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1. Interactive Exploration of a Dynamical System

9 months ago

A user interface for exploring systems of differential equations. Every variable is shown as a plot; every parameter has a knob that can be adjusted in realtime. This ubiquitous visualization and in-context-manipulation helps the user develop a sense for how the parameters of the system influence its behavior.

Part of the Kill Math project: worrydream.com/KillMath

By Bret Victor: worrydream.com

Credits

627 Likes

tim rechin
8 hours ago
arthur smit
1 day ago
flavio coelho
1 day ago
Szymon Nowak
1 day ago
Todd Akita
2 days ago
Robert Kosara
2 days ago
todd budnikas
2 days ago
Michael Schröder
2 days ago
Nikolay Matrosov
3 days ago
charlie Lim
3 days ago

Tags

Achraf Kassioui 9 months ago

Very interesting.
I keep reading ("reading"?) your website.
Noel Cornell 9 months ago

Brilliant.
Zhe Jenny Zhang 9 months ago

Such a good interface. Way to go with "Kill Math Project"!
Cy 9 months ago

Great!
Jeffrey Goldberg 9 months ago

All my life, I've hated other people's visualizations of things things like this because I preferred what was in my head. Finally there is something that manipulates and represents the data and more importantly the relations, in ways that really make sense to me.
InsightVR 9 months ago

Excellent. I love how the iPad has caused a lot of creative thinking about direct manipulation of data. Our children are going to have amazing tools to use for learning and work.
satz casio 9 months ago

Lovely interface; great programming. This would be perfect to teach a sophomore Ecology class.

The Lotka-Voltera equation is one of the worst and best parts of ecology; it's one of the first models learned - and then when grad school hits, it's all about describing how and why the actual data points differ from the theory.

Like hearing stories from my professor about sitting in the desert for 15 years measuring rabbit populations and finding the explanation in a missed constant.

The math behind more complex Lotka-Volterra equations (more species interacting - the tiger is really eating more than just antelope) is similar to Riemann manifolds or quantum matrices.
Bret Victor 9 months ago

Right, I used Lotka-Voltera because it's one of the simplest "interesting" non-linear systems. When designing a tool, I find it's easiest to start with an example that is very simple yet interesting enough on its own, to figure out how the user will be interacting with the details. And then gradually figure out how to scale up to more realistic examples.
Pnutus 9 months ago

This is fantastic!

Do you plan on releasing this in one form or another (iPad app?)?
Bard Ermentrout 9 months ago

Interesting. Does it exist on the iPad yet? Search dynamical systems in the iTunes store for related apps
s4l4x 9 months ago

Fantastic Bret!! Would be awesome to have a simulation running as well. Sweep/wedge that and you might end up w/ a more digestible differentiation between predator and prey at a given time.
Stanly 9 months ago

Imagine what that can do in education! Making not only the goal, but the process itself interesting ... great job!
Free Fall 9 months ago

Surprisingly interesting
interstar 9 months ago

Brilliant! Love it.

But I do wonder how you will handle systems with more than 2 dimensions.
Bret Victor 9 months ago

I can neither confirm nor deny the n-dimensional iPad.
arig 9 months ago

sick! congrats
I am a Fractal 9 months ago

this is very cool... now take that tutorial in blocks returning blocks and pointers to blocks returning blocks taking blocks and graphic-ize it to make it make some kind of sense.

btw is there anywhere to dl this to my ipad and play with it?
ihor charischak 9 months ago

move over Salman Kahn, this is wonderful!
Roy Nieterau 9 months ago

Did he just say two-dimensional somewhere around 2:03 to explain the connection that there is back and forth. I guess he means bidirectional? :)
Bret Victor 9 months ago

No, I meant two-dimensional. The phase plane is two-dimensional -- it represents two variables. Adjusting the initial conditions via the knob in phase space is two-dimensional manipulation -- I can drag the knob up and down to change one variable, and drag it left and right to change the other.
Roy Nieterau 9 months ago

Aah! You're totally right! I thought you were talking about that you could either use the knob or the sliders to adjust the value making it a bidirectional constraint.

By the way, this is amazing stuff. The Kill Math project seems wonderful too! I'm a 3D Computer Animation and Visual Effects student from the Netherlands and am doing my Master Thesis on how to improve the current workflow of animating in 3D software, and your 'look' on things is really interesting! Keep it up. Show me more! :)
Daen de Leon 9 months ago

It's very good, as a first order approximation, but one of the really interesting things that emerge from predator/prey interactions is the chaotic behaviour, which can be seen in, for example, overdriven regions of the logistic map.
Pierre Nel 8 months ago

Mind. Blown.
Markus Vad Flaaten 6 months ago

Delicious UI! Go Pranav!
Daniel Ely Rankin 5 months ago

brilliant. I have a degree in physics and a few hours in software engineering, and you've definitely got something here.
david maas 4 months ago

Fantastic to see this type of exploration happening with something as dynamic as predator/prey relations... my mind's eye immediately jumps to what interface structures will be necessary to bring a third element into the equation, ie. available plant matter. Trophic cascades warrant something as beautiful as you've started!
Mac Rutan 4 months ago

Great job!. Thanks for such a fine example here. Simple and yet scalable. Good luck and keep going!
Jarrett Byrnes 4 months ago

Where can you download this app? It's fantastic!
Autobotika.Niko 4 months ago

Kill math!!!!!!
Johan Bové 3 months ago

Simply eye-opening and inspirational! Thanks for taking the time to share these precious ideas and results with us in such a pleasant way.
Jonathan Byrne 2 weeks ago

Do you plan on releasing this app at some point?