have been viewed over a million and a half times! This makes me happy because even though the game is not out yet it has already done a lot of good for the world, with hundreds of people saying the above video is "the best explanation of 4D they have ever seen." Not many games have trailers that stand on their own as useful things. It's also good because a lot of what I say in the videos cannot be said via the game, because games should mostly teach non-verbally, so they are complementary.

To the people who have been waiting for a long time, thank you for your patience. I am making sure the game that comes out will be accessible and beautiful so that more people can experience how amazing the concept of 4D is.

I will do a bunch of blog posts in the next few weeks, talking about the lighting, the world building we have been doing, etc...

New Video: A Grove scattered with 4D Spherinders

We are working on making every level in the game beautiful right now! Here is quick nice-looking video to make you happy!

Old tales say that deep within the Ancient's Grove one can sometimes find scattered stone pillars, remnants of the old gods and those who worshiped them. Some people even claim they have seen stones levitate above the ground, held in place by a strange power.

But as you may start to know by now, it is not quite as it seems.

First, if you haven't seen the game yet, this video is a good introduction:

This is way to much detail and nothing explained here is required to play the game, but I still think it's really cool.

Spherinder Columns

The columns are in fact spherinders, which are one way to generalize the concept of a cylinder to four dimensions.

Extruded Circle

A cylinder can be thought of as a circle that has been extruded upwards (perpendicular to the plane of the circle).

Extruded Sphere

In a similar way, a spherinder is a sphere that has been extruded in the fourth dimension (perpendicular to all 3 directions of the sphere).

Depending on how you slice a cylinder with a plane you might get a circle, an ellipse (if slicing at an angle), or a rectangle (if slicing straight down the main axis). (One may also get a truncated ellipse if the slice goes through the top end of the cylinder)

Cylinder Slices

Rotating a cylinder while stuck in a 2D plane

Similarly, if you slice a spherinder with a 3D plane you might get a sphere, an ellipsoid (if slicing at an angle), or a cylinder (if slicing straight down the main axis). (One may also get a truncated ellipsoid if the slice goes through the top end of the spherinder)

Rotating 3D Cross Section of a 4D Spherinder (source)

Many of the spherindrical pillars found in this grove have tilted over the ages, and so one may look at many different slices of them. The ones still standing straight will look like cylinders, but the tilted ones may look like floating ellipsoids. Look for the one that has completely fallen to the ground and hence sometimes appears as a sphere.

Concentric Spheres Carved into the Ground

Concentric Spheres Carved into the Ground

While dirt and moss have mostly reclaimed the area, one can still see that around each spherinder the stone surface was carved in a series of concentric spheres. Yes, an entire 3D sphere can lay flat on the ground in 4D!

In a 3D game the ground is 2D, and so in a 4D game the ground is 3D. That means that if you are standing on the ground there are six possible directions you may go: forward/backward, left/right, and ana/kata. However, in the game, because you are only seeing a 3D slice of the 4D world, you only see a 2D slice of the 3D ground at any given time (only two pairs of directions out of three).

Slicing ConcentricS pheres

And therefore the concentric spheres look like concentric circles to a regular 3D person. Depending on which slice a person sees, the circles might look larger or smaller (if one takes a slice near the side of the sphere the circles will be smaller than if the slice is taken near the middle of the sphere).

Because the spherinder lies in the center of the sphere pattern, during the transition (when the character changes which way they are facing i.e. the orientation of their slice), one can see each spherical pattern “anticipate” or “follow” the spherinder that stands at its center: the circles grow larger before the spherinder is about to become visible, and after the spherider disappears the circles shrink. I think this effect looks so freaking great!

4D Grass

4D grass

Other curious things one may find in the Ancient's Grove are blades of grass that appear to float in mid-air. This is because the point at which they grow out of the ground is out of sight in the fourth dimension. (The same effect makes certain slices of spherinders look like floating ellipsoids) Some grass bunches are more prone to this effect, based on which direction their blades tend to grow.

Seeing Inside Trees

Seeing Inside Birch Trees

While the character is facing the fourth dimension, they may also examine the inside of the Birch trees. This is just like how for a 2D being a house only needs four walls but us 3D beings can see inside the house by just looking at it from the third dimension.

2D Temple

I love how art and mathematics blend in this game!

IndieFund is backing Miegakure

This is helping us finish up the game! Here's the announcement.

A look at the Technology behind the 4D Game Miegakure

Development is going well... so that means it is time for another video!

This time about the crazy tech we built for this game. Tetrahedral Meshes instead of Triangle Meshes! Also 4D Crystals.

Talk: Exploring and Presenting a Game's Consequence-Space

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.

How do you even develop a 4D game?

A question I get a lot is: How do you even develop this game? This is related to the question: how can you think in 4D?

Personally when I approach a problem in 4D the key is to find which dimension is the least important and mostly ignore it, so I can think in 3D instead. For example to understand something about the main mechanics, I might think about the 2D/3D levels which I have shown in the trailer. In these levels, the up axis is obviously important, and the rotation is happening in the other two (horizontal) axes, switching from one to the other. In the 4D there is an additional axis, but it is not affected by the rotation of the character, so it can often be ignored.

Later, when I need to write down the 4D math for the model I was thinking about in 3D, it is often the exact same math as in the 3D case. This is because in linear (and geometric) algebra we strive to work in a “coordinate-free” manner, which means we don't write down the x,y,z, and w components of a position but rather work with all the coordinates at the same time, without needing to write them down. Any operation we do works on all the components, one by one, implicitly. For example adding two 2D vectors means adding their x and y components, and adding two 3D vectors means also adding their z components. Having an additional component does not fundamentally change anything about the operation. We are working in a way that does not depend on the number of dimensions. This also works for rotations, which are fundamentally two dimensional in the sense that they rotate one vector into another, regardless of the number of dimensions. I sometimes use 4D Rotors, which have the same interface as Quaternions but for 4D.

That's it! I got better at finding which dimensions to ignore over time.

This approach kind of breaks down a little bit when thinking of objects that change in all dimensions at once (such as duocylinders for example), but the general idea is the same: you can work with math without needing to see all of what it represents at once. Imagining different parts of it one at a time is often enough. The math, and the computer that works with it to display it, can do the rest.

By the way, someone asked a similar question about Intuitive crutches for higher dimensional thinking on mathoverflow and a few outstanding mathematicians even provided answers. I certainly used many of the other things mentioned as well.