Screenshot of Mandelbrot program

Links: video, image 1, image 2

The Mandelbrot set is defined as the set of all complex numbers for which the sequence Z(n) as n nears infinity is unbounded, where Z(n+1) is defined as Z(n)^2 + c, Z(0) = c, and c is the number that is being checked. For example, using 1 + i as c will result in (1 + i), (1 + 3i), (-7 + 7i), (1 + 99i), ... You can see that this sequence is unbounded as the magnitude -- or absolute value -- of the number will forever increase. If, however, i is used as the number c, then the resulting sequence is i, -1 + i, -i, -1 + i, ... Since this sequence remains bounded, it is within the Mandelbrot set. The pictures of the Mandelbrot set that are generated are essentially complex numbers plotted on a Cartesian plane -- with the a (real) value on the y axis, and the b (imaginary) value on the x axis. For the calculations, the real and imaginary parts are represented as separate doubles, and are converted to screen coordinates when rendering.

The controls are arrow keys to move, '[' and ']' to increase/decrease number of max iterations (high number is better when zoomed in a lot, as precision is lost otherwise), minus to zoom out, click and drag to zoom in to a specific area on the screen.

I use two threads to render the fractal -- one for each half of the screen, as I wanted to make use of my dual-core to make rendering faster. The colours are based on the number of iterations it took to determine that the point is not within the set. If the iteration count reached the maximum iteration limit, then the number is in the set. Otherwise, the higher the iteration count, the brighter the colour. The more iterations, the more accurate the drawing (and obviously takes longer to draw), so as you increase max iterations you will see that there is less and less black (as some of the numbers on the outside edges of the black parts that were originally determined as being in the set turn out not to be in the set when going through more iterations).

If you want to try running it yourself, here's a JAR file: link

Illustrator CS4 screenshot. Bottom image is the original, top image is the vector one that I traced over the original.

CS4 is so cool.

They want the people who would otherwise take AP Functions to take the U course in order to increase the U course's averages. Because, of course, averages are EVERYTHING, and what the students themselves want has absolutely no importance. What the hell! They're limiting our knowledge and achievement potential by making us be a part of a program that is of a lower standard. I mean, if you want high averages, you might as well make the whole school take COLLEGE math! People  who take AP take it because they WANT the enriched program it offers; they WANT the challenges it provides. The administration is ignoring the real reason why the U averages are low -- that is, people taking the U course who should be taking the M or C course. Make THEM take the lower level course, not the gifties.

I, for one, am going to do two things: 1) complain to Eschle about it (being a gifted teacher, I'm sure he wouldn't be indifferent to something like this, and he has way more influence than any of us), and 2) get my parents to call the school and complain. I suggest EVERYONE do that, because they're way more likely to listen to our parents than they are to listen to us. Also, we should like organize a day where everybody goes to complain to the principal during their lunch, to the point of annoying them. Or make a petition, or something. And go join the facebook group; too lazy to find the link but balh. AGH you can tell I'm really pissed -______-.

update: YAY so apparently there WILL be a MCR3U2 course if enough people take it..... but no brar(?!)

"A Russian businessman has trademarked the emoticon — or combination of punctuation marks — used to convey a wink in text messages and e-mail."

http://www.google.com/hostednews/ap/article/ALeqM5gE4Zc6sqIDqyfBQ1WlTKBf5GdInwD950NQ680

http://mnweekly.ru/business/20081211/55360588.html

This is fun. here are a few I made:

Takes about 10 minutes (on my 1.8GHz dual-core) to render each of these at a res of 1680x1050 at 1000 quality, but w/e, they make cool wallpapers

http://www.mugglenet.com/app/news/full_story/1973

Watch the high res one. It's really AWEOSMEE!

http://www.theglobeandmail.com/servlet/story/RTGAM.20081101.wpalintranscript1011/BNStory/usElection2008/home?cid=al_gam_mostemail

It's a 22-inch Dell E228WFP. Not actually from Dell though, got it at Future Shop for the same price. I didn't bother trying to do a dual-screen thing with my laptop 'cause the laptop's screen is too small and it takes too much effort looking from one to the other. The new monitor runs at 1680x1050 while the laptop is 1440x900 (the laptop screen is 14-ish inches btw. I think. Actually it might be 15. Whatever, who cares.)

In a previous post I showed how you can make an HDR image from 3 exposures - which is considered the "proper" way to do it. However, I also mentioned that this is possible using only one exposure. This is done using the RAW file created by the camera (you usually need to enable a setting to make it do that). The reason for this is that a RAW file stores much much more colour information (hence the larger size, usually 3x that of the JPG for the same photo). A JPG can only store a limited amount of colour information (24 bits is around 16 million colours). Now, if you don't intend on doing anything with the image, then keeping only the JPG file is just fine - since computer monitors can't display more colours than that anyways. However, with good cameras, the light sensor is actually a lot more sensitive and captures more detailed colour information than that which can be described by a JPG file (ie. 16 bits per channel rather than 8). Using the additional colour information available in a RAW file, it is possible to recreate conditions necessary to make an HDR image.

To my knowledge, Photoshop cannot do this, but Photomatix can. You just 'drag-and-drop' the RAW file (extensions vary, btw. My dad's Nikon makes them .NEF, Canon I think does .CRW) into Photomatix, and it informs you that it has converted your RAW file into a pseudo-HDR image, and that using more exposures is recommended. Following that you take the same steps as you would have if you had been making a multiple-exposure HDR. Click "Tone Mapping", and adjust stuff until you like it. Here is the result from one of mine:

Original Image (ISO: 250, Shutter speed: 1/250s, Aperture: f/8)

View of Eiger, Monch, and Jungfrau from Mannlichen / HDR with Photomatix

You can see that the original image is slightly overexposed. The sky and mountains are too light and appear sort of hazy and faded. In the HDR one however you can see that the colours are more saturated and the mountains and sky are more detailed and visible.

Here's how it turned out with 2 exposures:

Original Exposure #1 (ISO: 250, Shutter speed: 1/250s, Aperture: f/8, 0.00 EV)

Original Exposure #2 (ISO: 250, Shutter speed: 1/500, Aperture: f/11, -2.00 EV)

HDR from 2 Exposures

Maybe it's just my opinion, but I like the first result much more (using one exposure only). The multiple-exposure one seems kind of.. flat, and too yellow.

Anyway, since I'm posting this, I might as well talk about the .. place this was taken, in general, cause it was really awesome there and it was probably my favourite day in Switzerland. Here's a map:

Jungfrau Region Map

The yellow circle is Mannlichen, where the above photos were taken from. The blue circle is Kleine Scheidegg, the town (if you can call it that) to which we walked from Mannlichen. This whole region has a privately-operated railway network (Jungfraubahnen), which one can use to get around between the places worth seeing. Of course, the major tourist attraction here is Jungfraujoch (the blue circle on the above map), which is the highest train station in Europe at 3471m. A round-trip ticket from Interlaken to Jungfraujoch and back costs about $160 per person (discounts if you have a Eurail Pass or a Swiss Pass). It's expensive, but worth it.

Something else I noticed when I was looking through the photos is you can see Mannlichen (where these were taken from) on another photo taken from Jungfraujoch.

View from Jungfraujoch, Switzerland (click and then mouse-over the image on the Flickr page to see where Mannlichen is labeled)

Anyway, that's everything for now.

[Edit]: I also changed the background on this site to that image cause I was getting bored of the old one.

I blame this all on workers' unions. Let's first clarify what one is. "A trade union or labour union is an organization of workers who have banded together to achieve common goals in key areas such as wages, hours, and working conditions, forming a cartel of labor. The trade union, through its leadership, bargains with the employer on behalf of union members and negotiates labor contracts with employers."

Basically, a labour union is an evil organisation which makes an agreement with the employers to represent the "rights" of the empoyees. There are several UN legislations which recognize the rights of labour unions and their members. One is Article 23 of the Universal Declaration of Human Rights which "identifies the ability to organise trade unions as a fundamental human right" and another is the Declaration on Fundamental Principles and Rights at Work, which defines the "freedom of association and the effective recognition of the right to collective bargaining as an essential right of workers."

The most important reason for my disapproval of unions is the increase in prices of everyday commodities. In this case, bus tickets. Let's look at the reasons for this strike. The Toronto Star quoted the leader of Amalgamated Transit Union Local 113 (the labour union which represents Viva bus drivers),  Bob Kinnear, as saying that "drivers are looking for paid sick leave, more consistent scheduling and a pay increase of 3 per cent in each year of a three-year agreement." The employer evidently doesn't want to go along with this price increase, so the union members decided to go on strike. And there is nothing anybody can do about it, as human rights legislations and labour laws seem to do nothing to prohibit strikes.

Think about how this situation would play out if it weren't for unions. A number of people who are unhappy with the employer's conditions refuse to work and go on strike - the employer fires them. The others learn from example and go back to work. However, the agreements made between the union and the employer don't let the employer do anything about it, and neither does law. What will usually end up happening is that the employer will accept the union's terms and raise the wage of the bus drivers. And how does this affect everybody else? The employer needs to make additional money to be able to pay the drivers more, so bus ticket prices go up. Not too long ago an adult ticket cost only $2.50, or even less than that. Now it's $2.75 or $3.00, I don't even remember.

The Toronto Star article also mentions another interesting piece of information - "The union proposal would put that rate up to $21.37, slightly more than the drivers at York Region’s three other contracted bus operators." Yes, York Region Transit has more than one contractor working for them. Different operators run YRT and Viva services. So, if Viva drivers are making more all of a sudden, what will the YRT drivers think? Will they not react in much the same way? And will the employer not give in to the demands the same way? And then think about the TTC. Did they not also have a strike recently? Well, if Viva drivers will be making a few cents more than them, who's to say they won't want to make more $ than them? Accepting the union's proposal would be another step in the already existing loop that pushes our transit prices higher and higher.

However, I do have some hope in the screwed up system in which we live. There was an incident where TTC drivers went on strike until the provincial government ordered them back to work. I just hope the same thing will happen here, and that the employers will not give in to the union's demands.