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Shucking Peas

...with peapicker... Reflections and introspection on games and game design, with a bit of other.
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The Next Big Thing - Nomography in Gaming?

John Holder
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I think nomography in gaming could be one of the 'next big things' as a tool for games and game designers.

They are an excellent way of linking things mathematically without requiring players to 'do math', we can just 'see' the results. While many, including myself, love math, the visual ease they can lend games while making the effects of changing variables (resources / spell energies / strength / etc etc etc ) much more clear than equations can.

But what is nomography?

"Nomography ... is the graphical representation of mathematical relationships or laws (the Greek word for law is nomos) These graphs are variously called nomograms (the term used here), nomographs, alignment charts, and abacs. This area of practical and theoretical mathematics was invented in 1880 by Philbert Maurice d’Ocagne (1862-1938) and used extensively for many years to provide engineers with fast graphical calculations of complicated formulas to a practical precision."(From "The Lost Art of Nomography" by Ron Doerfler)

Here is an example from the open source PyNomo project showing a nomogram used for computing BMI (body mass index):


Nomographs are also often used in things like airplane manuals and the like -- when your engine dies, you still want to be able to calculate your range based on things like speed and altitude -- and under conditions where cranking through the math might not be fast enough.

Not fast enough... nomographs will allow us to add depth and complexity of relationships between in-game resources, power levels, etc without requiring anyone to crunch numbers!

Nomography in Gaming

The first time I saw these used in connection with gaming (wargaming in specific in his case) was at Winchell Chung's "Project Rho", an example of his is seen here:



Some pretty amazing stuff Winch has done.

It recently occurred to me that nomographs could be decoupled from the purely mathematical (i.e., no specific formula used to derive the graph) and used to image all sorts of in-game relationships -- sort of an ad-hoc application.

Game designer and artist Todd Sanders and I got to talking about their application to games in the Design forum, and he posted an exciting nomograph for a work-in-progress that you can see here:



Without even knowing how to use the thing, I find it super cool and compelling, and I want to play that game. What is also cool about Todd's graph is that he is producing it primarily as an artist to visualize relationships he knows should occur... and hasn't explicitly created a system of formulas to use to generate the nomograph.

I figured it could be applied as well to CRTs in games like WarpWar (fittingly, Winchell Chung was an artist for this one) which don't appear to be from any strict mathematical formula and then created a nomograph to suit:

Original CRT:


Nomograph (soon to be in 'files' section):


This both may be more useful and less useful, depending on the kind of gamer a person is -- but it sure looks cool!

Now, I'm excited to continue game relationships that could result in a useful nomograph. I'd love to see this mechanism used more in games.

Would you? Is this a thing that people would use, or would it just be a hassle?

Personally, I think this would allow for a game to put in some super-mathy relationships, and remain completely playable, which would add another degree of freedom for game design.

--John

EDIT: Other games that have come up in the comments that have nomographs:

1) Birds of Prey: Air Combat in the Jet Age
2) Attack Vector: Tactical
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Subscribe sub options Tue Sep 27, 2011 10:37 pm
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Brian Train
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Great idea, and something that could be used a lot more.

I saw Winchell's Project Rho page too, and actually used a nomograph recently to illustrate the potential impact of a tax credit program with four variables. But people looked at me funny when I used the word "nomograph", and backed away quickly when I showed them how it worked.

This sort of thing arouses admiration in the kind of people who use slide rules, or could be persuaded to use them (kind of the same principles). But no one else seems to understand. Still, it's worth a try in game design as it can be graphically compelling. I'd like to see what you come up with!

Brian
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  • Posted Tue Sep 27, 2011 10:58 pm
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Andreas Krüger
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I would have fun with them, but I guess people would rather use a smartphone app than a pencil nowadays.
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  • Posted Tue Sep 27, 2011 11:44 pm
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John Holder
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Thamos von Nostria wrote:
I would have fun with them, but I guess people would rather use a smartphone app than a pencil nowadays.


I do wonder about that... it seems we boardgamers enjoy the tactile process of playing real boardgames rather than doing so on a smartphone; at least, that would be my preference.
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  • Edited Wed Sep 28, 2011 2:03 am
  • Posted Wed Sep 28, 2011 12:29 am
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todd sanders
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thanks for the mention john. i agree these are really interesting visual aids. i definitely find your WarpWar table much easier to follow (though i know i am visually biased since i am a graphic designer) than the more traditional text lookup table.

one thing that has my design wheels spinning is how you've embedded width into your nomograph so that you can have subset values within a larger context (target tactic dodge). i definitely could see many applications for that.

you are right that i am not working from a formula basis but rather from what i feel should be the balance of values in the game i am working on so i can stretch and subvert my scalar lines to weigh the end product values.

in the case of my scales E and F above it dawned on me you could twist a scale inside of itself and shrink and enlarge the tick marks as needed.

the other gain i see is one of compactness. my nomograph above gives 4 different results. if i were to do this with regular text tables i'd need much more real estate to display everything. and in the particular contest this game is for, real estate is at a real premium
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  • Posted Wed Sep 28, 2011 12:42 am
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John Holder
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dumarest123 wrote:
thanks for the mention john. i agree these are really interesting visual aids. i definitely find your WarpWar table much easier to follow (though i know i am visually biased since i am a graphic designer) than the more traditional text lookup table.


Sure thing, Todd. I'm also very much a visual person... I almost went into graphic design and instead went into computer science; ironically, thanks to having some talent, I'm currently doing a bunch of icon design for a new UI we are shipping. I've also been heavily involved in PDF generation / digital typography for awhile, which I really enjoy. (Had to go with Univers for my WarpWar table since it feels so 'wargamey', probably thanks to SPI)

Quote:
one thing that has my design wheels spinning is how you've embedded width into your nomograph so that you can have subset values within a larger context (target tactic dodge). i definitely could see many applications for that.


Excellent! I was designing the table over some lunches just playing with the values, and width seemed to be the best way to keep it coherent. Really, I could have put one scale on each side of the tactic line and had the same result, but I wanted dimensionality.

Quote:
the other gain i see is one of compactness. my nomograph above gives 4 different results. if i were to do this with regular text tables i'd need much more real estate to display everything. and in the particular contest this game is for, real estate is at a real premium


It sure is! I've got some really cool ideas I'm playing with, but as of yet, they haven't jelled into a game... even if they do, it may be too big for the contest....
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  • Edited Wed Sep 28, 2011 2:42 am
  • Posted Wed Sep 28, 2011 2:08 am
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Dale Withroder
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Birds of Prey from Ad Astra uses nomographs
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  • Posted Wed Sep 28, 2011 3:46 am
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John Holder
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dalewith wrote:
Birds of Prey from Ad Astra uses nomographs


Thanks! I'll look into it.
 
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  • Posted Wed Sep 28, 2011 5:06 am
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Russ Williams
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This is very interesting food for thought! Thanks for the interesting post and examples.

But I admit I find a text table much easier to read. E.g. with the WarpWar CRT, I immediately see that Attack versus Dodge needs a differential of 2, 3, or 4 to hit. With the WarpWar nomograph, I'm looking at it and can't tell if 2 hits or if 2 goes between the 2 red regions in the Dodge column. Similarly it's not obvious to me from merely looking at the nomograph that Attack versus Retreat needs specifically 3 or 4 to hit, whereas I instantly get that by looking at the CRT.

Having to physically put a straightedge on the nomograph is a significant and annoying slowdown. If I can do something by just looking and not by having to physically manipulate a straightedge and measure/judge some physical measurement, I certainly prefer just looking.

(I wonder now if others have the same problem, or if it's just me. I have astigmatism, so perhaps that makes it harder for me to eyeball such lines accurately without using a physical straightedge.)

===

The 2nd issue that immediately occurs to me with this kind of "physical analog function evaluation" is that (depending on the specific nomograph), there can be unclear cases ("is the line hitting the red region or not?") analogous to LOS questions that come up in some wargames. I don't want that kind of ambiguity in game rule resolution!

Contributing to that problem of physical measurement ambiguity/error is ambiguity of exactly which physical points you're supposed to be using as reference points: in the WarpWar nomograph, I'm not sure if you intend the center of the colored A, R, D circles on the left, or if you intend the black + intersections to the right of the A, R, D circles. I hesitantly suppose the latter, but it's not 100% obvious.
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  • Posted Wed Sep 28, 2011 6:49 am
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Darren Webber
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I am assuming that Attack Vector: Tactical has already been seen, as I am certain that some nomograms are in the game...
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  • Posted Wed Sep 28, 2011 2:11 pm
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John Holder
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russ wrote:
This is very interesting food for thought! Thanks for the interesting post and examples.

But I admit I find a text table much easier to read. E.g. with the WarpWar CRT, I immediately see that Attack versus Dodge needs a differential of 2, 3, or 4 to hit. With the WarpWar nomograph, I'm looking at it and can't tell if 2 hits or if 2 goes between the 2 red regions in the Dodge column. Similarly it's not obvious to me from merely looking at the nomograph that Attack versus Retreat needs specifically 3 or 4 to hit, whereas I instantly get that by looking at the CRT.

Having to physically put a straightedge on the nomograph is a significant and annoying slowdown. If I can do something by just looking and not by having to physically manipulate a straightedge and measure/judge some physical measurement, I certainly prefer just looking.


Russ, I do see that point for sure. Your question about "Does 2 hit, or not?" will probably have me re-do that portion to be clearer. And I do see your point also about having to use the straightedge all the time. I agree, it probably would become unwieldy. However, I think for certain people, it would be more enjoyable that the traditional CRT. I'm still not sure if _I'm_ one of those people.

The WarpWar CRT may not be the best example of something to "nomographfy" anyway, but it just seemed somehow right to try it.


russ wrote:
The 2nd issue that immediately occurs to me with this kind of "physical analog function evaluation" is that (depending on the specific nomograph), there can be unclear cases ("is the line hitting the red region or not?") analogous to LOS questions that come up in some wargames. I don't want that kind of ambiguity in game rule resolution!

Contributing to that problem of physical measurement ambiguity/error is ambiguity of exactly which physical points you're supposed to be using as reference points: in the WarpWar nomograph, I'm not sure if you intend the center of the colored A, R, D circles on the left, or if you intend the black + intersections to the right of the A, R, D circles. I hesitantly suppose the latter, but it's not 100% obvious.


This is a great point. I've tried to make enough overlap between the areas that sloppy rulering should still result in no ambiguity... but, when I did so, I did so from the black + intersections as you surmised, and I admit that the circles may present some more ambiguity then I intended in this regard. In fact, the white gap in the dodge column was something I originally put in to avoid ambiguity between "H" and "H+1" columns.

I think I've a possibility in mind that will clear the whole thing up... I'll not get to it till tomorrow, as I have a team lunch at work today, and that's when I've been playing with this.

Rather than blame nomograph, please, blame the (very amateur) nomographer!
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  • Edited Wed Sep 28, 2011 2:49 pm
  • Posted Wed Sep 28, 2011 2:43 pm
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John Holder
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Darren Webber wrote:
I am assuming that Attack Vector: Tactical has already been seen, as I am certain that some nomograms are in the game...


No, indeed! I'll look into it as well, thanks!
 
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  • Edited Wed Sep 28, 2011 2:44 pm
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Phil Markgraf
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Birds of Prey uses nomography extensively to greatly simplify a physics simulation of jets fighting in close-quarters dogfighting. The game stuffs a remarkable amount of math into a handful of line draws operations that your average board gamer can drive late into a convention night of gaming.

Birds of Prey Play Concepts Sheet

This is a sheet I put together a few years back to show some of the unique concepts in Birds of Prey (which is not limited to the nomography). This shows the use of one of the two N-charts (there is also a pair of parallel-scale nomograms used in normal play and another parallel-scale nomogram used with specific aircraft) and the other tools that model 3D flight.

If anyone is looking for more details, you're welcome to catch me here or in a private email.

As an aside, Birds of Prey and Attack Vector share independent origins and subsequent cross-pollination. The PHAD (aka AVID), 3D move-aids and nomograph calculators originate with Birds of Prey; while the the tilt-block, altitude tile and box-miniature combination games from Attack Vector.

-- Shaken - out --
 
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  • Edited Sun Jan 29, 2012 6:02 am
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Tom Higgins
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Not only nomography...but specially constructed slide rules of a game related purpose(s).

Perhaps a game dedicated device along the lines of the CARDIAC for simple AI or decision branching chores ( http://en.wikipedia.org/wiki/CARDboard_Illustrative_Aid_to_C...).

Could Napier's Bones be used to set up ever changing maps, responses..say for instance a dungeon adventure that unfolds based on the paths you take as dictated by a specifically written set of Bones?

If I had the free time to muck with these ideas I would love to make a PnP game that incorporated all and more, it would be a heck of a build and learning experience- I hope those reading this will take the ideas and run with them.

(Much love for Todd Sanders, the joy of making and playing his games are the bright spots of any week.)

-tomhiggins
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  • Edited Fri Feb 10, 2012 12:09 am
  • Posted Fri Feb 10, 2012 12:06 am
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Tom Higgins
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Some more on nomograms http://www.myreckonings.com/modernnomograms/
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  • Posted Mon Mar 12, 2012 1:29 pm
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