Akano

For pendulum motion? It's the correct equation of motion. The right hand side, for small angles, corresponds to a restoring force directly proportional to the displacement from equilibrium, which leads to oscillatory motion. In what sense of complexity? The Kolmogorov complexity of a fractal is pretty low due to its recursive nature. ~B~ Consider the Mandelbrot set. No matter how far you zoom into the boundary to examine its curve, you'll never get to a point where the curve simplifies to a straight line. It is in this sense that I mean complexity. I take it that you mean complexity as the amount of information needed to describe the fractal, in which case, yes, the complexity is small, so I think it's just a difference in our definitions. Welcome to my childhood. I grew up with this dork. Learning is fun! 8D

I'm taking a second pass at this one. Instead, I'm going to talk about chaos. Chaos is complexity that arises from simplicity. Put in a clearer way, it's when a deterministic process leads to complex results that seem unpredictable. The difference between chaos and randomness is that chaos is determined by a set of rules/equations, while randomness is not deterministic. Everyday applications of chaos include weather, the stock market, and cryptography. Chaos is why everyone (including identical twins who having the same DNA) have different fingerprints. And it's beautiful. How does simplicity lead to complexity? Let's take, for instance, the physical situation of a pendulum. The equation that describes the motion of a pendulum is where θ is the angle the pendulum makes with the imaginary line perpendicular to the ground, l is the length of the pendulum, and g is the acceleration due to gravity. This leads to an oscillatory motion; for small angles, the solution of this equation can be approximated as where A is the amplitude of the swing (in radians). Very predictable. But what happens when we make a double pendulum, where we attach a pendulum to the bottom of the first pendulum? Can you predict whether the bottom pendulum will flip over the top? (Credit: Wikimedia Commons) It's very hard to predict when the outer pendulum flips over the inner pendulum mass, however the process is entirely determined by a set of equations governed by the laws of physics. And, depending on the initial angles of the two pendula, the motion will look completely different. This is how complexity derives from simplicity. Another example of beautiful chaos is fractals. Fractals are structures that exhibit self-similarity, are determined by a simple set of rules, and have infinite complexity. An example of a fractal is the Sierpinski triangle. Triforce-ception! (Image: Wikipedia) The rule is simple: start with a triangle, then divide that triangle into four equal triangles. Remove the middle one. Repeat with the new solid triangles you produced. The true fractal is the limit when the number of iterations reaches infinity. Self-similarity happens as you zoom into any corner of the triangle; each corner is a smaller version of the whole (since the iterations continue infinitely). Fractals crop up everywhere, from the shapes of coastlines to plants to frost crystal formation. Basically, they're everywhere, and they're often very cool and beautiful. Chaos is also used in practical applications, such as encryption. Since chaos is hard to predict unless you know the exact initial conditions of the chaotic process, a chaotic encryption scheme can be told to everyone. One example of a chaotic map to disguise data is the cat map. Each iteration is a simple matrix transformation of the pixels of an image. It's completely deterministic, but it jumbles the image to make it look like garbage. In practice, this map is periodic, so as long as you apply the map repeatedly, you will eventually get the original image back. Another application of chaos is psuedorandom number generators (PRNGs), where a hard-to-predict initial value is manipulated chaotically to generate a "random" number. If you can manipulate the initial input values, you can predict the outcome of the PRNG. In the case of the Pokémon games, the PRNGs have been examined so thoroughly that, using a couple programs, you can capture or breed shininess/perfect stats. Dat shiny Rayquaza in a Luxury ball, tho. So that's the beauty of chaos. Next time you look at a bare tree toward the end of autumn or lightning in a thunderstorm, just remember that the seemingly unpredictable branches and forks are created by simple rules of nature, and bask in its complex beauty.

And how!

'Sup, BZPeoples? I've been away a while attending friends' weddings, visiting various peeps, rereading Harry Potter (still as magical as always), and working on research. If all goes well, this Friday will see me submitting a paper to the Journal of Chemical Physics. All in all, it's been a good few months. But now is the season of autumnal haunts, and I have grown very happy with the drop in temperature and the swap of palette. Over my fall break, I visited KK in the land of cheese, Wisconsin, and he introduced me to the joys of Punch Out!! for Wii and Super Mario Maker. I now own both, and have been having loads of fun playing others' levels and designing levels of my own (mostly goofing off). When I've finalized a level I'll post it for you all to play if you like. In particular I've been working on a Ghost House.    It's been super fun. Also, RubberRoss' levels are utterly evil. EDIT: Untimely Haunt v2: CD1D-0000-00C8-8D19 Happy Halloween!

I'm about 200 pages into book 5 (for at least the fourth time ). Glad you're enjoying it!

I don't see a complaint about a lack of a Minish Cap GBA present, either. But...but I...okay... [/alsojoke]

feat. Neil deGrasse Tyson.

I don't know what you're talking about. (P.S. Stable 3D is the best thing ever. Totally worth the upgrade.)

Cheese is serious business. Also, I love Brie cheese, but I've never had Camembert. I feel like if I do, my taste buds will reach a new level of Nirvana.

Haldo, everypeoples! I just wanted to check in (as I haven't posted in well over a month). The semester is wrapping up pretty well. I've started writing a paper to published this summer (!) and have been deep in spectrum assignment land. I also have some friends getting married at the end of the month and will be playing trumpet for their wedding with two of my friends. After that happens, I'm going to a conference to give a talk on my research (a first!). So, yeah, a lot of exciting stuff coming up. Basically, pretty busy up until mid-June.

I never knew that this was a debated topic amongst fans. This blog entry has opened my eyes. Pretty much this for me. I have yet to actually watch the series in Machete Order, but it sounds like an utterly brilliant movie/story experience.

I knew it. You were debating putting a disco ball in the comvee again. Everyone is for it; I don't know why you're hesitating or bringing Eastern philosophy into the mix.

Quantum mechanics and wave physics for me. Waves explain a lot of phenomena: sound, light, quantum particles, earthquakes, sonic booms, ... Also, quantum mechanics is incredibly counter-intuitive and yet is how everything fundamentally works, which is super neat, and on large scales it cancels out to produce what we call classical physics. It's really awesome.

The more I see of this, the more I want it. Any news on a US-localized version yet?

Source: Gravity Falls Topic Discuss! 8D

Guys, don't pick on him; you'll make him feel hawkward.

I'd like to describe to you all the most memorable scene from my morning walk into school. I emerged from the tunnel under the train tracks and headed towards the last intersection on my walk on my way to school. In the bare bushes of one of the office buildings on the street twittered a bunch of small sparrows, not a care in the world. I watched them as they chattered, when all of a sudden a brown blur appeared in my periphery. A hawk (I believe a broad-winged hawk) was in a dive, ready to snatch up a meal from the group of sparrows. It swooped, then crashed into the bare branches of the bushes. I could tell immediately after it crashed that it was unsuccessful in its quest, and as it looked around during its shocked stupor, I could see in its face the expression of "Well, this is just great." The poor thing sat there for a moment and eventually freed itself, its ego more bruised than its body, as it flew atop the building and reconsidered what its next move was. All in all, it was really cool, and I'm glad I got to witness it.

One day I will witness a solar eclipse, but it was not this day. Glad you were able to enjoy it, though. +100 Internets to you, sir!

What is your favorite physics topic/phenomenon? Who or what inspires your art the most?

Has this actually been established? We know something bad happened that caused McGucket to found the Society, but we don't know exactly what that event is, so On another wonderful note, "Not What He Seems" was a fantastic episode. That last scene, though. So many rewatches. ♥ EDIT: So, the Bill Cipher AMA happened on reddit yesterday, and there were lots of funny and interesting revelations. Things I found noteworthy:

That'd be fascinating. I also heard a bit of a Wild Mass Guessing theory that suggests that I think this would be a funny possibility, but unfortunately there isn't too much evidence to back it up. It would be amusing to say the least. I was really impressed at all the dark imagery of the last episode. It felt truly haunted and scary in a way that I'm not familiar with in cartoons. A lot of "scary" stuff tends to be jump scares and weird lighting/dark shadows, but this was genuinely creepy. It reminded me a bit of the screaming head that Bill summons for Dipper in "Sock Opera."

Source: Gravity Falls Topic I made a Gravity Falls discussion topic in Completely Off Topic. Feel free to fuel the discussion over there if you're a fan of the awesome Disney show.

But...the others... Also, super ahead of the game on this one. Five stars. Thanks for the birthday wishes, everyone! We had a fantastic weekend.

I noticed that the old topic for this awesome show was past the revival limit, so I thought I'd try to reboot discussion. The most recent episode was Not What He Seems, and the next episode will air in June, 2015. So, let the discussion begin!

As brothers tend to do, KK and I spent our Saturday evening watching a cartoon about brothers navigating an unfamiliar world simply trying to get home. Over the Garden Wall is a brilliant miniseries, and if you haven't seen it, you should. The story is captivating, mysterious, and makes you ask all sorts of questions to the very end. The animation is beautiful (similar but different to Gravity Falls), the characters are incredibly fun and interesting, and the plot doesn't necessarily progress the way you think it will, but at the same time has many familiar story elements. Also, the celebrity voice acting is done really well, which isn't always the case when you have big names in your cartoon credits. Go watch it. It's a great ride. Also, slightly related, new Gravity Falls tonight! 8D