Wednesday, August 10, 2016


Painting of space shuttle Columbia during reentry

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 get so hot?

Saturday, July 2, 2016

Retractable Pen

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 would not function well; the pin would snap off right away. I designed it this way to make it easier to see the mechanism; a stronger pin would obstruct the view.

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Wednesday, June 1, 2016

Spring Skiing

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.

Vail EpicMixOne 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.

Tuesday, May 24, 2016

Jelly Ball

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, there's gravity. The gravity isn't strong enough to drag the blob, but it is strong enough to stretch it slightly. When you first create the blob, it bounces slightly as a result of the gravity.

The graphics was probably one of the most interesting parts of writing this program. First I included my Firetools.js library for some simple graphics functions. Then I simply stacked a series of filled translucent circles. I placed the circles on a straight path from the base to the tip of the blob, and determined the size and color using some simple math.

One of the biggest challenges I faced in designing this blob was setting it up to move around the page. It took a long time to figure out how to disable the highlighting of text and the clicking of links below the blob. (For geeks who are interested in my solution, it involved disabling pointer events on the canvas, and using an event listener in the window to turn them back on whenever the mouse was over the blob.)

Overall, I'm really happy with my final result. I hope you enjoy it!

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Friday, May 20, 2016

Boeing 747 Drawings

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 up being somewhat realistic.

Next I used watercolor pencils. This is the first detailed drawing I made using watercolor pencils. It was a neat experience. Watercolor pencils are basically like regular colored pencils, but the pencil lead is water-soluble so the drawings can be smoothed out with water and a paintbrush. The pencil tip can also be moistened, making it like a tiny paintbrush capable of rendering fine details.

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Monday, May 2, 2016

Black Holes

On February 11, scientists at the Laser Interferometer Gravitational-Wave Observatory announced that they had detected gravitational waves from one of the most powerful events in the universe: the collision of two black holes. In light of this event, I thought I'd post a basic overview of black holes.

Black holes exist in that fuzzy realm on the border between theory and fact. A surprising amount of information regarding these mysterious objects has been determined through mathematical proof, and yet there are still dozens of questions to answer and apparent contradictions to explain. We don't completely understand how they work, but we know they exist.

Because of its strange nature, the idea of the black hole plays a large role in the average person's concept of the universe. Everybody knows about black holes. The problem is, most people don't understand what a black hole is. Some people imagine black whirlpools sucking everything in. Other people imagine powerful vacuum cleaners, from which nothing can escape. The truth is a little different.

Monday, March 14, 2016

How to Find an Algorithm

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.

Monday, February 29, 2016

Efficient Acceleration

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.

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Friday, January 22, 2016

2015 in Photos

Cumulus over a sunset

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.