I think I’ve decided

I’m going back to including a short summary and linking to the page with the demo. Unfortunately, there are just fewer issues that way. So I’ve got another view of the inverse square potential, this time, many test bodies starting at the same point with multiple velocities. Some of the interesting features of this setup are that it covers elliptic to hyperbolic orbits. Those that are bound to the main body and trajectories that escape it.

Unlike the things we deal with on a day to day basis, there is no friction in these equations. That makes things very simple. Either a test mass is bound to the body or not. There aren’t any complex orbits that lead to the body being captured, or slowly spiraling into a collision. Either it is in an elliptic orbit and bound to orbit forever, or it will travel out to infinity in a hyperbolic or parabolic orbit and never return again.

So please click through and check it out. More gravity.

I’m thinking about how best to handle this

I like the idea of putting demos up directly on the blog like the last one. However, they don’t show up on feed readers so you either get the text without the image and then click through. I can throw down some javascript to include a place holder link to the demo in the feed, or do excerpts, which I really don’t like, or go back to the old format of talking about something and linking to it at the end, which I don’t really like either.

Does anyone have any ideas or suggestions on how they handle this issue?

The best surprises come from unexpected places

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This time I'm back with some more physics visualizations with a flat 2d canvas. I'm skipping over some demos of basic physics to get at some orbital mechanics animations that I found surprising. I've derived and calculated solutions for two objects gravitationally bound to each other from my freshman physics classes back in college. Then I did it again with more sophisticated mathematics, and again when I did quantum mechanics of the atom. As I think about it, I was writing BASIC programs back in high school to simulate the 3 body problem. All of those equations and simulations had some pretty severe limits. For one they only involved one or two bodies in motion. What you are looking at here are roughly 185 test particles orbiting one massive object like planets in circular orbits around the sun. While each of these test particles start close to each other, their mutual interactions are ignored. If they weren't there would be much more complicated dynamics going on. What caught me off guard was how fast the inner bodies were moving in relation to the outer planets. Whenever I had pictured the slow ponderous motion of the planets, I had pictured them moving more or less like a uniform disk. Whoa, was I wrong. The inner bodies are just whipping around at a frenetic pace, while the outer ones just plod along at a snail's pace. In fact there is a rather conspicuous divergence in the speed of motion as the distance between the particles decreases. I plan to have something more to say about that in the future. You might be wondering why I picked 185 test bodies? In this case it comes from looking at orbits in the range of 5 to 375. Which corresponds to Mercury (.4AU) to Neptune (30AU) a ratio of 1 to 75. If our solar system was build from evenly spaced bodies in circular orbits, this is what it would look like. So when I set this up, I never expected the slow graceful curve of the spiral slowly winding around the center. As I play with it, it seems so obvious, but that's why I find this stuff so fascinating. I've calculated and simulated these same orbits for well over 20 years now, and they can still surprise and awe me with just the slightest change of perspective.

Just a quick update

I’ve uploaded my very very super rough fractal canvas image editor. This is what I’ve been putting the galleries together with. It’s super rough, I’ll be improving it in random fits and spurts, and putting some demo posts up as well. Also, someone please please suggest a decent title for this one. I’ve got nothing.

Fractal Draw?

three.js particle system

Well, I’ve caught a bug, and it’s a bad one. I’m hooked on WebGL demos. If you follow me on twitter, I’ve been tweeting a few of my favorites. I’ve also been downloading them and playing around with the base api, through the lessons on Learning WebGL and with a number of different frameworks.

The latest particle system demos from three.js caught my eye, and I hacked together my latest demo with the three.js code. Given the raw horsepower of my brand spanking shiny new video card, and the complexity of many of the demos, I was expecting more from my hacking around. The page is generating around 30-40 thousand points a second, where the fractal editor page will crank out around a million or so.

I’m sure it has to do with pumping the geometry over to the video card, and rendering points. That’s the downside of trying to do anything performance dependent, or pretty looking, or both. Polish take time, and a lot of it. I’ve got to run some tests and profiles to see what the issue is.

In the mean time, I played around with the point sizes, number of points and functions. The images show more of the shape of the actual attractor. In the previous demo, I was trying to get something more particle-ish, rather than show off the details of the fractal.

A lot of work, but a lot of fun too. Latest creation: 3d particle webGL

PS. This page requires WebGL, which means that you need Chrome 9.0 or higher or Firefox 4.0.

This is one of the coolest things I’ve seen in quite a while

Sometime back in college I got the idea that it would be really interesting to listen to the waveforms generated from some of the dynamical systems I was studying at the time, namely the Lorenz equation, predator prey equations and the like. I never got off my butt to do anything about it and it’s been a pipe dream of mine to do something like that from then on. I was also going to build the uber-function plotting-equation editing-fractal and dynamical system viewing-better than mathematical-all rolled into one software that also did sound, but I’m sure you can imagine where I got with that.

Like all great ideas, this one has sprung up in more than one place, and now you can listen to the sounds of chaos from your own browser. Check it out.

I’m just playing around with particles for this one

This has come together more quickly than any of the other demos. I wanted to see what I could do with a more abstract particle system driven through the same equations I’ve been using for fractals. The old formulas didn’t have quite enough pizazz, so I moved over to the sylvester library for matrices and bumped it up to 3d, which gave me the twisting, darting and zooming I was looking for.

Bubbles 3d