Cosmos Computed

The visible world around us is constantly changing. One second we may have the sun in our eyes, and another we're in a dark closet trying to find the light switch. Such fluctuations in brightness could have ended up being a serious problem for our vision if it weren't for a handy built-in feature: our eyes automatically adapt to the lighting conditions of the surrounding environment. Most people are well aware that their pupils change size to handle lighting conditions. A larger pupil admits more light and makes the scene brighter, while a smaller pupil admits less light and makes the scene dimmer. This mechanism is fast and effective, and is controlled by the brain stem, which acts autonomously - you don't even have to think about it. As useful as this type of adaptation may be, it has some limitations. For example, most artificial lighting is 20 times dimmer than the sun, while pupil dilation only brightens light by a factor of 4 (when compared with a fully constricted pu...

A bright star streaks across the sky, leaving behind a glowing trail that soon fades back into the blackness of the night sky, leaving no perceptible trace. A minute later, another streak appears; this one has faint hues of pink and orange. Each streak lasts only a couple seconds, but its quiet beauty is not easily forgotten. Maybe I could write a kid's book about it: Fast star, slow star Red star, blue star The sight I'm describing is called a meteor (as I'm sure you already know). Meteors have been observed for as long as humans have existed, and have been a mystery for almost as long. It didn't take long to figure out  that they occurred high in the atmosphere - in fact, the name "meteor" was originally used for any atmospheric event - but it wasn't until the 19th century that somebody finally realized what they actually were: small bits of space debris burning up as they fell through the sky. The question that naturally comes next: how does a meteor ge...

The retractable pen is an interesting little device. You press a button, and the tip comes out. Press it again, and it does the opposite: the tip disappears back inside. How can the same action lead to different results? In this post, I'm including a CGI animation I created using Blender. I actually modeled this pen in early 2012 (a little over 4 years ago); I recently fixed it up and re-rendered it. A retractable pen has 5 main parts: 1. Frame 2. Thruster 3. Ink cartridge 4. Spring 5. Cam (a special mechanical piece; 1 or more is used) The basic design is for the cam to rotate each time the pen clicker is pressed; the rotation allows for a pin (built into the frame) to slide into a different slot. Different slots have different lengths, and depending on the length of the slot, the ink cartridge will extend by a different amount. There are many ways to work out the details, and the animation I created shows only one possibility. Of course, the design of the pen in the animation wou...

Nothing beats a nice spring day on the slopes. The warm sun beams down, with its barely-filtered UV rays piercing through the thin air and frying all unprotected skin. The snow starts out icy, but before long it becomes soft and smooth, with slushy snow flying out at every turn. The weather can be really crazy - a couple years ago, Vail reopened for an extra weekend after closing when it was hit with a snowstorm that dumped 3 feet of snow. One of the best Spring skiing days I've ever experienced was nearly two months ago at Vail, a week before the closing date. Due to some lucky weather events, I experienced all three main types of snow conditions in a single day: ice, slush, and powder. The day started out like any other: hard snow covered the trails, frozen solid from the cold night before. Turns were difficult to make on this surface, as the skis could not carve on the ice. Clouds covered the sky. It was cold, but not frigid. View of the back bowls and Blue Sky Basin, taken from...

One thing I enjoy when programming is to make weird interactive computer-generated objects. In this post, I'm showing you... a blob. To see the blob, simply click on the black box. The blob will immediately appear. Once you have the blob, you can drag it around with your mouse - just press down and move it around. When you let go, the blob will snap back with a little jiggle. Click here! There are a few things I'd like to point out about the blob: First, when you stretch it, it actually gets narrower. When I designed this, I wanted it to shrink enough to look realistic, but not far enough that it looked weird. Second, notice that it drags faster depending on how far you stretch it. The speed at which it drags is proportional to the square of the distance stretched. I found that this was much more realistic than making it directly proportional to the stretch. Also, if you only stretch it slightly, it doesn't drag at all (this simulates static friction). Finally, the...

I am fascinated by man-made transportation devices. Besides the fact that they can be very advanced technologically, they almost always look really awesome. The ones that fly are the coolest to look at; I love their sleek appearance and clean, smooth colors. It makes them really fun to draw. In this post, I'm including a two different drawings of a Boeing 747. One interesting thing about the Boeing 747 is that there isn't only one type. The 747 comes in several variants, each with different dimensions and characteristics. The 747SP is the shortest of the variants, with a length of 185 feet; the longest is the 747-8, with a length of 250 feet. I decided to draw the 747-400, which is 231 feet long. The first drawing is a sketch I made using a regular graphite pencil. To prepare for my watercolor sketch on special paper, I thought I should make a quick practice sketch first. Once I started sketching I decided to go the whole way and make it good, so my final result actually ended ...

For some reason I felt like this was relevant Happy Pi Day! The digits of the date - 3.14 - contain the first couple digits of π. But that's not all. If you add the year to get 3.14.16, you have the first 5 rounded digits of π. This is better than last year's version (3.14.15), which contained a truncated version of π. Today's date contains the more accurate rounded version. In this post, I'll describe the process of finding an algorithm to approximate the number π. There are three main types of algorithms. The first type converges very quickly to the correct solution; we use algorithms of this type in computers and calculators. The second type converges slowly, but is interesting to think about; we take this type of algorithm to mathematics conferences. The third type is slow to converge, and is boring to think about; these are pretty much useless so we get rid of them. This may be interesting to know, but I wasn't too worried about it when I wrote my Pi Day post l...

Here's a simple physics puzzle: suppose you're launching a model rocket. You want the rocket to go as high as possible. Is it better to design the rocket to: A. Use all of its fuel very quickly, and then use its momentum to travel high B. Use the fuel gradually over the whole duration of the flight In other words, what is the fuel consumption rate that will maximize the height of the flight path? For this problem, we can assume that the thrust is proportional to the fuel consumption rate. I'll try to post a solution to the problem in the future. New posts every month - subscribe for free !

First off, apologies for this long-overdue post. I've had a busy month, and although I would have liked to post this within a few days of the beginning of 2016, I wasn't able to get it done until now. 2015 was a great year, and I think the images in this post will reflect that. In the previous year's image collection ( click here to view ), the images were only photographs. The image editing was restricted to cropping; I didn't need anything more. In this collection, though, I have drawings, CGI, and microphotography. These new types of images required more processing to prepare them for viewing. Of course, I used GIMP. I can't afford to pay for software. Instead of listing tons of images, I picked out the most important ones. I also tried not to add the images from previous blog posts; the majority of what follows is new stuff. I also attempt to analyze the images from both a scientific and artistic standpoint. Most likely, by the time most of you read this, you...

Planet original Last month, I drew a couple astronomy-related pictures using a graphite pencil on a sheet of white paper. The problem with pencil sketching is that it's hard to draw white glowing objects... so I sketched a negative, and then uploaded the images to my computer and inverted them. Then I increased the contrast to improve the black background and enhance the white. The image at the top of this post is a ringed planet, possibly Saturn. I included three moons and some lighting on the backside from the rings. The whole image was smaller than a dime. Black hole original The image below is an imagined view of a black hole. I included high-energy jets of ejected material and an accretion disk. Most black holes are not actively consuming material, and do not have jets. But those are boring to draw. New posts every month - subscribe for free !

Imagine the universe is filled with water. Instead of empty space, every inch of it contains pure water. No planets, no stars, only water. What happens? And what would happen if an air bubble formed? The answer to this question requires a basic understanding of gravity. Gravity is very important. It helps hold matter together, bends light, and distorts space-time (which, incidentally, is how it bends light). It also makes it possible to play football, and as Americans are big football fans, they would certainly agree that we couldn't live without it. Unfortunately, many Americans don't understand how gravity works. Admittedly, scientists haven't figured out a lot of things, but we do understand it well enough to make predictions and model physical events. One of the important things about gravity is that its strength is proportional to the inverse of the square of the distance. In other words, it gets weaker as you get farther away, based on the equation: F = c/d 2 where c ...

Keystone on opening day Keystone Ski Resort just opened for the ski season on Friday. I went up to the resort that same day. There was only one run open (not including the beginner area at the top of the mountain), but it was awesome nevertheless! One of the main downsides to skiing on opening day is the number of people. There must have been about 2500 people on the mountain at the same time as me (not including the people snacking in the lodge). To keep the lines moving, the lift attendants made sure that the lift was completely full, with 4 people per chair. Even so, the wait to get on the lift took a long time. At one point when I was standing in line, a thought came to mind: the line was constantly being filled with more and more people, but it never got longer because the chair lift was carrying the people away at the same rate. So what would happen if the lift attendants only put 3 people on each chair, instead of 4? This would disrupt the balance: the inflow of skiers would be ...

Over my fall break (which lasted 1 day), I wrote a JavaScript program that would render a sphere. I thought it would be a fun way to practice math and programming skills simultaneously. As usual, I used my FireTools.js library to help with graphics as well as some other functions. To render the sphere, I wanted to take every pixel on the screen, and calculate the color of the pixel. The color would vary depending on which part of the sphere the pixel was displaying. If the part of the sphere was facing the light source, it would need to be brighter than a part of the sphere facing away from the light source. To find the brightness of each point on the surface, I first calculated the XYZ coordinates of that part of the sphere. This is also equal to the normal vector at that point. I took the dot product between the light source's direction and the normal vector. This is a mathematical operation that tells me whether the surface is aligned with the light source, as well as the percen...

Near the end of last month, the moon passed entirely through Earth's shadow, resulting in a full lunar eclipse. The moon didn't completely black out, due to sunlight scattering through Earth's atmosphere. Instead, the moon had a dim reddish-brown glow. Of course, I took I lot of photos of this celestial phenomenon. I started taking photos during totality. I kept taking photos a couple times per minute, for a period of about 1.25 hours, until the moon was fully lit. My goal was to put the photos together, for an animation of the moon passing through the shadow of the Earth. "Fake" crescent One thing I thought was pretty neat was when the partial lighting of the moon formed a perfect crescent. The crescent looked a lot like the waning crescent phase of the moon, but there was something strange about it. It reminded me of the artificial images of the moon that you'll see when you use a star-mapping program. The reason is this: for a real crescent moon, the lighti...