Mapping the World in Hexes: Part II

Going back to our unfolded icosahedron, we see that it is divided into three distinct bands: The row of five triangles (with separations) at the top pointing upward, the center band of ten triangles both pointing up and down, and the row of five triangles at the bottom pointing downward. The gaps in the top and bottom rows are where the triangles fold inward to touch each other, coming together at a five-sided north (and south) pole.

The center band of the unfolded icosahedron has the equator of the planet running through its middle and is bounded by the 30 degree north line of latitude at the top and the 30 degree South line of latitude at the bottom. This means that the top row of triangles runs from 30 degrees North to 90 degrees North at the tip top, with the 60 degree North line running through their middle. Similarly the bottom triangles run from 30 degrees South to the pole at 90 degrees south. Each band covers 60 degrees of latitude of the planet's surface.

How Long is that Edge?

In order to find the scale of our triangles, we need to know how long the edges are in miles (noting that each edge of each triangle is exactly the same). There are several ways to do this. The first way, is to note that the middle band contains the equator, and is as wide as five edges. Thus to find the length of a single edge, we just take the circumference of the Earth (24900 miles), and divide it by 5. This gives us an edge length of 4980 miles.

Or, if we note that the edges of the central band of triangles are at the 30 degree lines, we can calculate the circumference of the Earth at these latitudes by multiplying the circumference of Earth by the cosine of 30 degrees (about .866) and then divide by five, for an edge length of about 4313 miles.

But the main reason why I'm calculating the coordinates for the map on my own, and not simply laying hexes over an existing map is because I want the areas of land under each hex to be as equal as possible and minimize distortion. Thus the method I'm choosing to use is to make the surface area of the icosahedron equal to the surface area of the Earth, and calculate the edge lengths from the total area.

The surface area of the Earth is 196,939,900 square miles. The formula for finding the surface area of an icosahedron is 5*squareroot(3)*s^2 where s is the edge length. Going backwards, we just divide the surface area by 5*squareroot(3), then take the square root of that result. (Strangely enough, 5*squareroot(3) is 10*cosine(30) which we mentioned above.) This gives an edge length of about 4769 miles, somewhat in between the two figures given earlier.

Since we said we were going to use 50 mile wide hexes for the large scale map (allowing us to put the continental US on two sheets of hex paper side by side) I will round that edge length to a spiffy, even 4800 miles, and thus the triangle faces are 96 hexes on a side. Easy peasy.

Next time, we cover how to convert each hex on a face to grid coordinates (latitude and longitude) for looking up on Google maps.

Where is the morning, where is the sun?

This needs to be turned into something gaming related: an adventure, NPCs, setting rules, campaign seed, SOMETHING!

I hereby command you all to do this. Don't disappoint me.

Mapping the Whole World in Hexes: Part I

The original Gamma World hex maps of North America were like magic in my brain. Here was something familiar, yet totally alien. You could throw anything together and call it a fantasy map, but if your campaign was based on real world places, the geography really meant something.

Now that I'm older, I've been wanting to re-do those maps with a little more accuracy, a little more (gasp!) realism. The problem with maps of big continent sized areas is that no matter how good they look, they are inherently wrong. The larger the area portrayed, the more distorted it has to be in order to be shown on a regular flat map. Consider this very familiar looking map:


Greenland is really not that huge compared to the rest of North America, the areas in this projection are greatly exaggerated the further you get from the equator. If you took this map and just slapped a hex grid over it, it would be very, very wrong.

Now all maps are inherently wrong, but some much more than others. I'd like to have a map of the post-apocalyptic United States (and ultimately, the whole world) where at least the areas of the hexes in various locations are comparable to each other, if not exactly the same. Wouldn't you? So how do we go about doing it?

The Icosohedral World

First, we need a way to flatten the sphere of the world a bit so that we can get large flat areas for mapping. These areas can be unfolded and shown on a flat surface, and then folded up again to make an approximation of a spherical shape. We do this by turning the world into a big d20 (an icosohedron).

Each triangular face is flat, and a shape that can easily be broken up into smaller hexagons. The entire icosahedron can be unfolded into a pattern of connected triangles that looks like this:


Our Triangular Face

The continental US fits reasonably well if we center one of the top triangular faces on the 96 degree West line of longitude. This makes the sides of the triangle the 132 degree and 60 degree longitudinal lines from left to right. The bottom of this triangle is the 30 degree North line of latitude. The US goes down further than 30 degrees, but that's fine for now. Since we aren't using all of the triangle above, we will also use only a part of the triangle below.

You can break up an equilateral triangle into a hex grid like so:


Notice that each line starting from the top has one more hex than the line previous and that there is the same number of hexes across the bottom as there is total rows of hexes. To find out how many hexes total there are on a triangle of X lines, the formula is (x * (x + 1)) / 2 or (x^2 + x) / 2. So for 1 line there is 1 hex, for two lines there are 3 hexes, for three lines there are 6 hexes, for 10 lines there are 55 hexes, etc.

A Sense of Scale

When finished, I want a map of the US broken up into 5 mile wide hexes (width from flat side to flat side). For a larger overview, however, I think I may use 50 mile wide hexes instead. To convert, 100 five mile hexes fit nicely into a single 50 mile hex like this:


But just exactly how big is the triangular face we will be using for our map? How many hexes is it across the bottom at the 30 degree North line, how many hexes across is the top of our map at the 50 degree North line, and how many total hexes are there?There's a couple of ways to figure this out, but one way in particular is the one I'm going to use.

...and that is where we will have to stop until next time. Stay tuned!

Races for Savage Dungeons

Well, I'm still not playing in or running any games. My latest game flyer is still on the bulletin board in the student center of the local community college, apparently untouched and unread. I played a short session of Barbarians of the Aftermath with my daughter (the one now at the college) several months ago, but that's the most gaming I've had in a year.

Last year I played a two session adventure with my wife and my daughter using my Savage Dungeons variant. The adventure was pretty good, I used an altered form of a free "one-page dungeon" I'd found on the internet (If I could remember which one it was, I'd give a shout out to the designer) over which I laid a mission to find the son of a local lord.

As it turned out, the son became a were-rat and hid in the local ruins. Since all the son could think about was the shame he would bring to his family if discovered, the party made a deal to bring back his signet ring and say that he was captured by beasts, but was killed while nobly trying to escape.

Even though I tried to fuse an old school Dungeons and Dragons feel into the Savage Worlds rules with my Savage Dungeons variant, I also wanted to change it up a bit and make the campaign world more my own. I decided to toss the Tolkien-inspired standard fantasy races from D&D, and just allow three races for player characters: human, wee-folk, and troll.

The rules for humans are standard, of course, but here are the Savage Worlds write-ups for the wee-folk and troll races:

Wee-folk

The wee-folk are an ancient and mysterious race. Averaging only 3-4 feet tall and only about 80lbs, they sometimes look so much like children (though somewhat wrinkled and time-worn children) that they are often overlooked or simply not taken seriously by larger folk. Of course, some larger folk sometimes end up dead for mysterious reasons...

Wee-folk are consummate artisans and crafters, with a sharp eye for details, and a fairly indomitable will for as humble as they look on the outside. Wee-folk as concieved here are a blend of the standard fantasy gnomes, dwarves, hobbits, elves and other fae-type little people.

It is said that goblins and other nasty things with their glowing eyes and pointy teeth are simply twisted, evil wee-folk . Or maybe they all just look like that in the darkness underground...

• Small: Wee-folk are Size -1 and get a -1 to their Toughness score. Individual wee-folk can still be Brawny (edge) or Small (hindrance) compared to the average.
• Slow: Wee-folk have a Pace of 5
• Spirited: Wee-folk are humbly confident and strong-willed. They start with a d6 Spirit instead of a d4.
• Talented: Because of their natural affinities, all Wee-folk start with a d6 in the Repair and Notice skills.
• Sharp-tongued: While not very powerful physically, wee-folk know how strong words can be. All wee-folk start with a d6 in the Taunt skill.

Trolls

Huge and brutish (and based somewhat on the trolls from Shadowrun), trolls are usually found living in nomadic bands in the wilderness, though many have come to see the advantages to civilized living. Most stand between 7 and 8 feet tall, averaging about 320lbs or so. Like the beasts of the wild, they have horns and claws, and some can be quite hairy, but they are just as capable as humans with the tools and rules of civilized life.

The one thing that makes them not quite fit in well with the humans and the wee-folk, however, is the fact that they tend to eat their prisoners and opponents, as well as anything else they can get their hands on. "Waste not want not," as the troll sages say.

• Large: Trolls are Size +1 and get a +1 to their Toughness score. Individual trolls can still be Brawny (edge) or Small (hindrance) compared to the average.
• Strong: Trolls start with a d6 Strength instead of a d4.
• Natural Weaponry: The claws, teeth, and horns of a troll do Strength+d4 damage and trolls are never considered to be unarmed.
• Bloodthirsty: Because of their habit of eating opponents, trolls get a -4 penalty to Charisma when dealing with the more civilized humans and wee-folk.
• Hungry: Trolls require twice the amount of food and water for survival purposes than humans or wee-folk.

Rolling up Edges

Being able to pick what you want is generally useful, but what if you're not sure what you want? That's when a random table is more useful!

So I'm in the process of making up a bunch of pre-gens for Savage Dungeons (my version of old school D&D using Savage Worlds) and since edges generally make the character in SW, I found it helpful to make a random table to roll up novice rank edges. Just grab two different colored six-siders (designating one as the "tens") and here we go:

1,1 Ace
1,2 Acrobat
1,3 Alertness
1,4 Ambidextrous (or Two-Fisted, Florentine)
1,5 Arcane Background (or Holy/Unholy Champion*, Gadgeteer, Mentalist, New Power, Power Points, Wizard)
1,6 Arcane Resistance (or Improved Arcane Resistance)
2,1 Attractive (or Very Attractive)
2,2 Beast Master (or Beast Bond)
2,3 Berserk
2,4 Brawny
2,5 Charismatic
2,6 Command (or Natural Leader)
3,1 Common Bond
3,2 Connections
3,3 Danger Sense
3,4 Fast Healer
3,5 First Strike
3,6 Fleet Footed
4,1 Hard to Kill
4,2 Healer
4,3 Investigator
4,4 Jack of All Trades
4,5 Luck (or Great Luck)
4,6 McGuyver
5,1 Nerves of Steel
5,2 Quick
5,3 Quick Draw
5,4 Rich (or Noble, Filthy Rich)
5,5 Scholar
5,6 Steady Hands
6,1 Sweep
6,2 Strong Willed
6,3 Thief
6,4 Trademark Weapon
6,5 Unarmed Warrior**
6,6 Woodsman

* This is the Champion edge from the core book. I don't like the Holy/Unholy Warrior edge (I think it should be one of the powers) but I do like the name so I merged them.

** From the Modern Martial Arts free supplement by Clint Black.

Some edges I've grouped together because they were similar or one required you first had the other to get it.

I just roll up two edges, use their requirements to figure out the rest of the stats, and pick either a different race, or make them human and give them another edge, a boost to one attribute, or two more skill points. Easy-peasy.

Thoughts on Class: Magic Users

Old school D&D is my kind of D&D, but there is still a lot of variation in rules, reactions, and assumptions even within the old school. Some people see idiosyncrasies in D&D rules as things which need to be fixed, some see them as features to be celebrated. I guess I'm a mix of both.

Some criticisms of the way magic-users work in older versions of D&D were that they were too weak and that they could only toss a couple of spells and then were pretty much useless. Now I suppose that may be true* if your idea of "useful" means strictly combat, but there is certainly more to old school play than killing monsters.



A magic-user cannot use a sword, we are often told, because he spends most of his time studying with his nose buried deep in musty old tomes. Well doesn't it seem natural, then, that an additional class ability of magic users ought to be obscure and esoteric lore? If there's one thing that 80's television has taught us, it is that "knowing is half the battle!" If the fighting-men have the monopoly on the first half of battle (a strong sword arm), then the magic-users should certainly carry the other half.

When faced with strange runes, strange creatures, or whatever in the dungeon, the magic-user ought to be the go-to guy for legends or rumors or scholarly information about them. A "Lore Roll" should be made, modified by intelligence bonus and perhaps by level, whenever something like this comes up.

For example, if you're using Swords & Wizardry, the single saving throw number could be used for it (that gets better by level, right?) Or perhaps start with a 1 in 6 or 2 in 6 chance (like certain actions in original D&D or the skill system in Raggi's LOTFP:WFRP) and allow the magic-user to gain a pip every few levels.

From the newer versions of D&D, I really like the idea of ritual spell casting. When your magic-user memorizes those precious few spells before adventuring, these aren't the only spells he knows or that he can cast, and he certainly doesn't "forget" them once cast. No, these are spells set up and prepared beforehand to go "pop" when needed. That's why there is only a limited number of slots for them.

A magic user at home in his temple/laboratory/sanctum sanctorum is not so limited and can cast any spell in his spell book as needed. Of course, it takes a long time, must be undisturbed, and probably burns through some of those much hated material components. How much of each? I dunno, let's say an hour per level of spell, and perhaps 100gp in components per level of spell squared (100, 400, 900, etc). Maybe some spells can only be cast this way. I can't imagine Find Familiar as being a spell anyone would prepare for the day when going forth into the dungeon.

What would even be cooler is if regular combat spells could be cast this way. Of course, you would need something to use to target the spell, like some hair or an article of clothing of the victim. Ray of Enfeeblement suddenly goes from a ho-hum dungeon combat spell to a nasty curse placed by an offended wizard upon the head of the town watch.

Magic users aren't useless...they just do things a little differently.

*In most versions (i.e. the couple I looked at) the magic-user has just as much of a chance to hit in combat as a fighter for the first couple of levels, and of course if you're using the "all weapons do d6 damage" rule, a dagger is as deadly as a bastard sword. Useless? Bah!

218th! W00t!

Looks like I made it on to the big Old School RPG blog list over at Cyclopeatron. It's about time I've been recognized for the invaluable contributions I've made to the gaming community.

Guess I'd better start adding some more content, huh?