R Lesson 31: Logarithmic Graphs

Hello everybody,

Michael here, and today’s lesson will be a sort-of contiuation of my previous post on R logarithms (R Lesson 30: Logarithms). However, in this post, I’ll cover how to create logarithmic graphs in R.

Let’s begin!

Two types of log plots

There are two main types of logarithmic plots in R-logarithmic scale plots and log-log plots.

What do these log plots do, exactly? Well, in the case of the logarithmic scale plot, only one of the plot’s axes uses a logarithmic scale while the other maintains a linear scale while with the log-log plot both axes use logarithmic scales.

When would you use each type of plot? In the case of logarithmic scale plots, you’d use them for analyses such as exponential growth/decay or percentage changes over a period of time. As for the log-log plots, they’re better suited for analyses such as comparative analyses (which involve comparing datasets with different scales or units) and data where both the x-axis and y-axis have a wide range of values.

And now for the logarithmic scale plots!

Just as the header says, let’s create a logarithmic scale plot in R!

Before we begin, let’s be sure we have the necessary data that we’ll use for this analysis-

This dataset is simpler than most I’ve worked with on this blog, as it only contains 11 rows and two columns. Here’s what each column means:

• Date-the date that the bitcoin mining reward will be halved
• Reward-the amount of bitcoin you will recieve after a successful mining as of the halving date.

For those unfamiliar with basic Bitcoin mining, the gist of the process is that when you mine Bitcoin you get a reward. However, after every 3-4 years, the reward for mining bitcoin is halved. For instance, on the first ever day that you could mine bitcoin (January 1, 2009), you would be able to recieve 50 bitcoin (BTC) for a successful haul. In 2012, the reward was halved to 25 BTC for a successful haul. The next halving is scheduled to occur in Spring 2024, where the reward will be halved to 3.125 BTC. Guess bitcoin mining isn’t as profitable as it was nearly 15 years ago?

There will likely be no more Bitcoin left to mine by the year 2140, so between now and then, the Bitcoin mining reward will get progressively smaller (a perfect example of exponential decay). I did mention that the Bitcoin mining reward will be less than 1 BTC by the year 2032.

• I mean, don’t take my word for it, but maybe the supply of mineable bitcoin won’t run out by 2140 and the reward instead would get progressively smaller until it’s well over 1/1,000,000,000th of 1 BTC. Just my theory though :-).

Now, enough about the Bitcoin mining-let’s see some logarithmic scale plots! Take a look at the code below.

First, we’ll read in our dataset:

bitcoin <- read.csv("C:/Users/mof39/OneDrive/Documents/bitcoin halving.csv", encoding="utf-8")

Next, we’ll create our logarithmic scale plot! Since there is only one axis that will use a log-scale (the y-axis in this case), let’s remember to specify that

plot(bitcoin$Date, bitcoin$Reward, log = "y", pch = 16, col = "blue", xlab = "Year", ylab = "BTC Reward")

Error in plot.window(...) : need finite 'xlim' values
In addition: Warning messages:
1: In xy.coords(x, y, xlabel, ylabel, log) : NAs introduced by coercion
2: In min(x) : no non-missing arguments to min; returning Inf
3: In max(x) : no non-missing arguments to max; returning -Inf

If we tried to use the plot() function along with all the parameters specified here, we’d get this error-Error in plot.window(...) : need finite 'xlim' values. Why does this occur?

The simple reason we got the error is because we used a column with non-numeric values for the x-axis. How do we fix this? Let’s create a numeric vector of the years in the Reward column (with the exception of 2009, all of the years in the Reward column are leap years until 2080) and use that vector as the x-axis:

years <- c(2009, 2012, 2016, 2020, 2024, 2028, 2032, 2036, 2040, 2044, 2048, 2052, 2056, 2060, 2064, 2068, 2072, 2076, 2080)

plot(years, bitcoin$Reward, log = "y", pch = 16, col = "red", xlab = "Year", ylab = "BTC Reward", main = "BTC Rewards 2009-2080")

Voila! As you can see here, we have a nice log-scale plot showing the exponential decay in bitcoin mining rewards from 2009 to 2080.

How did create this nice-looking plot? Well, we set the value of the log parameter of the plot() function equal to y, as we are only creating a log-scale plot. If we wanted to create a log-log plot, we would se the value of the log parameter to xy, which would indicate that we would use a logarithmic scale for both the x and y axes.

As for the rest of the values of the parameters in the plot() function, keep them the same as you would for a normal, non-logarithmic R scatter plot (except of course adapting your x- and y-axes and title to fit the scatterplot).

Now, one thing I did want to address on this graph is the scale on the y-axis, which might look strange to you if you’re not familiar with log-scale plots. See, the plot() function’s log parameter in R uses base-10 logs by default, and in turn, the y-axis will use powers of 10 in the scale (the scientific notation makes the display a little neater). For instance, 1e+01 represents 10, 1e+00 represents 0, and so on. Don’t worry, all the data points in the dataset were plotted correctly here.

And now, let’s create a log-log plot

Now that we’ve created a log-scale plot, it’s time to explore how to create a log-log plot in R!

loglog <- data.frame(x=c(2, 4, 8, 16, 32, 64), y=c(3, 9, 27, 81, 243, 729))

plot(loglog$x, loglog$y, log = "xy", pch = 16, col = "red", xlab = "Power of 2", ylab = "Power of 3", main = "Sample Log-Log Plot")

In this example, I created the dataframe loglog and filled both axes with powers of 2 and 3 to provide a simple way to demonstrate the creation of log-log plots in R.

As for the plot() function, I made sure to set the value of the log parameter to xy since we’re creating a log-log plot and thus need both axes to use a logarithmic scale. Aside from that, remember to change the plot’s axes, labels, and titles as appropriate for your plot.

Now, you might’ve noticed somthing about this graph. In R, both log-log and log-scale plots utilize base-10 logs for creating the plot. However, you likely noticed that the scale for the log-scale plot displays its values using scientific notation and powers of 10. The scale (or should I say scales) for the log-log plot doesn’t use scientifc notation and powers of 10 to display its values. Rather, the log-log plot uses conventional scaling to display its values-in other words, the scale for the log-log plot bases its values of the range of values in both axes rather than a powers-of-10 system. Honestly, I think this makes sense since the plot is already using a logarithmic scale for both axes, which would make the whole powers-of-10 thing in the scale values redundant.

• Of course, if you want to change the scale displays in either the log-log or log-scale plots, all you would need to do is utilize the axis() function in R after creating the plot. Doing so would allow you to customize your plot’s axis displays to your liking.

Thnaks for reading!

Michael