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*Mathematica* Q&A: Excluding Points from Plots

March 14, 2011 — Andrew Moylan, Technical Content Specialist, Technical Communication and Strategy Group

Got questions about *Mathematica*? The Wolfram Blog has answers! Each week, we’ll answer a selected question from users around the web. You can submit your question directly to the Q&A Team.

For our first post in this new series of *Mathematica* Q&A articles, we’re going to address a very frequently asked question about plotting in *Mathematica*.

**How can I control the appearance of discontinuities in a plot?**

The short answer is, use the options `Exclusions` and `ExclusionsStyle`! Let’s see how they work.

By default, `Plot` shows the function 1 ⁄ sin(*x*) with lines joining its discontinuities:

You can use the `Exclusions` option to exclude points from the plot:

Instead of excluding the points, you can specify a style to apply to them:

For explicitly piecewise functions like `Floor`, points are excluded automatically:

(You can use `Exclusions` → `None` to disable this.)

The exclusions options work with many other *Mathematica* functions, such as `Plot3D`:

We specified two styles using `ExclusionsStyle`: the first style is applied to the excluded region, while the second style is applied to its boundary.

You can create some spectacular visualizations with these options. Download the Computable Document Format (CDF) file for this post to see how to generate this one:

And don’t forget you can submit your own questions to the Q&A Team anytime.

## 13 Comments

Mathematica Q&A is a great idea! In this first posting was raised an excellent question, thanks!

I second the comment that Q&A is a great idea. I have a question that I hope isn’t too trivial. What would you recommend as the most reasonable Mathematica way to simulate simple BASIC-like plotting of arbitrary points, where statements like Plot x,y “turn on” a particular x,y points in a bitmap or grid? Mathematica makes the complicated stuff so easy that I sometimes feel unsure where to begin with the very simple stuff.

If I have numerical solution as interpolation function from NDSolve:

sol = NDSolve[{x'[t]==5,x[0]==0}, x, {t, 0, 100}]

And I want to plot the solution in this way:

Plot[(x[t] – Floor[x[t], 100]) /. sol[[1]], {t, 0, 100}]

Then Mathematica doesn’t exclude discontinuities automatically. How do I get rid of these joining lines?

Wow, I am a idiot of math, and you guys so smart…and I even can’t understand what’s the stand for?

Good idea. But should this really be in the blog? Shouldn’t this be in a separate section?

I like this a lot. It will also increase the frequency of update. How does one submit proposals for content? Is this a good place to ask questions or do you have a user forum?

Good and thank you for posting. I’m also in the camp that’s thinking that a separate section for this type of posting will be in keeping with the organized structure on your website.

Re: NDSolve by Josef

After observing that the discontinuities happen at multiples of 0.2, I chose to do the following exclusions statement, successfully eliminating the discontinuities.

Exclusions -> Table[0.2 n, {n, 1, 5}]

Ref: NDSolve by Josef

Submitting entire code, from M7 Student.

sol = NDSolve[{x'[t] == 5, x[0] == 0}, x, {t, 0, 100}];

y = Evaluate[(x[t] – Floor[ x[t] ]) /. sol ] ;

Plot[y, {t, 0, 1},

Exclusions -> Table[0.2 n, {n, 1, 5}]]

Nice tutorial. The Mathematica documentation is first class as of version 6, but there is still room for improvement. The examples in this Blog should replace the examples in documentation for the Exclusions option. I hope Wolfram Research will strive to make it easy to find the answer to every FAQ they know of, and put them all in the documentation. The key is to include good examples, and provide links connecting related topics.

@Isaac: Well, it was just a trivial example. In fact I have differential equation where I cannot predict discontinuities caused by Floor function. I mean, how to suppress this InterpolationFunction-behaviour in general. Anyway, thank you for your time and answer. :)

Hi Paul, You can submit questions and ideas for Q&A blog posts using the form at https://blog.wolfram.com/ask-a-question/.

Hi Mark, I think ListPlot may be the function you are looking for.