What the Heck is a Logarithmic Graph? And Why is it Used in MineCraft?

I was playing MineCraft the other day, mining for gold which I could use to build powered rails. As I was going along I wondered to myself just how rare gold was at each elevation. So I went to the internet, and found an article on altitude in the MineCraft wiki. Sure enough, they had data on the rarity of in-game resources. However, I thought to myself:

WHAT KIND OF GRAPH WAS THIS?

It took me a second to realize that I had seen a graph like this before. The graph uses logarithmic layout to illustrate large Y-values of data. I had used logarithmic graphs back in my high school AP Chemistry class, so with that in mind it didn’t take long to analyze the information I was seeing on my screen. Then I got to thinking…

Just how many people know how to read logarithmic graphs? For that matter, how many people have actually seen a logarithmic graph? Today, I am going to illustrate the ins and outs of logarithmic graphs; how to read them and how to get the most out of MineCraft's Altitude Logarithm Graph.

Your traditional graph (also known as a Cartesian graph or coordinate plane) has a horizontal and vertical axis, and equally spaced lines running through each quadrant. The one you see to your right is numbered -14 to 14 horizontally; this means that you advance by 1 for every line you cross going from left to right (the opposite if you go right to left). The graph is also numbered -10 to 10 vertically, meaning you advance by 1 for each line going up (the opposite if you go down).

You can modify the axes to change the pace of the numbers. For example, you can change the X axis to go from -28 to 28 (each line representing an increase of 2). You can change the Y to go from -50 to 50 if you wanted (each line representing an increase of 5). However, the pace must be linear. You cannot make an axis go in powers (meaning you cannot make the lines of the Y axis 0, 1, 10, 100, 1000, etc). It simply does not work. That's where logarithmic graphs come in.

Logarithmic paper looks a little something like this. Note the horizontal, or X, axis is very similar to the traditional graph shown earlier. However, lines for the Y values scrunch up, then unscruntch, then scrunch, and so on and so forth. You might be asking yourself why this is.

The graph is designed to show exponential values. For example, this one goes up by powers of 10. Its Y-values are as follows: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, etc.

To better quantify these values, you can use 10^x. For example, the range of numbers from 10² to 10³ (100 to 1000), can be rewritten as 10², 10^2.30, 10^2.47, 10^2.60, 10^2.69, 10^2.77, 10^2.84, 10^2.9, 10^2.95, 10³. This should explain a little easier why the numbers scrunch up toward the top of each major axis. The first leap is .3, the second is .17, the third is .13, the fourth is .09, the fifth is .08, the sixth is .07, the seventh is .06, the eighth is .05, and the ninth is .05.

For the sake of this example, let's look at the line for gold ore, which is what I was spelunking for in the game. According to the graph's X axis, gold ore is primarily found at altitude levels 2-31, before dropping to zero at altitude level 32. The rarity is consistent through all altitude levels in this range. The line shows that there are roughly 6000 blocks of gold ore from levels 2 to 31.

If you want to know the total possible amount of gold in your game map, you simply need to find the sum of gold resources for all levels. Thankfully, since it's a straight line, you can simply multiply 6000 by the number of levels, which in this case would be thirty levels. After some simple calculation, you find that there are 180,000 gold ore units loaded into a world map in the game. And that's good to know, because if you do manage to mine that much ore, and need more, then you're obviously doing something wrong.

Now let's say you need a more common resource, like coal. According to the graph, coal is most common from levels 6 to 56, with around 50,000 coal ore blocks at each level in this range. Combined, that's over 2.5 million units of coal. Of course, you want to mine efficiently to save time.

What you decide to do is pick an altitude of say, 43, and mine a tunnel in a straight line. By bearing in mind that there are around 50,000 coal pieces you can just say on a path at this elevation until you find it all (granted it will take a very long time).

By utilizing a graph like this you can find the ideal elevations to acquire any resource. Let's say you need wood, and lots of it. According to the map, you can find wood from levels 58 to 126. However, the ideal elevations would be levels 64 to 76. These are locations where the amount of wood resource is over 10,000 per altitude level. Any higher and the amount of wood drops by the thousands.

The map also reveals where the greatest spikes in resources are. For example, the amount of lava drops from 1000 at level 60, all the way to 100 at level 64, before doubling to 200 at level 65. If you don't want to deep mine, then level 65 would be your ideal spot to find lava.

I hope I was able to give you a little better explanation on how logarithmic paper is plotted on, as well as how gamers can use it to improve their MineCraft approaches. Hopefully now, you can find all the resources you require with as little effort as possible. Thank you for reading!