Rogers–Ramanujan identities

$$1+\frac{q^2}{(1-<!--\; -\; -->q)}+\frac{q^6}{(1-<!--\; -\; -->q)(1-<!--\; -\; -->q^2)}+\cdots <!--\; \cdots \; -->=\underset{j=0}{\overset{\mathrm{\infty <!--\; \infty \; -->}}{\prod <!--\; \prod \; -->}}\frac{1}{(1-<!--\; -\; -->q^{5j+2})(1-<!--\; -\; -->q^{5j+3})},\text{for }|q|<1.$$

Maxwell’s Equations

$$\begin{array}{rl}\mathrm{\nabla <!--\; \nabla \; -->}\times <!--\; \times \; -->\stackrel{⃗<!--\; ⃗\; -->}{\mathbf{B}}-<!--\; -\; -->\frac{1}{c}\frac{\mathrm{\partial <!--\; \partial \; -->}\stackrel{⃗<!--\; ⃗\; -->}{\mathbf{E}}}{\mathrm{\partial <!--\; \partial \; -->}t}& =\frac{4\mathrm{\pi <!--\; \pi \; -->}}{c}\stackrel{⃗<!--\; ⃗\; -->}{\mathbf{j}}\\ \mathrm{\nabla <!--\; \nabla \; -->}\cdot <!--\; \cdot \; -->\stackrel{⃗<!--\; ⃗\; -->}{\mathbf{E}}& =4\mathrm{\pi <!--\; \pi \; -->}\mathrm{\rho <!--\; \rho \; -->}\\ \mathrm{\nabla <!--\; \nabla \; -->}\times <!--\; \times \; -->\stackrel{⃗<!--\; ⃗\; -->}{\mathbf{E}}+\frac{1}{c}\frac{\mathrm{\partial <!--\; \partial \; -->}\stackrel{⃗<!--\; ⃗\; -->}{\mathbf{B}}}{\mathrm{\partial <!--\; \partial \; -->}t}& =\stackrel{⃗<!--\; ⃗\; -->}{\mathbf{0}}\\ \mathrm{\nabla <!--\; \nabla \; -->}\cdot <!--\; \cdot \; -->\stackrel{⃗<!--\; ⃗\; -->}{\mathbf{B}}& =0\end{array}$$

All I had to do was insert a javascript in my wordpress header file. But I am already loading too many javascript files in my header, So I added a custom field in my wordpress called “math”. If its set to yes then it loads this MathJax otherwise it wont. Also I had to put the MathML code inside a pre tag to keep it clean.

Can you see it? if not what browser and OS are you using?

The universe of the Game of Life is an infinite two-dimensional orthogonal grid of square cells, each of which is in one of two possible states, live or dead. Every cell interacts with its eight neighbours, which are the cells that are horizontally, vertically, or diagonally adjacent. At each step in time, the following transitions occur:

1. Any live cell with fewer than two live neighbours dies, as if caused by under-population.
2. Any live cell with two or three live neighbours lives on to the next generation.
3. Any live cell with more than three live neighbours dies, as if by overcrowding.
4. Any dead cell with exactly three live neighbours becomes a live cell, as if by reproduction.

The initial pattern constitutes the seed of the system. The first generation is created by applying the above rules simultaneously to every cell in the seed—births and deaths occur simultaneously, and the discrete moment at which this happens is sometimes called a tick (in other words, each generation is a pure function of the preceding one). The rules continue to be applied repeatedly to create further generations.

The initial code was borrowed from Ran Tao’s java based program. I rewrote in Javascript version of Processing. Also added player buttons for more control. Also added a way to start with your own seed through it starts with random seed. One more change to the original Life is that you can introduce a living cell while its playing. Just click on the grid. Its kind of against the actual game, but it seemed more fun to me.

Clear it and introduce your own seed using mouse or just intrude, you are God. Go to full page version its more fun. Source code is on GitHub.

One of the requirement was to pull the latest mobile picture post, to display on my main blog. By default wordpress provides RSS feed for each author, category and tag. It wasnt that difficult to get the latest post but it is difficult to use XML in JavaScript. JSON seemed more useful than RSS. In the mean time Dave Winer was also thinking on similar lines. I thought about writing a plugin to convert RSS feed into JSON feed. But then whole wordpress family seems to like Dave (Remember WP.com supports RSS cloud). So I searched wordpress plugins. I found the one which I wanted – Feed JSON .
So it gives me JSON feed for my mobile picture stream and also has call back feature.

http://thej.in/?feed=json&author=4

//with callback

http://thej.in/?feed=json&callback=mymethod

&author=4

It also works with permalinks if that is enabled in wordpress. Here comes my widget for latest camera pics.

<script>
function writeWidget(posts){
alert(posts[0]["title"]);
}
</script>
<script src="http://thej.in/?feed=json&author=4&
callback=writeWidget">
</script>

Now with this its easy for any wordpress blog to create JavaScript based widgets, that can be embedded any where on the web. Well for some use cases the full content JSON could be heavy. So try it before you widely deploy. Let me know what you think.

“Processing.js is an open programming language for people who want to program images, animation, and interactions for the web without using Flash or Java applets. Processing.js uses JavaScript to draw shapes and manipulate images on the HTML5 Canvas element. The code is light-weight, simple to learn and makes an ideal tool for visualizing data, creating user-interfaces and developing web-based games.”

The Processing language was originally created by Ben Fry and Casey Reas for Java. In 2008, John Resig ported the 2D context of Processing to JavaScript. It needs Canvas. So make sure you are using HTML5 capable browser like Firefox ¹.

Setup: Download the processing.js. That is the only file you need.

Initialize processing: We need to initialize the processing engine on a canvas. We will have that in the init.js and will include that.

<html>
<head>
<script src="init.js"></script>
<script src="processing.min.js"></script>
<title>Analog Clock using Processing.js</title>
</head>
<body>
<script type="application/processing" target="clock">
//your processing code
</script><canvas id="clock">You need HTML5 canvas support.
Try latest Firefox</canvas>
</body>
</html>

The above code snippet shows the basic setup to run. We need to add our processing code inside

<script type="application/processing">
//your processing code
</script>

The init.js code actually searches for all the script tag type=”application/processing” and applies processing the code on the target canvas. init.js was borrowed from JResig‘s code examples.

Logic for the clock:
Circle has 2PI radians. So for each second/minute we have to move 2PI/60 radians. Given the center of the circle (a,b), radius r and angle t radians. we can find any point on the circle, using
x = a+r cos(t);
y = b+r sin(t);
or
x = a + r (1-t²)/(1+t²)
y = b + r (2t)/(1+t²)

I have used the first set of formula. Processing.js supports time and trigonometric functions by default.

But the 0 degrees start at horizontally and I wanted 0^th hour to start at 90 degrees. And hence the subtraction of quarterCicrle which equals = PI/2.

The two main important methods are
void setup() – called initially when canvas gets loaded.
void draw() – called at the rate of frameRate.

You can see I have set frame rate to 1 sec. I guess the rest of the code is self explanatory.

int radius=90;
int a=100;
int b=100;
int nx,ny;

void setup(){
  size(200,200);
  strokeWeight(5);
  //run every second
  frameRate(1);
}
void draw(){

	r = radius;
	background(100);
	ellipse(a,b,2*radius, 2*radius);
	int quarterCicrle=PI/2;

	//second
	int t=((2*PI/60)*second())-quarterCicrle;
	nx = a+r*cos(t);
	ny = b+r*sin(t);
	strokeWeight(2);
	stroke(100);
	line(a,b,nx,ny);

	//minute
	t=((2*PI/60)*minute())-quarterCicrle;
	nx = a+r*cos(t);
	ny = b+r*sin(t);
	strokeWeight(5);
	stroke(100);
	line(a,b,nx,ny);

	//hour
	t=((2*PI/12)*hour())-quarterCicrle;
	nx = a+r*cos(t);
	ny = b+r*sin(t);
	strokeWeight(8);
	stroke(100);
	line(a,b,nx,ny);

}

launch in a separate page
With processingjs graphics in JavaScript has become very easy. This is just an example and processing.js can do much more complex things, Their website has lots of good example. Go explore.

Foot Notes:
1. Browsers like Firefox 3.0 Beta 5, WebKit and Opera 9.5 have canvas support.↩

<script type="text/javascript">
if (top !== self) top.location.href = self.location.href;
</script>

This code in fact doesn’t allow anybody to display your content in their frame. Here is the demo url http://digg.com/u1BSW to check. It should work on all browsers.
Let me know if you have any other suggestions.

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Go to jFotoNotes project page

jFotoNotes is java implementation of famous FotoNotes in php. A variation of FotoNotes is also used by flickr. Fotonotes is a standard, specification, and collection of scripts for annotating images. In jFotoNotes I have used the same JavaScript libraries but I have completely rewritten the server side components in Java.

1. Its an open source, you get to participate and allows you to write plug-ins
2. Each tab is a separate process.so the effect of one tab is not seen in another tab.
3. Within each tab you have separate thread for JavaScript. So your JavaScript execution will be fast.
4. JavaScript now runs inside a virtual machine called V8. The JavaScript is compiled to machine code before running. Now that’s an advantage for heavy JavaScript applications like Gmail. Where most of the JS resides on client side and simply gets the JSON from server to show the data. You don’t have to re-interpret the JS every time. Compile once and keep running again and again. Your apps will be super fast now. Now GWT developers don’t have worry about JS performance.
5. Rendering is by webkit which is again open source.
6. Looks like they have better garbage collection algorithm for garbage collection. Which will again makes my work simple.
7. Gears is part of browser now. Your offline apps will have better performance now. Think -> Gears API is loaded as soon as browser is loaded, JavaScript is compiled to m/c code, runs in separate process and thread. What more you want? Your offline application might be as fast as any native application if not faster.

Anything else you want to add.