Tag Archives: creativity

Isomorphism

Have you ever considered all of the empty space on a Checkers board? Half of the squares are unused. You might legitimately ask why they’re even there.

Transformed checkerboardThat, of course, raises the question of whether there’s any way for them not to be there, and it turns out that there is. Imagine removing all of the light spaces from the board, then rotate every dark space 45°. There’s some empty space now, so just sort of slide all the squares together. You’ll end up with something like this:

This is an example of what is called an isomorphism. Loosely put, an isomorphism is a translation between two things that preserves a certain set of their properties. In this case, the playable squares on the original board, with adjacency defined as diagonal, is isomorphic to the new board under orthogonal adjacency. In game design, isomorphism can be used to transform a game into a cosmetically different game, without altering the structure of its gameplay (a well-known example is that Tic Tac Toe is isomorphic to a game of picking numbers from a magic square).

I consider it a feature that the squares that were diagonally adjacent before are now orthogonally adjacent. Orthogonal moves are much more typical in most games, after all. This also seems like a good illustration of just how small the state space in Checkers really is. Of course, I’m talking about Anglo-American Checkers, or Draughts; most international variations are bigger.

Speaking of International Checkers, this leads us to something this variation might be good for. That game is played on a 10×10 board, is reputedly a better game, but is not readily available in the United States. I’ve just started reading R. Wayne Schmittberger’s New Rules for Classic Games, where he discusses both regional variants, and how to make your own equipment. If you were going to do that, you could use a lot less material (and have a more compact board for the same size of checkers) by throwing out the unused squares. Whether you’d like the un-Checkerslike appearance of the board is up to you.

Octagon grid for International CheckersBut, as long as we’re going with a different look, let’s go all the way. The checkers themselves don’t occupy all of the space within their squares, do they? You could squeeze things down a bit more by knocking the corners off. To preserve the common edge between adjacent spaces, let’s go with octagons. This actually restores the unplayable squares to the board, but in a form that can’t be mistaken for the playing spaces. And the pattern you end up with (shown here with the 10×10 international board) is, I think, very attractive.

It turns out, by the way, that this is only 75% of the width and height of the same thing as a square grid. This could be cramped to play, but is probably easier to print. At least it fits on an 11″×17″ sheet. In case you want to try, I’ve posted the same image at 10″×10″, 300 dpi.

This is the kind of thing my mind sometimes does when I’m falling asleep at night. I spent some time this morning coding up the pattern in nanDECK; maybe later I’ll put together a proper board.

Prototyping

If you’re like me, you have some dandelion syrup in your refrigerator waiting to be used. Which just goes to prove that you’re probably not like me.

Nevertheless, time to take a break from the dice deck project. It’s been pretty hot lately where I am, so let’s make ice cream.

I’ve made dandelion ice cream (and sorbet, and soda pop, and popsicles) before, but today I’d like to experiment. Making something exactly like I’ve made before probably doesn’t count. Now, syrup keeps long after the dandelions bloom, but it’s the right base if what you want to make is sorbet, not ice cream. So, you’ve got to fortify your syrup into something more milk-like before you begin. You could skip this, but then you’d have more of a sherbet than an ice cream.

I’ve done this before with evaporated milk (not sweetened condensed milk; the syrup already has all the sweetener you need). And in a pinch, I’ve seen success just by mixing the syrup with a goodly amount of heavy cream. I’ve been wondering how powdered milk would serve (the goal being to keep the ratio of other liquids down, so as to get the strongest dandelion flavor).

The dandelions won’t bloom again in New England until next spring, so I don’t want to risk my supply on this. What I need is a prototype. My big concern is, as we all know from watching Good Eats, that sugar is very hygroscopic. That is, it tends to hold on to water molecules and keep them from being available for other things, like dissolving milk powder.

I’ll try my experiment, then, on a batch of simple syrup first. More precisely (and this was not my own idea), a batch of rum-flavored simple syrup, so if it goes well I will have rum ice cream instead of milk-flavored ice cream.

Sure enough, the simple syrup doesn’t take up nearly as much of the milk powder as its constituent amount of water would suggest. Nevertheless, it does take up a fairly good amount after a lot of stirring, about a quarter-cup of powder per cup of water. So this is not a complete solution, but is a reasonable way to at least start fortifying before mixing in other dairy.

For the record, the recipe I’m going with is:
1½ cups dandelion syrup
about 3 Tbsp milk powder
1½ cups heavy cream
yellow food dye (as preferred)
Chill in ice cream maker according to manufacturer’s instructions

… which I think is proportionately about 50% more dandelion syrup by volume than the last time I tried this ice cream. The verdict: success!

Meanwhile, I accidentally found myself confronted with both sumac berries and wild grape vines today. I wasn’t actually planning on cooking with more wild edibles any time soon, but I guess fate is calling me.

Using the Whole Buffalo

Now we get into some technical details. Whenever you’re making cards, you’re probably printing more than one of them on a sheet. This is one of those things that’s so obvious that it goes without saying, even when it should be said. I can name at least one entire game (the eleven-card Pico) that was created simply because there was space left on a card sheet in another project.

In our case, we need thirty-six cards to represent all dice combinations. It’d be good to also include a card you could stuff in the lower part of the deck to trigger a re-shuffle (to keep the last few cards from being entirely predictable). I happen to be thinking of printing through The Game Crafter, which at the time I was first thinking of this project used sixteen-card sheets. Okay, so it happens that they’ll soon be switching to eighteen-card sheets, which starts making just thirty-six cards look attractive again, but travel back in time with me here. Thirty-seven cards on three sheets leave a lot of wasted space. Eleven cards’ worth, in fact. What can we do with that (aside from re-publishing Pico)?

domino cardWell, another game accessory that looks an awful lot like a pair of dice is a domino. The cards we’re already planning on cover twenty-one out of the twenty-eight that appear in a set of double-six dominos. So, we could include that feature for zero extra cost of goods. This also helps with the previously mentioned problem of the narrow scope of the project. It supports more experiences, plus a portable domino set makes the whole project not just an expansion to other games.

Sure, this is all pretty basic. But I think it’s a good simple example of a broadly-applicable design principle. In the end, we’re looking at making real usable objects with tools that have their own constraints and affordances. In this case it’s a printing method, but it’s always something, and that always influences the design process.

One side note: I spent some time fixing the white points on the photos I took, so the white die now looks white and not pale grey. The grey background looks better by contrast. I only mention it because it’s something I learned about photography in the course of this project. Yay, learning!

Next: I don’t know; do the indices throw the balance of the cards off a bit? Would it look bad to also have another index over the shadow in the lower right, or should I move the background image a bit? Maybe I’ll just make ice cream.

Click the Camera

I touched yesterday on one of the problems I wanted to solve with this dice deck, which is the limited number of games that use exactly two six-sided dice. Nothing against The Settlers of Catan or Backgammon, but let’s see what we can do to broaden the scope of the project just a bit.

First, we can include many other games that use just one die at a time, and even a few that use two distinct dice for different purposes. So, we’ll make the dice distinguishable, one white and one shaded. While we’re at it, by varying the color of the shaded die we can produce random colors (and yes, I can name games where that’s useful).

Now, how to produce the needed images? I have little skill as an artist, but I can program, and I can take non-embarrassing photos (the latter thanks in part to the excellent discussions of board game photography on BoardGameGeek.com, particularly the advice of BGG user EndersGame). I start with photos. But this means I need to be able to take very consistent photos of thirty-six different sets of dice.

dice cardThe solution is an inexpensive tripod and a foam core jig, with marks for the positions of tripod and dice. Natural light is best for this sort of thing in the absence of real lighting equipment (thanks again, BGG), so I set up out on the back deck.

All of this was actually done some days ago, and I’m reasonably happy with the results. I’m not 100% sold on the grey background of the foam core, but I want something that’s not going to argue with the shades of any of the dice. If I were a better photographer I’d probably be able to polish it up more in post. I did edit out a number of blemishes to the pips on my actual dice.

dice cardSo I printed up some prototype cards using these images. And, sure enough, the prototype is serving its purpose, which is in part to tell me what I did wrong. I didn’t think, at first, that I would need indices on the cards. Indices are the notations found in the corner, so you can hold the cards fanned. Those aren’t necessary if you’re just going to flip cards off the deck to give die results. But once you have the cards, you open up a lot of possibilities other than that one. You can easily imagine more variants, such as drafting or auctioning the cards. Or, yes, playing a hand of them. Plus, I’ve got another cunning scheme for this deck that would absolutely necessitate hands. So, indices it is. Well, the photos aren’t going to provide those.

I can think of few things I’d rather do less than editing little corner symbols onto thirty-odd cards, and then having to redo them all again consistently if I want to make changes. So, the solution for this part is nanDECK, a neat if quirky little card-rendering programming language by Andrea “Nand” Nini. Yes, there really is a programming language for everything.

That’s what I’ve mainly been doing this morning. You can see the results as they currently stand. I’m thinking I may want to further annotate the index for the color-blind, now that I’ve gone this far.

Tomorrow: Aren’t these cards starting to look a little bit like dominoes?

Overcoming Self-Editing

One of the big problems with starting any creative project is getting over self-editing. Most people (well, most adults, anyway) are very self-critical, and fearful of the disapproval of others. This is no way to galvanize you into action.

When I run creativity exercises, I often start with a warm-up where each participant is expected to come up with three bad ideas first, and share them. This is usually very effective at liberating people from their self-editing. If bad is now good, then that little voice telling you that all of your ideas are bad suddenly becomes encouraging. Not being in the mood for that, though, I’m going to try something similar that I’ve also seen work: start off with something so unthreateningly easy that self-criticism would be just kind of embarrassing. Sort of like the first round of a Limbo contest where you can just sort of duck under the bar.

So, let’s start with a dice deck.dice card

The idea behind this is pretty simple. In any game with dice, you’ll occasion­ally get lucky or unlucky streaks that hit a particular player. In a well-designed game these are often mitigated by the sheer number of die rolls involved, or by other factors. But it happens often enough to leave a taste for some kind of response. So: you make a deck of cards showing all of the possible pairs of rolls on two six-sided dice, and use that instead. No more streaks, because there are only so many of each combination in the deck.

Now, this is a very niche item. It addresses only the subset of board game players who are involved enough to try variants, and then only fans of those games that use two six-sided dice (which does include a lot of mass market games like Monopoly and Parcheesi, but not all that many games overall). On account of this, I suppose, a dice deck is hardly among the standard accessories you can just go out and buy (but yes, I do know about the cards that come in the Traders and Barbarians expansion for The Settlers of Catan).

This is actually a little silly in the world of the 21st century. Even something with a very small audience can be published print-on-demand, because nobody has to stock any inventory of it. The only serious cost keeping it from happening is the up-front development effort. So, hey, great project for someone who’s looking for something to do anyway, right?

Tomorrow: designing the best possible version of something that nobody sensible would spend that much time on anyway.

Making Stuff (Day 0)

It’s about six months now since the end of my stint at 4mm Games, and I’m falling into one of the classic traps. The first three months, I focused on networking opportunities like GDC and PAX East, but lately I’ve been too often sidetracked by daily distractions.

I need to take a hard look at what it is I want to do. But I’m lacking external structure, so I’m thinking I need to impose some milestones on myself, specifically to make stuff. Committing to outputs should help my overall focus; and creative work might provide a better context for my goal-setting, which could otherwise be awfully nebulous.

“Make stuff” still isn’t a milestone, though, so I’m adding the additional layer to document making stuff. The goal will be to write about some type of creative project every day, for let’s say twenty-one days.

I suppose I could count this as Day 1 of documenting that project, but let’s not cut too much slack right out of the gate. I declare today Day 0.