It's show-and-tell time! Below are two movies I made using the volume rendering tools of yt. I've been using yt for a few years to analyze and visualize the cosmological simulations I make with Enzo, and only recently have I had time to begin to play with the new volume rendering stuff.

The first movie is a slow rotation around the entire volume of a simulation at a contemporary epoch, which means that this image is produced from the state of simulation at its end, 13 billion years after it started. The colors correspond to the density of matter in the volume, from dark blue to white as density increases. The simulation is a periodic cube with dimensions 20 Mpc/h on a side. In comparison, the diameter of our galaxy is somewhere around one thousand times smaller. This means that the whitest areas correspond to clusters of galaxies, and our galaxy would be just a small part of one of the white blobs. Be sure to watch the movie full screen!

Below shows the time evolution of the simulation from beginning to end. This is a thin slab of the center of the simulation (10% thickness) viewed from a corner of the cube. Notice that early on the matter is very clumpy everywhere, but rapidly forms dense knots connected by thin filaments. This is how the real universe looks! After about the half-way point of the movie you'll notice that not much happens. Again, this is how the real universe looks! Much of the large-scale evolution of the universe was finished about 7 billion years ago. This movie uses comoving coordinates, that compensate for the expansion of the universe. If I were to use proper coordinates, which are the kind we use every day to measure normal things with rulers, the movie would show the simulation starting very small and then blowing up. Again, use the full screen option for the best image.

Don't worry about the physical meaning of the two plots below:

Taken from Baldry et. al. (2004),figure 3 (plot 7).

My plot of entirely fake data that means almost nothing.

Just notice that the two peaks are pretty much in the same places on both graphs, 1.5 and 2.2. The first graph shows physical data (stars) and a double-Gaussian fit (light solid line). The second graph is the result of my using Monte-Carlo fitting to make entirely fake data using the first curve. The real graph has over 10,000 items to make that smooth distribution, while with only about 100 items Monte-Carlo is already starting to look like the real thing. Of course, it will take much more items to capture the smoothness and the "long-tail" on each end.

I just wanted to share because the whole thing I wrote, which includes a simple function integration (for normalization), worked on my first try.

Lately I have been enjoying flying my Blade CP helicopter. I've purchased a new battery/motor combination that has extended my flight times to about 15 minutes. I've also become proficient enough that I can (usually) run the battery down before I break anything crucial. However, there's still limits to my flying. The battery takes roughly two hours to charge. I try to keep myself from overstepping my skill level. Of course I have to try new things in order to learn, but I've found that if I get too aggressive, I make costly mistakes.

It is time for me to greatly increase my practice time through the magic of personal computers. Behold the Realflight G3.5 RC Flight Simulator. This simulator comes with a USB controller with the same look and feel as a RC transmitter. The program has a large library of fixed wing aircraft and helicopters that can be flown in a variety of locations, indoors and out. It has a good physics engine and "real" obstacles. This means that if you try to fly through the scenery, you'll crash into it. The plane will even break apart in a realistic amount. For a small crash it might lose a tail. For a big crash, it will break apart into many parts.

The best thing about the simulator is the big red button on the USB controller that instantly resets everything after a crash. That's much cheaper than the real world!

As is usually the case, this is a Windows-only program. Luckily for you, you don't have to buy me a PC so I can play this, as Melissa has a Dell. It isn't the fastest thing, but it is capable of running the application.

Below is a little animation that I made yesterday that shows what I have been doing lately. The green dots correspond to the positions of dark matter particles, while the little yellow squares are the locations of dark matter haloes that I'm interested in. The white lines are the edges of the simulation volume, and you can see the axes triad in the bottom-left corner. To give you an idea of the scale of what's depicted here, each edge of the cube is 50 Mpc, or 163 million light years. Our entire galaxy is only about 20 kpc or 65,000 light years across.

In the first part of the movie, the cube is rotated about its center. Next, while looking along the z-axis, the volume of the cube plotted is reduced until only 1/10th of the cube is shown. Then, this 1/10th thickness is scanned through the entire cube, and then the volume plotted is replenished back to full.

The things to notice are how the dark matter form areas of high density, which are connected by filaments. Between these are areas of relatively few particles, which are called voids. This is how our universe really looks, with huge collections of galaxies clustered together, separated by huge expanses of nearly empty space. I should point out that there are many more galaxy haloes in this box besides the yellow boxes.

What I was looking for was one of those yellow boxes which is fairly isolated from areas of high density dark matter. I picked one, and now I am doing this same simulation again, but with higher resolution boxes centered on the area of interest. The simulations I'm doing right now are fairly cheap (in computer time currency). I want to be sure that when I run big, time-intensive simulations in the future that I've picked a good area to focus my attention on.

I did this visualization with Visit, a stereo, 4D visualization tool out of the Livermore National Lab. The "stereo" means that it can create two images of the same data that are slightly offset, which create a 3D effect if viewed correctly. The fourth dimension is for time, as it can handle time-ordered data sets. I then used Visit's Python scripting features to output 800 individual PNGs, which I then stitched together (exactly like my time lapse movies) to make this movie.

Above is a part of what I've been working on lately. It's a small part of the galaxy family tree that I've derived from a large simulation. In the simulation there are several ingredients that are thrown in the "box." Relevant to this are the dark matter particles, which coalesce into consituents of galaxies. The dark matter particles have unique id numbers. Using a some code I didn't write, I process the simulation data and make a list of galaxies along with the particles in each galaxy. Then, using some code I did write, I track particles and galaxies over a number of time steps, which builds a relational mapping. Then, I use Graphviz to make a nice tree, as you see above.

Inside each box are either three or four data values. The top grid shows what percentage of the particles in that group came from no group, the middle grid shows both the number of dark matter particles that are in the group and the position of the group, while the bottom grid shows the percentage of the particles that go to no group. The simulation takes place inside of a 3D box with length 1 on a side and periodic boundaries (which means the distance between 0.9 and 0.1 is 0.2, not 0.8). The colors of the box correspond to its ranking in size, red is the largest, green the smallest. The numbers next to the arrows are what percentage of the parent group goes to the child group.

The goal of this is to get an idea of how the galaxies form over the course of the simulation. Of course the simulation tries to mirror reality, so this family tree may be worth something.

About a month ago I received my iPod settlement gift certificate worth $50. The money was only good at the Apple store. As you can find out for yourself, there's not much for $50 on the Apple store, save for a few iPod accessories. I didn't really want any iPod accessories, and besides, most wouldn't fit my second generation iPod. Of course Apple was hoping that I'd just go ahead and use the $50 as an excuse to by a quad-G5 desktop system for $3,300 (make that $3,250).

Look for the one-way streets, wide boulevards, and train tracks.

Above the iPod accessories, the lowest price items are software titles. I browsed through them and discovered that there was a Mac OS X version of Sim City 4. I've always liked the Sim City series, starting with the orginal Sim City. I like the planning of a citys infrastructure. As the "mayor" of the city, the player has to lay roads, freeways, railways, subways, power lines and water pipes. The mayor has to also balance a budget of expedatures and taxes (more on that later). The goal of the game can be as simple as building the largest city possible, or the most asthetically pleasing, or one with the "happiest" residents, or one with the best finances. My goal has usually been to have a high population combined with a happy population.

Look for the railroad crossing guards, various species of trees and the accurate railroad "Y".

The newest version has many improvements over the previous versions, Sim City 2000 and Sim City 3000. For one, this version supports regions, whereby you can build dozens of cities that are neighbors on one big map. Each city is independent in that you can only edit one at a time, but cities influence neighbors by way of jobs & trade. One of the biggest improvements has been in the graphics. This new game has beautiful graphics with very high level of detail. There are something like six levels of zoom. The closest one is so close you can see individual "sims" (people) on the streets (look for them on the above image of the train station).

See if you can find the county fair & golf course.

One of the keys to a well-functioning city is the transportation system. Sims are very touchy about how long it takes to drive to their job. Sim City 4 introduces a very useful tool that allows you to see what kind of traffic goes where through your transportation system. In the picture linked on the right, you can see all the commute traffic that goes through a train station in the center of town (in the lower-left of the picture). You can trace foot traffic onto a passenger train, which gets off at a different station and walks to a jobsite.

I must admit that one key element of Sim City, collecting taxes and balancing a budget, I've never really liked. I either cheat to get the cash to run the town, or find some other way to make money, like building a magic building found on the internet. I'm no libertarian -- I just don't really care too much about the fiscal part of the game. If I were really going to play the game for real, I would not cheat. But I don't want to play it for real, so I feel no guilt.

One nice thing about this game is there is no death & violence, no princess to save, and I can stop the game at any time without losing my progress.

For the better part of half a year now I've been working slowly on a project with Mike Norman, my advisor. I'm basically implementing a test of the efficiency & accuracy of the cosmological simulation code his group uses. I do this by sticking a ring of gas into the simulator and watching the gas spread out. I compare the computer simulation to how it should go if all things were perfect (which the simulation is not). The two plots below are a culmination of my accelerating efforts.

Above is a 3D plot of the gas density. The two horizontal coordinates are the x-y position, while the vertical gives the density at that point. I'm doing my simulation in two dimensions right now, eventually I'll go to three.

The white line above (hidden by the red line) is a sideways slice of the density, starting at the center going out. The red line is a best curve fit of the white line. The curve fit is very good because the white line was generated by the same function I'm using for the best fit, but the picture shows my fitting technique works, and that's what matters.

I hope to make further, faster progress! I'll post things here as I go along.