The rise of explorable explanations

Something I strongly believe in seems to be taking off lately: explorable explanations.

It may be that I’m just late to the party, but the last couple of months some very interesting mixes of text and small, interactive graphics explaining quite complex mathematical, statistical and other concepts came into my view. Here I list some of these new and powerful explorable explanations.

The inspirator

The term ‘explorable explanation’ was coined 4 years ago by Bret Victor, in his essay with the same title. Victor argues that readers will be more engaged and will learn and remember better when they are ‘active readers’.

Active reading requires ‘reactive documents’: text and visuals enriched with small interactive handles for the user to play and interact with. In Victor’s words, this is the definition of a reactive document:

reactive document allows the reader to play with the author’s assumptions and analyses, and see the consquences.

Victor also introduces the ‘explorable example’:

An explorable example makes the abstract concrete, and allows the reader to develop an intuition for how a system works.


By adjusting the parameters in the graphs at the bottom, the values in the diagram and the formulas change. In this way, active readers immediately see the effect of changes in the parameters. See the live example.

In a following essay, Up and Down the Ladder of Abstraction, Victor applies his concept of the explorable example multiple times, every time adding some more interactivity and complexity:


One of the many small interactive playables in Up and Down the Ladder of Abstraction.

Explained visually

Victor’s essays and examples inspired the recent wave of explorable explanations. Explicitely citing Bret Victor’s work as a source of inspiration, Victor Powell and Lewis Lehe created Explained Visually. Every episode of Explained Visually demonstrates a mathematical or statistical concept, ranging from conditional probability over π (pi) to image kernels.

Explained Visually

The episodes of Explained Visually published so far.

Explained Visually provides small graphics, animations and controls that the reader can manipulate in order to better understand the concepts layed out in the text. Visuals serve as direct controls themselves and/or give direct feedback when controls are manipulated.

Conditional Probability

Screenshot of an interactive animation from Conditional Probability Explained Visually. Changes in the sliders adjust probabilities, which are reflected graphically in the animation and the bars at the bottom.

Seeing circles, sines and signals

Just as I was preparing this article, Jack Schaedler published Seeing circles, sines and signals, ‘an eccentric piece of not-so-rigorous literature with a preoccupation for explaining things using interactive visualizations, animations and sound’. With this impressive piece Schaedler explains waves, sines and cosines, imaginary numbers and Fourrier transformations.


One of the many small interactives from Seeing circles, Sines and Signals.

I never managed to get my head around Fourrier transformations completely. But only halfway the text and the little interactives, I think I understand it better than ever before. Schaedler also mentions the work of Bret Victor as a source of inspiration.

Earth Primer

Explorable explanations are not confined to mathematics and statistics and can also work on tablets. That is what Earth Primer, an iPad app by Chaim Gingold, proves. It was released only a couple of weeks ago.

Readers are guided through geological, ecological and meteorological concepts with text and images, but most important are the zoomable and rotatable game-like interactive transects of earth. At the end, the active reader can play around with all the controls in a Sandbox.

Earth Primer

The controls in Earth Primer enables you to see the effects of rain, changes in sea level, wind direction, temperature and relief on vegetation and geography.

Visualizing algorithms

In June last year Mike Bostock, inventor of the fantastic D3.js library, published Visualizing Algorithms, the written cristallization of a talk he gave at the Eyeo 2014 festival. The intro says it all:

“Algorithms are a fascinating use case for visualization. To visualize an algorithm, we don’t merely fit data to a chart; there is no primary dataset. Instead there are logical rules that describe behavior. This may be why algorithm visualizations are so unusual, as designers experiment with novel forms to better communicate. This is reason enough to study them.

But algorithms are also a reminder that visualization is more than a tool for finding patterns in data. Visualization leverages the human visual system to augment human intellect: we can use it to better understand these important abstract processes, and perhaps other things, too.”

He proceeds by illustrating various sampling, shuffling and sorting algorithms with images, animations and playables.


A sampling algorithm illustrated with an animation.

Parable of the Polygons

Parable of the Polygons, by Vi Hart and Nicky Case is an interactive story that explains how segregation in society works. It is a very playful work, with ‘shapist’ triangles and squares. It also ends with a sandbox to play in. Parable of the Polygons proves that explorable explanations can also be used in social sciences.


Animations and interactives illustrate how a society of blue squares and yellow triangles gets segregated.

Design patterns and considerations

With the subtitle Explorable Explanations. Interactive non-fiction. Active essays. Glogs. Nicky Case (the same one from Parable of the Polygons) shared the insights she and others gathered at ‘a 20-person workshop on figuring out how to use interactivity to help teach concepts.’


One of the principles for making explorable explanations is to first explain small parts, than combinations and in the end letting them all play together.

If you’re interested in making explorable explanations, the article gives some very good advice on how to lay out your story, how to integrate interactivity and other do’s and don’ts.

The future of education

I strongly believe in the power of explorable explanations. Allowing the reader to actively test his own hypotheses, guided and nudged by the maker of the explanation, leads to much more knowledge then simple text with only some formulas and static images thrown in. Concepts I never really understood (like eigenvectors, for example) suddenly seem to be well in my mental reach when I can explore them visually and interactively.

That is why I think the textbook of the future will explain things explorably. Bret Victor sowed the seeds some years ago and today a lot of people from a lot of different fields are experimenting. Lessons learned from these experiments are already starting to take shape.

I hope (and think) that explorable explanations will be popping up more and more. Maybe I’ll make one myself?


  1. Will Moffat

    Hi Maarten,

    Great article! I’d seen Bret Victor’s articles but not the other ones, thanks for bringing this together.

    Would you say an app like Dragon Box fits into the genre of Explorable Explanations? If you’re not familiar with it, kids learn algebra in the guise of a fun game. There’s a good review here:

  2. Ivan

    Oh that’s cool! It’s tricky as it requires an author to embed a lot more context than just an ordinary answer. I want more of these, so you should definitely create a one 😉 Also the more examples people have – the easier it is to grasp a concept 🙂

    Thank you!

  3. Simon Dell

    This is a great round-up! I’ve recently become interested in this field, and am similarly inspired by Bret Victor. I’ve seen one or two of your other sources before but the rest were new to me. I’m just starting my journey in this area so your article serves me as a good source of inspiration and something of a road map for some rich future study. Many thanks!

  4. Jacek

    more examples related to game design can be found on a blog by Red Blob Games – they tend to include a lot of interactivity to their explanations
    Here are just two examples but there are more on their site

  5. Pomax

    Nice! Wondering whether you’d seen (actually also linked from the redblog site links recommended by Jacek)? This started in 2011 because I needed to understand Bezier curves, and the best way I knew of how to do that was to explain them to the rest of the world as best I could. Interactivity was important there, and while working on it, Brett Victor came into the limelight with his ladder of abstraction and “kill maths” work.

  6. Alex Kluge

    Cool collection. I also believe that active and adaptive content are powerful forces for education, and that they are significantly underappreciated. I feel strongly enough to create free and open source tools to enable easy active content creation in math and physics like this Thoug I guess explorable explanations is a catchier phrase 🙂

    Ivan’s comments are also important. This is a highly effective teaching tool, but it requires more work. This pushes it off the low hanging fruit that is attractive to large publishing companies with their extensive marketing engines. We need to continue to advocate for explorable explanations and produce easier ways for teachers and other content creators to use them.

  7. Shahbaz

    Awesome article!

  8. Sabrina

    Thank you so much for writing this.
    I’m helping to host a “game” jam in Pittsburgh in May 1-3, 2015 to create these kinds of experiences, though the term “explorable explanations” is not one I had heard before. I’ve struggled to simply and clearly convey what the jam is about so I may have to adopt this term- I will definitely point people to this post!
    (ps- If you’re into this kind of thing and you’d be willing to join us in Pittsburgh, considering signing up for the jam:

  9. Prof Steven Abbott

    Your page here is wonderful. So I’ve blogged about it at the link shown in the Site field. I started AbbottApps long before I’d heard of Victor and my own attempts fall far short of your lovely examples. But still, they are an attempt in large areas of practical interest, adhesion, surfactants, solubility, to do what Explorable Explanations are aiming at. How I raise their standard to a higher level I don’t yet know – but clearly I’ve got a lot to do. Thanks for provoking some fresh thinking.

  10. Amit Patel

    Great list! Ian Johnson has also been making a list —

    There were several people experimenting with interactive web explanations before now (I started in 2004 and had seen some going back into the 1990s), but it was a bit more awkward with Java applets and Flash. Java and Flash made it hard for the applet to interact with the rest of the page, so those interactive diagrams tended to be standalone. The first “mostly text interspersed with many interactive diagrams” format I saw was . It looks dated now but it was different from the “one big interactive diagram with a little bit of text” format that was more common back then.

    These days, with browsers becoming more capable, it’s much easier to make *both* the diagrams and the text of the page interactive. Bret Victor’s “Tangle” library ( lets the reader manipulate text, and other text will respond. I’ve experimented with letting the reader manipulate text and sample code, and diagrams will respond. (I also want to experiment with the reverse.) We’re also no longer limited to the “box” layout where text is in one box and diagrams are in another box. With control over transparency and clipping, text and diagrams can be placed over each other. Instead of things like “see figure 4” we can link diagrams and text together in more direct ways.

    I’m looking forward to seeing a great deal of experimentation in interactive content in the next few years.

  11. Jurjen Verhagen

    Thanks for this post! I saw some of the pages you linked before and I very much like the idea of these Explorable Explanations. Personally I love to learn by exploring and experimentation. Not only may it convey the meaning better or faster, I also think it is fun and thus more motivating to continue to study the subject more.
    I am actually planning to experiment in creating an explorable explanation as it is apparently called. Your post really gave some great places to start. I’m very curious to play around with this app you mentioned Earth Primer, it looks awesome!

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