Colliding N-body spheres: Particle Mayhem!

When Giants Collide — WGC for short — is one of the “fun” projects I am working on. Once finished, it will be a small in-browser simulator where you can collide giant planets together (with some degree of realism). You can see my progress on my GitHub repo and the series of blog posts under this category.

In this little demo app, you can run an N-body simulation in your browser where you make two spheres made of point masses “collide”. You can tweak various parameters (collision speed,  impact parameter, distance and number of particles) to change the outcome of the simulation.

Underneath it all: TreeSPH.js

The app above is powered by the portion of WGC’s code that computes the gravitational force between a set of point particles (a gravitational N-body system). The gravitational force is computed using the Barnes-Hut tree gravity algorithm, and the coordinates of the points are evolved using a third-order embedded Runge-Kutta algorithm. The code is available in the GitHub repo for WGC.

I am now working on writing the hydrodynamical part (via the SPH algorithm), which will let me simulate the collision between two gaseous spheres. The resulting library will be called treesph.js.

treesph.js will be an open-source JavaScript library able to power small-scale hydrodynamical simulations — either in the browser (through web workers), or within a JavaScript environment (e.g. Node.js). It comes with:

– a library to set up initial equilibrium conditions (e.g. Lane-Emden spheres, or N-body spheres with isotropic velocity dispersion);
– a canvas-based library to plot and animate the simulation snapshots;
– a fast library for operating on vectors and matrices that minimizes allocations and copying, and other math routines.

Performance notes

While playing with the app, you may be wondering (a) why there is a “buffering” stage before you can see the evolution of the system, and (b) why so few particles?

Buffering: it’s all about delayed gratification

The app animates the particle motion at 30 frames per second. This requirement places a hard and fast constraint: if you want to compute the particle motion at each frame request, then the computation must take less than 1/30th of a second, otherwise the webpage will freeze as the JavaScript engine tries to catch up with the accumulated frame requests. For reasonable number of particles (say, 100 or more — see below) and the time steps required by the above app, this requirement is way overshot.

This issue can be ameliorated by running the numerical computation in a separate thread (a web worker), and drawing frames on the main thread as soon as they are computed. This is still not as optimal: while it solves the UI freezing issue, the particle motion will appear very jerky as it will be animated at (typically) less than a frame per second!

In order to solve this issue, I created a small JavaScript library (streamingcontroller.js; available in the same GitHub repo, documentation upcoming). Streamingcontroller.js first estimates the expected wall time — the time in seconds — needed to complete the simulation. Then, within the web worker thread, it “buffers” the simulation snapshots by adding them to a pool of snapshots. Once the buffer is big enough that the simulation can be run in real time without hiccups, the library starts streaming the snapshots back to the main thread where the animation is drawn. In the main thread, a second buffer receives the snapshots; the second buffer is then emptied at 30 frames per second.

More particles, pretty please?

The default setting of the app is to animate 250 particles (125 per sphere). Why so few, when typical number of particles quoted for N-body simulations routinely exceed millions — or even billions! — of particles?

There are three bottlenecks at work. The first is obvious: the code isn’t fully optimized and profiled yet, and I am certain there is room for improvement. I am writing a small math library of common mathematical routines called math.js (also in the same GitHub repo) which will be fully optimized for V8.

The second is also obvious: simulations with lots of particles are usually run at full-speed, on multiple cores, and in the background. These simulations can save their snapshots, to be plotted and animated at the end of the run. An online app (or game) with real-time requirements (or, say, a <1 minute buffering time) doesn’t have this kind of luxury!

The third is the worst hurdle, and it is inherent to the nature of JavaScript: JavaScript is slow. I am not a JavaScript guru by any means, but I do have a good amount of experience writing performant numerical code in a variety of languages (mostly C). While JavaScript is typically fast enough for most tasks on the web, it is slow on personal computers and even slower on mobile platforms for physically-motivated, accurate simulations. In its present form, it is not well-suited to run these kinds of numerical tasks as quickly as the underlying hardware allows. Although JavaScript interpreters have been improving by leaps and bounds, and careful code can exploit some of these optimizations, they are hitting a wall of diminishing returns. Since JavaScript is the only runtime available on browsers, it is the ultimate bottleneck.

You can check out the other demos using code from WGC in this webpage.

An interactive Barnes-Hut tree

[TL,DR: if you’d like to play with a simple Barnes-Hut octree code, scroll down to the little embedded app.]

Gah! It’s been quite a while since my last post. Despite my best intentions, work (and a lot of feedback from Super Planet Crash!) has taken precedence over blogging. I do have a sizable list of interesting topics that I’ve been meaning to write about, however, so over the next few weeks I’ll try to keep to a more steady posting clip.

Super Planet Crash has been a resounding success. I have been absolutely, positively astounded with the great feedback I received. My colleagues and I have been coming up with lots of ideas for improving the educational value of SPC, add new, interesting physics, and addressing some of the complaints. In order to have the ability to dedicate more time to it, over the past few months, we’ve been furiously applying for educational and scientific grants to fund development. Hopefully something will work out — my goal is to make it into a complete suite of edu-tainment applications.

When Giants Collide

I’ve recently started experimenting with a new  visualization that I think will turn out pretty darn cool. Its draft name is When Giants Collide. When  Giants Collide will address a common request from planetary crashers: “Can I see what happens when two giant planets collide”?

A sketch of the interface.

When Giants Collide will be a super-simple JavaScript app (so it will run in your browser) that will simulate the collision of two massive spheres of gas. The simulation will have to model both gravity and the dynamics of the gas: to address this, I’ve been dusting off and reviewing an old Smoothed-Particle Hydrodynamics (SPH) code I worked on for a brief period in graduate school. SPH is a very simple technique for cheaply simulating gas flows with good spatial accuracy, and is somewhat straightforward to code. There are some shortcuts that have to be taken, too — large time steps, low particle counts, and more (e.g., a polytropic equation of state for the gas giants; more on this in future posts). These shortcuts come at the expense of realism, but will enable fast, smooth animation in the browser.

Gravity with the  Barnes-Hut algorithm

Gravity is an essential ingredient of When Giants Collide! Even with very low particle counts (say, N = 1000), a brute force calculation that just sums up the mutual gravitational force between particles won’t do if you want to run the simulation at 60 frames per second. Direct summing is an N^2 operation:

(this is a simple force accumulator written in R).

A better way that involves only a slightly more complicated algorithm is to use the Barnes-Hut algorithm (a short Nature paper with more than 1,000 citations!). The algorithm involves recursively subdividing space into cubes and loading them with particles, such that every cube contains either 0 or 1 particles. This is represented in code with an oct-tree structure.  Once such a tree is constructed, one can calculate the gravitational force on a given particle in the brute-force way for close particles, and in an approximate way for distant particles; whether to use one or the other is determined by walking the tree down from the top. An excellent explanation (with great visuals!) is provided in this article.

The other advantage is that, once the tree has been already built for the gravity calculation, it can be used to identify the nearest neighbors of a given particle through the same tree-walking procedure. The nearest neighbors are needed for the hydrodynamical part of the SPH algorithm (see, e.g., this review article by Stefan Rosswog or this one by Daniel Price).

An interactive tree

Below is an interactive JavaScript applet that subdivides space with the Barnes-Hut algorithm. You can add new points by clicking on the surface, or using the buttons to add new, random ones.

The code for building the Barnes-Hut tree from an array of 3D positions is available at the GitHub repository for When Giants Collide. I will be developing the code in the open, and post periodically about my progress. Hopefully by the end of summer I will have an attractive app running on any modern device and web browser. Any ideas on how to gamify it?

Go Crash Some Planets!

Super Planet Crash
A screenshot of Super Planet Crash playing in Safari


If you enjoyed playing Super Planet Crash, please consider donating to the Science Education Fund at McDonald Observatory. Every little bit counts. Go support science!

Update 2: 2,000,000 systems were created!
: Systemic and Super Planet Crash were featured on io9Space.comGlobalNews, Motherboard, Huffington Post, The Verge, and two press releases by UC Santa Cruz and McDonald Observatory. Thank you!

Super Planet Crash is a little game born out of some of my work on the online version of Systemic. It is a digital orrery, integrating the motion of massive bodies forward in time according to Newtonian gravity. It works on any recent web browser and modern tablets.

The main goal of the game is to make a planetary system of your own creation be stable (i.e. no planet is ejected, or collides with another body). This is of course exceedingly easy when your system comprises of a few Earth-mass planets, but dynamical instability can quickly set in when adding a lot of heavier bodies (from giant planets, all the way to stellar companions).

The challenge is then to fit as many massive bodies as possible inside 2 AUs (twice the distance between the Earth and the Sun), teetering close to instability but lasting at least 500 years. Accordingly, the game rewards a daring player with more points (proportionally to the mass of each body added to the system). A few simple rules are listed under the “Help” button.

The game always starts with an Earth-mass planet in a random location, but you can also have fun overloading known planetary systems! Clicking on the “Template” dropdown brings up a list of planetary systems to use as starting templates, including the compact system Kepler-11 and the super-eccentric planet HD80606 (more systems to come). You can even share your creations with your friends by copying the URL in the “Share” box.

The game is open-source, and still under active development. The entire code will be downloadable from GitHub (as soon as I get a bit of work done!).In the near future, I will be adding integration with Systemic Live, a longer list of template planetary systems and smartphone support. In the meantime, have fun crashing planets!


The game was made possible by the wonderful paper.js library, which let me quickly prototype the app despite having little experience in web gaming. The palette draws from the base16 color set.

Many many thanks to my wonderful testers: Rachael Livermore, Mike Pavel, Joel Green, Nathan Goldbaum, Maria Fernanda Duran, Jeffrey SilvermanAngie Wolfgang, and other cool people.

My work is funded by the W. J. McDonald Postdoctoral Fellowship. If you enjoyed the game, please donate to the McDonald Observatory fund to support science education.

AstroTRENDS: No so weaselly after all


Substitute damn every time you’re inclined to write very; your editor will delete it and the writing will be just as it should be. — Mark Twain

Damn right!

In my last post, I showed a plot of the number of abstract that contained weasel words, as tracked by AstroTRENDS:

chart-2I interpreted this trend as a steady change in the style and “audacity” of astronomy papers, and I believed that a possible cause was hedging. (See Writing without conviction? Hedging in science research articles.) Note that I was not making a statement about the quality of the research, but merely about an interesting trend I had not seen mentioned elsewhere.

Perhaps I should have used more weasel words in my post! I acted upon Ben Weiner’s suggestion: use a set of non-weasel words as a control to verify whether the trend was due to an increase in verbosity instead. I track this set of keywords (a mix of adverbs and adjectives that I deemed to be neutral):

Fast OR Slow OR Large OR Small OR Before OR After OR High OR Low OR Many OR Few OR More OR Less OR Inside OR Outside OR Recently OR Just

This is available as “Non-weasel keywords” in the AstroTRENDS drop downs.

And here’s the plot!

The two appear to be tracking each other pretty well. It seems to me to be a strong indication of the correctness of Ben’s guess that verbosity is the main driver here. However, simple keyword search may still not be telling the whole story (e.g. because certain keywords “saturate” as the abstracts get longer, appearing more than once), so a better approach could be to study a small sample of abstracts through the years.


Weasels (green) vs. non-weasels (yellow)
Weasels (green) vs. non-weasels (yellow)

Turns out that there’s a comprehensive ADS API, described on GitHub here, so with a bit of rejiggering I will be able to let AstroTRENDS do free-form queries (via Michael Kurtz.), and do a bit of abstract munging myself.

AstroTRENDS: Weasel words

Credit: Cliff

I added a bunch of new keywords to AstroTRENDS, mostly suggested by friends and people in the community who had read my Facebook post.

A thought I had yesterday is the following: has the astronomical literature become more speculative, and perhaps less committed to audacious claims, in recent times? It is difficult to test this hypothesis  by merely querying ADS for abstract keywords. It would certainly be better served by a natural-language processing analysis of the full text, although this is just my uninformed speculation.

A much simpler way is to search for the so-called “weasel words” (such a funny way of describing them from a non-native speaker POV!). Matthew Might (a CS professor from the University of Utah) has a really interesting article about the different abuses of language that are common among technical writers, and he created some automated tools for detecting them. It’s a great read. (There’s even an emacs minor mode called writegood based on his recommendations, which I will be testing for sure). Although I don’t necessarily agree with a strict adherence to all of his points, there are certainly some great pieces of advice there.

Taking his post as a reference, I added a new “weasel words” pseudo-keyword to AstroTRENDS. The “weasel words” keyword shows the result of an ADS query of refereed abstracts containing the following boolean expression:

Could OR Possibly OR Might OR Maybe OR Perhaps OR Quite OR Fairly OR Various OR Very OR Several OR Exceedingly OR Vastly OR Interestingly OR Surprisingly OR Remarkably OR Clearly OR Significantly OR Substantially OR Relatively OR Completely OR Extremely

We can easily disagree on whether using these words in an abstract constitutes “weaseling”, or has any sort of nefarious purpose (I certainly pepper my writing with more than my fair share of those). It is still an interesting exercise to verify whether usage of those words has increased over time. The following plot shows the fraction of articles containing those words (i.e. number of articles containing the words normalized by the total article count) each year.



Keeping all the caveats above in mind, there is a definite upward, pretty linear-by-eye trend going on. I’m not sure whether it has to do with simple evolution of language and style, less boastful writing, an accident of fate/bug on my part, or some other factor.

This is of course a super-shallow analysis that would require far more insight than what I offered in this post, but it’s still intriguing. I tried to altavista whether this is well-known, but have come empty handed so far. Any ideas?

You can play with the interactive plot itself by clicking this link.

UPDATE: Ben Weiner made a really good point on the Facebook astronomer group.   He suggests that an additional, alternative explanation could simply be that abstracts have become, on average, more verbose with time, which would explain the higher frequency of fluffy adjectives and adverbs. This could be checked with a control set of non-weasel words… which I will definitely try.

How did this post do with writegood-mode? Pretty nicely… but I got a grade of “11” on Hemingway, with about 9 out 24 sentences being hard to read.  Oh well.
Weasel image credit: Cliff

AstroTRENDS: A new tool to track astronomy topics in the literature

A screenshot of AstroTRENDS, showing three random keywords: Dark Energy, Spitzer, and White Dwarf.
A screenshot of AstroTRENDS, showing three random keywords: Dark Energy, Spitzer, and White Dwarf. White Dwarfs are the “old reliable” of the group.

Inspired by this post by my good friend Augusto Carballido, I created a new web app called AstroTRENDS. It’s like Google Trends, for astronomy!

AstroTRENDS shows how popular specific astronomic topics are in the literature throughout the years. For instance, you could track the popularity of Dark Energy vs. Dark Matter; or the rise of exoplanetary-themed papers since the discovery of the first exoplanets in 1992. As an example, check out this post I wrote about whether the astronomical community has settled on the “extrasolar planet” or “exoplanet” monicker.

You can normalize keywords with respect to one another, or the total article count, to track relative trends in popularity (say, the growth of “Transits” papers compared to “Radial Velocity” papers). Finally, you can click on a specific point to see all the papers containing the keyword from that year (maybe that spike in a keyword is connected to a discovery, a new theory or the launch of a satellite?).

How does it work? I crawled ADS for a small number of keywords that I thought were interesting (but you can ask me for more!), and counted how many refereed articles were published containing that keyword in the abstract for each year between 1970 and 2013. Keywords containing multiple words are contained within quotes, to specify that all words must be in the abstract.

Play and have fun with it, and if you find an interesting trend, you can share it with others by copying and pasting the address from the “Share” box. (Feel free to send it to me, too!)

Open AstroTRENDS