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Mandelbrot Set in Java

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

Firefox Logo in Illustrator

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

CS4 is so cool.

AP Maths

So apparently our school not only wants not to run AP Calc next year, but they're thinking of not running MCR3U2. And the reasoning behind it is, to put it bluntly, retarded.

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(?!)

“How much would you pay for a ;-)?”

This is stupid.

"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

Apophysis

http://www.apophysis.org/ - "Freeware fractal flame editor for Windows"

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

HP6 Trailer

OMG YAY!@~

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

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