Fhuaran

25 Oct 2010, 06:51 PM

http://help.travian.co.uk/img/buildings/gid27.gif

Artifact Spawning Locations Guide

This guide deals with the locations of the artifact-holding Natar villages which appear on server types 3.1 or later, at a date roughly half way between the beginning of the server and the start of the endgame. It is not intended to be stand-alone – users unaware of the fundamentals of artifacts should consider first reading Avi's "Artefacts; the facts" guide which can be found here (http://archive.forum.travian.co.uk/showthread.php?t=47415), and the FAQ page on artifacts which can be found here. (http://help.travian.co.uk/index.php?type=faq&mod=508)

The relevance of this guide springs from the fact that while most able players have a good understanding of how to take an artifact, only a small number of players give due consideration to locating their villages to maximise their chances of getting the artifact they desire without having to steal it at a later date. This guide will attempt to demonstrate that planning ahead in this way can tip the odds massively in ones' favour, and that attaining the most sought-after artifact combinations (diet+academic or haste+large academic pairs for example) needn't be all that difficult.

The importance of artifacts should not be underestimated, and while they carry an associated risk of theft, choosing not to seek the best artifacts given the opportunity can give both players and alliances a considerable handicap.

Contents

1. Guide Limitations

2. Basic Mechanism

3. Unique Artifacts

4. Large (Account) Artifacts

5. Small (Village) Artifacts

6. Overview of Relative Radii

7. Applying the Information in this Guide to your Game

1. Guide Limitations

This guide will assume a working understanding of artifacts, their types (Unique/Large/Small) and effects (Artifact of the Fool etc), and the map's Cartesian co-ordinate system. Almost all numbers contained in the guide are approximate, primarily because co-ordinates must take integer values (all artifacts must land on a specific square) but also because if a calculated artifact location is already occupied by a village or oasis, the village instead spawns in a nearby free square. To avoid the need to frequently mention this potential error, the guide will instead describe locations assuming that the map is entirely empty. This will not cause enough inaccuracy to make a noticeable difference. Mathematics and numbers are an unfortunate necessity in describing locations but I will try to keep them to a minimum and instead use pictorial demonstrations and verbal description for those who prefer a qualitative analysis.

This guide is not complete, nor do I expect it to ever be truly complete, since determining certain constants and factors is too much work for one person (see part 3). The data which forms the basis of the guide is taken from six T3.1-3.6 UK slow servers and so I cannot vouch for other domains. Due to the incomplete nature of my personal understanding, I will leave some of the interpretation of the results to the reader. While I know which parts of the map I would go to in order to obtain a certain artifact/set of artifacts, I cannot fully mathematically prove the justification and so will not give "hard and fast" suggestions. I also invite other players to fill the gaps in my own understanding and point out any perceived mistakes.

While the Travian map has no mathematical centre, the result of rounding the mean location of all artifacts on a server is always the origin (0|0) so this will be referred to as the centre. Radii (straight line distance from the centre to a given artifact) will be given in the basic travian unit of distance, i.e. the width of a field. Angles will be entirely given in degrees.

In all maps, white dots represent Unique artifacts, blue dots represent Large artifacts and yellow dots represent Small artifacts. All maps were produced using Blender, Inkscape and GIMP. Map data taken from gettertools (http://www.gettertools.com) and in-game.

2. Basic Mechanism

The polar co-ordinate location (radius and angle from an axis- see this page (http://mathworld.wolfram.com/PolarCoordinates.html) for a full understanding) of a particular artifact relative to any other artifact is proportionally identical on any given server.

This means that as shown in figure 1, the artifact spread on one server can be made to identically resemble the spread on another server simply by scaling and rotating their maps. Since there is only one of each Unique artifact, we can know the location of every other artifact on the server given the location of a single Unique. And so the location of Uniques will be looked at first in the guide.

figure 1 - Four rotated and scaled semi-transparent server maps overlayed (uk1r4,uk3r3,uk4r3,uk5r3 - all the currently running post-artifact servers at the time of writing)

http://img214.imageshack.us/img214/7340/overlayk.jpg

3. Unique Artifacts

These are the closest artifacts to the centre and their radii are equal, so they all lie on a circle - while all identical artifacts on each server lie on a circle just like this, the uniques are the only artifacts to share a radius without also having the same artifact effect (3x troop speed, 5x building strength etc). I will call this radius Ru for future reference. The difference in angle between vectors from the centre to two adjacent Unique artifacts is always equal, meaning that they make the vertices of a regular heptagon as shown in figure 2. The value of Ru is difficult to calculate from the available data, but there is a general trend for servers with more players to have a higher value for Ru than servers with fewer players. It is possible but not yet confirmed that Ru is non-linearly dictated by by the radius at which new account spawns occur on the server at the time of release. A general rule of thumb is that Ru usually takes a value between 40 and 70.

figure 2 - Unique artifact locations (uk4r3)

http://img63.imageshack.us/img63/2958/uk4unique.png

As stated previously, the locations of each Unique artifact on a server will be a scaled rotation of the above diagram about the map centre i.e. the Unique Military Haste will always be (360/7)° clockwise of the Unique Architect's Secret, which in turn will always be (360/7)° clockwise of the Unique Artifact of the Fool etc. The variable governing the overall rotation of the Unique artifacts is not widely known, however it is quantifyable. One Unique artifact on each server will always be an integer number of 1/8th turns from any axis. This means one artifact either lies on (or extremely close to) the horizontal/vertical axes OR half way between them at a 45° angle. This gives eight possible positions. Since there are seven Unique artifacts, there are a total of 8*7=56 different rotations which the artifacts can take. In the above example it can be seen that the Unique artifact of the Fool is half way between the axes. The uncertainty does make predicting locations more difficult, however the odds can still be played and a huge advantage gained without a complete prediction of the rotation on a given server.

4. Large (Account) Artifacts

Large artifacts come in seven varieties of effect and there are four artifacts of each variety. One of each variety dictates the locations of the other three since they always make a square (i.e each one is 90° away from two others and at the same radius). To make their locations easier to interpret, instead of looking at all the large artifacts, we will look at one of each, as shown in figure 3.

figure 3 - one of four large artifact spirals (uk4r3)

http://img513.imageshack.us/img513/6116/uk4large.png

As can be seen, the artifacts form a spiral which radiates out in a clockwise direction. Each artifact is roughly 26° clockwise relative to the previous one, and 0.4Ru further from the centre. This linear angle to radius relationship is called an Archimedean Spiral. The scale and rotation of this spiral are such that the Rival's Confusion artifacts are at a radius of 3.5Ru and lie at integer numbers of right angles relative to the Unique Haste artifact. This means one will lie on the same line as a vector from the centre to the Unique Haste.

5. Small (Village) Artifacts

Small artifacts come in eight varieties of effect. There are ten small artifacts of the fool and six of each other variety. Artifacts of the fool will be dealt with later, and first the other seven varieties will be analysed. One of each variety dictates the locations of the other five in this case since they always make a regular hexagon**. As before, let's look at one of each, as shown in figure 4.

figure 4 - one of six small artifact spirals (uk4r3)

http://img294.imageshack.us/img294/3034/uk4small.png

Again the artifacts form a spiral which radiates out in a clockwise direction, however the order of occurence of each variety has been reversed when compared to the Large artifact spiral. Notice that the small diet and small academic are always adjacent on the spiral, making it straightfoward to potentially take one of each (though you may want to borrow a friend's hero to save time if you split your army in two). Each small artifact is 20° clockwise relative to the previous one, and roughly 0.56Ru further from the centre. The scale and rotation are such that the Small Diet artifacts are at a radius of 4.3Ru and one lies 45° clockwise of the Unique Diet. The others will of course be at multiples of 60° from this angle.

The ten small artifacts of the fool on the other hand make the vertices of a regular decagon as shown in figure 5. Their radius is 4Ru and their rotation is such that one lines up with the Architect's Master Secret (Unique) artifact.

figure 5 - a decagon of small artifacts of the fool (uk4r3)

http://img101.imageshack.us/img101/1616/foolsuk4.png

**For those who are interested, this means that given the location of one (x,y), the co-ordinates of the other five are roughly given by x'=x*cos(a)-y*sin(a), y'=xsin(a)+ycos(a) where a={60°,120°,180°,240°,300°}.

6. Overview of Relative Radii

Since rotation remains the primary unknown, the most effective way to summarise the key information in this guide is an arbitrarily scaled map of the radii of each type of artifact, given in figure 6.

figure 6 - relative radii (scaled to Ru=50 where major gridline spacing =100) - May take a while to load.

http://img219.imageshack.us/img219/138/radii.png

7. Applying the Information in this Guide to your Game

Hopefully the information in this guide is useful to plenty of people, it can massively improve your chances of getting the artifact of your choice. At the most basic level, if artifacts are a fundamental part of your gameplan, I'd strongly consider using the map of relative radii and after making a rough estimate of Ru based on the size of the server, locate your hammer village on the circle representing your desired artifact.

Key factors when choosing where on your chosen circle to settle may be 1) nearby farms and defensive allies or 2) reasonable distance from other players who might be seeking the same artifacts- the border between quads can be ideal because most top players don't like to be too far from the centre, leading them to seek lower numbered co-ordinates. It seems daft but there's a very real trend for the area around (142|141) for example to be more densely populated than (0|200) despite both being similarly far from the centre. Being on the border will also allow you to take artifacts from two quads, which can be useful if one quad has been heavily warring and/or has fewer players.

It's probably a controversial suggestion but I'd in fact suggest that if you have personal or alliance goals which rely heavily on good artifacts, you should try not to be the first player on the server to settle your second village. Allowing other players to make the first move will mean you can get an idea of the lay of the land and where your main rivals are likely to be. However, if your desired artifact is a fairly central one, leaving the settling late will probably hamper your chances of finding a good 125%-150% 15c for your capital. As with so many variables in Travian, there is a trade off and you must decide which is more important to you.

Artifact Spawning Locations Guide

This guide deals with the locations of the artifact-holding Natar villages which appear on server types 3.1 or later, at a date roughly half way between the beginning of the server and the start of the endgame. It is not intended to be stand-alone – users unaware of the fundamentals of artifacts should consider first reading Avi's "Artefacts; the facts" guide which can be found here (http://archive.forum.travian.co.uk/showthread.php?t=47415), and the FAQ page on artifacts which can be found here. (http://help.travian.co.uk/index.php?type=faq&mod=508)

The relevance of this guide springs from the fact that while most able players have a good understanding of how to take an artifact, only a small number of players give due consideration to locating their villages to maximise their chances of getting the artifact they desire without having to steal it at a later date. This guide will attempt to demonstrate that planning ahead in this way can tip the odds massively in ones' favour, and that attaining the most sought-after artifact combinations (diet+academic or haste+large academic pairs for example) needn't be all that difficult.

The importance of artifacts should not be underestimated, and while they carry an associated risk of theft, choosing not to seek the best artifacts given the opportunity can give both players and alliances a considerable handicap.

Contents

1. Guide Limitations

2. Basic Mechanism

3. Unique Artifacts

4. Large (Account) Artifacts

5. Small (Village) Artifacts

6. Overview of Relative Radii

7. Applying the Information in this Guide to your Game

1. Guide Limitations

This guide will assume a working understanding of artifacts, their types (Unique/Large/Small) and effects (Artifact of the Fool etc), and the map's Cartesian co-ordinate system. Almost all numbers contained in the guide are approximate, primarily because co-ordinates must take integer values (all artifacts must land on a specific square) but also because if a calculated artifact location is already occupied by a village or oasis, the village instead spawns in a nearby free square. To avoid the need to frequently mention this potential error, the guide will instead describe locations assuming that the map is entirely empty. This will not cause enough inaccuracy to make a noticeable difference. Mathematics and numbers are an unfortunate necessity in describing locations but I will try to keep them to a minimum and instead use pictorial demonstrations and verbal description for those who prefer a qualitative analysis.

This guide is not complete, nor do I expect it to ever be truly complete, since determining certain constants and factors is too much work for one person (see part 3). The data which forms the basis of the guide is taken from six T3.1-3.6 UK slow servers and so I cannot vouch for other domains. Due to the incomplete nature of my personal understanding, I will leave some of the interpretation of the results to the reader. While I know which parts of the map I would go to in order to obtain a certain artifact/set of artifacts, I cannot fully mathematically prove the justification and so will not give "hard and fast" suggestions. I also invite other players to fill the gaps in my own understanding and point out any perceived mistakes.

While the Travian map has no mathematical centre, the result of rounding the mean location of all artifacts on a server is always the origin (0|0) so this will be referred to as the centre. Radii (straight line distance from the centre to a given artifact) will be given in the basic travian unit of distance, i.e. the width of a field. Angles will be entirely given in degrees.

In all maps, white dots represent Unique artifacts, blue dots represent Large artifacts and yellow dots represent Small artifacts. All maps were produced using Blender, Inkscape and GIMP. Map data taken from gettertools (http://www.gettertools.com) and in-game.

2. Basic Mechanism

The polar co-ordinate location (radius and angle from an axis- see this page (http://mathworld.wolfram.com/PolarCoordinates.html) for a full understanding) of a particular artifact relative to any other artifact is proportionally identical on any given server.

This means that as shown in figure 1, the artifact spread on one server can be made to identically resemble the spread on another server simply by scaling and rotating their maps. Since there is only one of each Unique artifact, we can know the location of every other artifact on the server given the location of a single Unique. And so the location of Uniques will be looked at first in the guide.

figure 1 - Four rotated and scaled semi-transparent server maps overlayed (uk1r4,uk3r3,uk4r3,uk5r3 - all the currently running post-artifact servers at the time of writing)

http://img214.imageshack.us/img214/7340/overlayk.jpg

3. Unique Artifacts

These are the closest artifacts to the centre and their radii are equal, so they all lie on a circle - while all identical artifacts on each server lie on a circle just like this, the uniques are the only artifacts to share a radius without also having the same artifact effect (3x troop speed, 5x building strength etc). I will call this radius Ru for future reference. The difference in angle between vectors from the centre to two adjacent Unique artifacts is always equal, meaning that they make the vertices of a regular heptagon as shown in figure 2. The value of Ru is difficult to calculate from the available data, but there is a general trend for servers with more players to have a higher value for Ru than servers with fewer players. It is possible but not yet confirmed that Ru is non-linearly dictated by by the radius at which new account spawns occur on the server at the time of release. A general rule of thumb is that Ru usually takes a value between 40 and 70.

figure 2 - Unique artifact locations (uk4r3)

http://img63.imageshack.us/img63/2958/uk4unique.png

As stated previously, the locations of each Unique artifact on a server will be a scaled rotation of the above diagram about the map centre i.e. the Unique Military Haste will always be (360/7)° clockwise of the Unique Architect's Secret, which in turn will always be (360/7)° clockwise of the Unique Artifact of the Fool etc. The variable governing the overall rotation of the Unique artifacts is not widely known, however it is quantifyable. One Unique artifact on each server will always be an integer number of 1/8th turns from any axis. This means one artifact either lies on (or extremely close to) the horizontal/vertical axes OR half way between them at a 45° angle. This gives eight possible positions. Since there are seven Unique artifacts, there are a total of 8*7=56 different rotations which the artifacts can take. In the above example it can be seen that the Unique artifact of the Fool is half way between the axes. The uncertainty does make predicting locations more difficult, however the odds can still be played and a huge advantage gained without a complete prediction of the rotation on a given server.

4. Large (Account) Artifacts

Large artifacts come in seven varieties of effect and there are four artifacts of each variety. One of each variety dictates the locations of the other three since they always make a square (i.e each one is 90° away from two others and at the same radius). To make their locations easier to interpret, instead of looking at all the large artifacts, we will look at one of each, as shown in figure 3.

figure 3 - one of four large artifact spirals (uk4r3)

http://img513.imageshack.us/img513/6116/uk4large.png

As can be seen, the artifacts form a spiral which radiates out in a clockwise direction. Each artifact is roughly 26° clockwise relative to the previous one, and 0.4Ru further from the centre. This linear angle to radius relationship is called an Archimedean Spiral. The scale and rotation of this spiral are such that the Rival's Confusion artifacts are at a radius of 3.5Ru and lie at integer numbers of right angles relative to the Unique Haste artifact. This means one will lie on the same line as a vector from the centre to the Unique Haste.

5. Small (Village) Artifacts

Small artifacts come in eight varieties of effect. There are ten small artifacts of the fool and six of each other variety. Artifacts of the fool will be dealt with later, and first the other seven varieties will be analysed. One of each variety dictates the locations of the other five in this case since they always make a regular hexagon**. As before, let's look at one of each, as shown in figure 4.

figure 4 - one of six small artifact spirals (uk4r3)

http://img294.imageshack.us/img294/3034/uk4small.png

Again the artifacts form a spiral which radiates out in a clockwise direction, however the order of occurence of each variety has been reversed when compared to the Large artifact spiral. Notice that the small diet and small academic are always adjacent on the spiral, making it straightfoward to potentially take one of each (though you may want to borrow a friend's hero to save time if you split your army in two). Each small artifact is 20° clockwise relative to the previous one, and roughly 0.56Ru further from the centre. The scale and rotation are such that the Small Diet artifacts are at a radius of 4.3Ru and one lies 45° clockwise of the Unique Diet. The others will of course be at multiples of 60° from this angle.

The ten small artifacts of the fool on the other hand make the vertices of a regular decagon as shown in figure 5. Their radius is 4Ru and their rotation is such that one lines up with the Architect's Master Secret (Unique) artifact.

figure 5 - a decagon of small artifacts of the fool (uk4r3)

http://img101.imageshack.us/img101/1616/foolsuk4.png

**For those who are interested, this means that given the location of one (x,y), the co-ordinates of the other five are roughly given by x'=x*cos(a)-y*sin(a), y'=xsin(a)+ycos(a) where a={60°,120°,180°,240°,300°}.

6. Overview of Relative Radii

Since rotation remains the primary unknown, the most effective way to summarise the key information in this guide is an arbitrarily scaled map of the radii of each type of artifact, given in figure 6.

figure 6 - relative radii (scaled to Ru=50 where major gridline spacing =100) - May take a while to load.

http://img219.imageshack.us/img219/138/radii.png

7. Applying the Information in this Guide to your Game

Hopefully the information in this guide is useful to plenty of people, it can massively improve your chances of getting the artifact of your choice. At the most basic level, if artifacts are a fundamental part of your gameplan, I'd strongly consider using the map of relative radii and after making a rough estimate of Ru based on the size of the server, locate your hammer village on the circle representing your desired artifact.

Key factors when choosing where on your chosen circle to settle may be 1) nearby farms and defensive allies or 2) reasonable distance from other players who might be seeking the same artifacts- the border between quads can be ideal because most top players don't like to be too far from the centre, leading them to seek lower numbered co-ordinates. It seems daft but there's a very real trend for the area around (142|141) for example to be more densely populated than (0|200) despite both being similarly far from the centre. Being on the border will also allow you to take artifacts from two quads, which can be useful if one quad has been heavily warring and/or has fewer players.

It's probably a controversial suggestion but I'd in fact suggest that if you have personal or alliance goals which rely heavily on good artifacts, you should try not to be the first player on the server to settle your second village. Allowing other players to make the first move will mean you can get an idea of the lay of the land and where your main rivals are likely to be. However, if your desired artifact is a fairly central one, leaving the settling late will probably hamper your chances of finding a good 125%-150% 15c for your capital. As with so many variables in Travian, there is a trade off and you must decide which is more important to you.