### November 2009

In my never ending quest to understand a little more of the Japanese language (and never succeeding because I never invest enough time in it), one thing that consistently frustrates me is old and ancient script. In the title wrote Chinese/Japanese because 1.) The Japanese kanji come from Chinese as everyone knows, and 2.) For many centuries after writing was first introduced to Japan from China, all writing in Japan was done in Chinese. In Japanese this is called kobun (古文, lit. old writing), and as Westerners we may think of it as analogous to medieval and renaissance Europe where all scholarly work was done in Latin, regardless of whatever language you might actually be speaking (i.e. Newton’s Principia Mathematica was written in Latin).

I have no hope of reading this ancient Japanese/Chinese, but that’s actually not what I’m referring to. I’m instead talking about the old way to write the characters. Just like how vocabulary and grammar for a language evolve and change over time, so did the way of writing the characters. In this picture from Wikipedia you can see the evolution of the character for tiger.

So even if I’m not trying to read ancient Japanese or Chinese texts, the old style of writing still shows up fairly frequently (similar to how old Gothic and Latin scripts and such still get used in English), but they can be nearly impossible to read, even if you can read the modern form of the character! One place they show up fairly often is in seals. In Japanese legal documents, instead of signing with a signature, you place a red stamp with your official seal (think of royalty using their signet ring to seal letters and documents). In order to prevent forgery, ideally your seal is hand made by a licensed seal craftsman so that it is unique, and then the seal itself is registered in your name at the government offices. The characters often used on these seals are called seal script, and it is the style that evolved during the Qin dynasty of ancient China. Some examples of seals using the seal script I got on google search are here, here, here, and some here.

For example, here are two seal script characters:

If I hadn’t looked up these specific two characters, I would have no chance in reading them even though their modern forms are characters I am very familiar with. In fact, the modern form of these two characters is:

Which is in fact the name of my blog, moroha.

So the question is, where did I look these up? Japanese dictionaries invariably never have them, but I did find a Chinese/English language site that has them. Just put the kanji you want to look up in the blank and click the button that says Etymology, and it will give you the modern character in both traditional and simplified Chinese, in addition to all known variants of seal script, bronze script, and oracle bone script (the really old stuff). As long as you’re using unicode the characters are interchangeable, so you can still do the input in Japanese.

For some real craziness, check out all the old variations for the character of horse, one of the oldest. All this craziness about having many different ways to write the same character was one thing that the 1st emperor of China, Qin Shi Huangdi, tried to do away with when he standardized the writing system for all of China.

Any geek that grew up in the 80’s or 90’s probably remembers the X-men cartoon that was on during the 90’s. The animation wasn’t all that great, but it was still entertaining for this teenager at the time. The intro here may bring back a few memories:

I just saw something that blew my mind though. In a rare exception to the norm, the X-men cartoon was ported and re-dubbed for a Japanese release. Here is the Japanese intro:

First of all, that heavy guitar J-pop totally reminds me of the theme to Fist of the North Star, which I have blogged about before, even starting with “Shock!” which is all too similar to Fist of the North Star’s “You are shock!”. There are also some weird inconsistencies like Magneto summoning the Brood, Cable in power armor, etc., but I’m not familiar enough with the Marvel universe to comment on them.

I can however, comment on the lyrics for the theme song. According to Wikipedia, the song is ライジング (Rising), by the Japanese band アンビエンス (Ambiance). Here are the lyrics and my attempted translation in parenthesis:

Shock!　嘘で固めたナイフ切り付け (Shock! Cut with the knife hardened by lies)
Shock!　夢を飲み込み街は輝く (Shock! Catch the dream as the city shines)

Break Out!
ライムライト　光るざわめき (Commotion in the limelight)
リアルタイム　濡れた幻 (Real-time wet illusion)
Cry for the moon

The translation is quite hard (for me, at least) because as often happens in song lyrics and poetry in general is that many particles (similar to prepositions, they identify the part of speech the word or phrase is) are completely omitted, so I have to guess what the relationship is between the different words. Those last two lines are the hardest, as they don’t make any sense to me, especially the 濡れた幻 (wet illusion). What in the world is that supposed to mean?

Although, that “Cry for the moon” at the end is pretty awesome.

Sometimes you see something on the interblags that is so awesome you have to share it, even though everyone has probably already seen it before you. This is one of those things. Yesterday I discovered the music videos of L. B. Rayne. He’s like some kind of parody/homage to 80’s adventure movies and electronic music. So far he only has two videos that I can find though. The first is Indiana Jones: The Lost Theme Song:

I first heard about L. B. Rayne over at TR though, where they showed his newest video, Skywalking.

A couple of years ago I wrote a post where I talked about taking the imaginary number i to it’s own power an infinite amount of times, essentially

$\LARGE{i^{i^{i^{i^{.^{.^.}}}}}}$.

I showed numerically at least that it converges upon a single value in the complex plane, but then I speculated about what would happen if I did the same for other numbers? I thought it would most likely be a fractal like the Mandelbrot set or the Julia set, but I never got around to actually solving it.

Well, for the class that I’m TA’ing this semester (intro to computing for Chemical Engineers), I got hold of some simple code for making the Mandelbrot set in MATLAB to show the students a fun and interesting example of using for loops. After I did that though, I figured that it would be fairly simple to modify the code to see if taking a complex number to it’s own power created a fractal or not. So my algorithm was the following:

For any point c in the complex plane, let
$\displaystyle{z_0=c}$
$\displaystyle{z_{n+1}={z_n}^c}$.
In the limit as n goes to infinity, if z remains finite, then c is within the set. Otherwise it is not in the set.

Since you can’t really evaluate it to infinity, what you do instead is implement an algorithm where you perform the iteration a large but finite number if times, and see if the iteration stays inside a set radius. So here is my fractal. The first plot shows the the complex plane from -20 to +20 on both the real and imaginary axis:

Here the blue football-shaped region in the center is centered at the origin. These points are considered to be ‘within’ the set, since a large number of iterations did not give numbers that were outside of the convergence radius (I set the number of iterations to 50, and the convergence radius to 1000). Any points that are not that deep blue are considered to be ‘outside’ the set, with the color being an indication of how many iterations it took for that point to leave the convergence radius. The dark red points took the least iterations, with the orange, yellow, green, and light blue areas taking progressively more iterations.

I think the feathery wing structures going in the positive and negative imaginary directions are really interesting. They continue up and down seemingly without end, or at least I didn’t see any end for even large plots that I made. This is in sharp contrast to the Mandelbrot and Julia sets which are confined to a finite area.

But the center looks the most interesting, so let’s get a closeup of that.

There’s a lot of interesting stuff going on in this area, with some really beautiful feathery wings, and a jumbled area that just looks like ‘static’. Here’s a zoom-in that let’s us see a little bit of both better.

Wow. Those feathers really are quite beautiful if I do say so myself. That random static-looking area bugs me though, since random noise really isn’t a feature of fractals. Instead they exhibit more of an ‘ordered chaos’ showing infinite complexity. So for my last image here is a much closer zoom on the static-looking area.

This last image has a width and height of just 0.005. Here we can see that it really is infinitely complex and not just random noise. I did another with a width and height of 0.0005, and it looks very similar, so there is some degree of self-similarity, much like we see in other fractals.

So the only thing this set is missing is a name. In reality probably someone has calculated this set and given it a name, but on the slight chance that no one has, I hereby name it the Bassett set. (How’s that for hubris? I bet Benoit Mandelbrot didn’t name the set after himself, but that someone else named it after him in honor of his discovery)