Illustrations of Infinity

Moved on

2006-07-03T09:02:00.000-07:00

Its been a long time since I have updated the blog because I was busy creating a new one. Blogger is not sufficient for hosting a gallery-cum-website-cum-blog. Also, there are nice plugins such as Falbum which work directly through flickr site. I like blogger but its just ...

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Gallery2

2006-06-14T12:12:00.000-07:00

Infinite swirling whirls

Dragons

Space-time tunnel

Gallery1

2006-06-14T12:00:00.000-07:00

The initial attempts in absence of I2

Below are certain illustrations from Julia Sets. All of them have been created using escape-coloring method. You can find details about this method on several other fractal websites.

Spiraling Roots

Mutation

Flower?

Galleries

2006-06-14T11:58:00.000-07:00

Take your time and browse through the galleries. These are mostly listed in chronological order.

Updates on I2

2006-05-26T07:44:00.000-07:00

I have done significant changes in I2. It supports Julia and Mandelbrot fractals with escape-coloring technique. The browser cache's all the generated fractals along with their corresponding parameters. You can navigate through these fractals using the navigation bar. It supports different modes

Explore Mode (Grab Off): You can generate fractals by tweaking several available parameters.
Explore Mode ( Grab On): This mode allowes you to pick a particular co-ordinate from the displayed fractal and pan/zoom-in/zoom-out in that location. A cross-hair moves along with the mouse for guidance. You can also monitor the X and Y components of the current coordinate in the navigation bar.
Animate Mode (Grab On/Off + Save): This mode allows you to iterate the parameters available with current fractal class from a start value to end value in certain steps. You can combine Grab option with it. It further provides allows you to directly save the images in hard-drive. It is particularly useful when you want to generate 100's of frames for some movie clip. This mode can also be used to create life-size fractals.
Animate Mode (Grab On/Off + Display): This mode can be used to see how the animation would look like by generating few frames. The More frames you would generate, the more memory you would require.

Right now, I am working on providing an option to rotate the coordinate system because certain fractals look better when viewed with a different rotation. It might be useful in creating movie frames.

As promised yesterday, here are some of the interesting fractals exhibiting the beauty hidden in Infinity.

The first ones

2006-05-25T06:52:00.000-07:00

Hi there. I know its been a long time since I have updated this blog. Hmm... I was quite busy with office work, and barely managed to keep improving I2. Also, I did generate some nice fractals which are in a sense true illustrations of infinity.

But I think, I should first show you some fractals from my preliminary work before I2. I did these a year back while enjoying my "official" trip to Austin. My colleagues including manager said, "So, is this why I had sent you to Austin, to make fractals?". But my boss is quite cool. He doesn't care how I manage to finish the assigned job. He himself is a fractal enthusiast and keeps sharing his experiences about the good old days at IBM, the place where Benoit Mandelbrot did his research on Fractals. The gallery for you

Ab-Initio attempts

2006-05-18T01:40:00.000-07:00

I was introduced to the fascinating world of Chaos Theory and Fractal Imaging through James Gleick's book. It was such an exciting read that all of a sudden my perspective towards several things in life changed drastically. Google-power helped a lot in discovering what is going on in this part of world, esp. the art side of it. The images created using certain iterative equations are full of details and self similarity that its tough to get away from them without gazing for a while. You might wanna visit some of these websites

There are several books on this subject, but one by Ian Stewart and another by Julien C. Sprott are best for beginners.

I started exploring world of fractals using GNUPLOT and few perl scripts which can create images only in XPM format. In absence of a GUI interface, it was quite cumbersome to zoom in a certain region, and also to save the plots as images. Plotting and editing C/C++ Libraries distributed as PNGwriter were quite helpful for this purpose. I wrote couple of programs in C++ for creating fractals, but as always, an easy GUI interface was required which can allow me to grab any co-ordinate from the pixel-map of the displayed. Very soon I gave up because X11, X/Motif or QT were not simple enough for me to create an intuitive GUI. I could have used the freely available tools for this purpose, but I was interested in developing one of my own. It definitely aids in-depth understanding of the involved concepts. Also, it brings something interesting to do apart from monotonous job work.

Meanwhile, I came across the book by Charles Seife on the history of mathematics and science which revolves around the concepts of Zero and Infinity. While reading the book, I felt the inherent relation between these concepts and Fractals. Every such image illustrates the beauty hidden in zero and infinity. I find myself speechless when it comes to describing this beauty. Anyways, I have decided to pursue fractals as my hobby.

Off-late, I have been developing an application in Tcl/Tk for GUI with C/C++ extensions for mathematical calculations. Creating your own GUI applications is intuitive with standard Tk's. It hardly took 5-man days to create a working application for my exploratory quest. I have named it, I2-Illustrating Infinity. It is a bare-bone application, but easily customizable with a little know-how about Tcl/Tk. Keep checking this space for further updates on I2 and my exploration on fractals. Please take some time and drop a comment about the article. This helps me in making it more informative and interesting.

Zero and Infinity

2006-04-27T21:59:00.000-07:00

Recently, I came to know about my fascination for any to everything which is mystic, unworldly and obscure. The concepts of Zero and Infinity kindled this fire and, it brought me a feeling of being found, a feeling distant vision, a feeling of purposeful life.

Zero and Infinity has always been intriguing to everyone. The more you want to get rid of them, the more often they pop-up. At the same time, the more you know them, the more elusive they become. More importantly, they are the mirror images of each other. They are inseparable. They alone have the power to shatter most acceptable theories of mordern science.

In Hindu religion, the ultimate source of everything is nothing, its nirakaar. It cannot be tasted, smelled, touched or seen. Every soul is in eternal search of it and finds the same in someone, something, somewhere. This similar concept has been embraced by early chinese philosophers as Yin and Yan. This chinese quote captures my thoughts perfectly, though told in a different sense

"There are only five notes in the musical scale, but their variations are so many that they cannot all be heard. There are only five basic colors, but their variations are so many that they cannot all be seen. There are only five basic flavors, but their variations are so many that they cannot all be tasted. There are only two kinds of charge in battle, the unorthodox surprise attack and the orthodox direct attack, but variations of the unorthodox and the orthodox are endless. The unorthodox and the orthodox give rise to each other, like a beginningless circle—who could exhaust them?" - Sun Tzu

There are several ways to represent these concepts, graphically, musically, mathematically etc. I have chosen to illustrate these concepts using mordern methods. The world of Computers Graphics combined with the mathematics of Chaos theory is an ultimate tool to dwell into the details of it.

I find the idea of blogs interesting and a good way to keep account of my quest. It also helps to share the idea with the world and to get their opinion.