Visualizing The Core of the Blogosphere

Interactive map of blogosphere. From Hurst. Click to enlargeThere's been a recent flurry of articles concerning visualization of the web itself, and what such visualization might say about the social networks that live and breathe because of the abilities of the net.  This topic is a necessary follow-up, then, to my previous posts on new visualization techniques in web searching.

A conference at UPenn in June 2006 titled The Hyperlinked Society focused on "the effects of digital links on people’s ability to understand and care about their larger society. " The following blurb is from the intro page; the program was quite ambitious:

Most internet users know hyperlinks as highlighted words on a web page that take them to certain other sites. But hyperlinks today are quite complex forms of instant connection—for example, tags, API mashups, and RSS feeds. Moreover, media convergence has led to increased instant linking among desktop computers, cell phones, PDAs, MP3 players, digital video recorders, and even billboards.

Through these activities and far more, “links” are becoming the basic forces that relate creative works to one another. Links nominate what ideas and actors have the right to be heard and with what priority. Various stakeholders in society recognize the political and economic value of these connections. Governments, corporations, non-profits and individual media users often work to digitally privilege certain ideas over others.

Do links encourage people to see beyond their personal situations and know the broad world in diverse ways? Or, instead, do links encourage people to drill into their own territories and not learn about social concerns that seem irrelevant to their personal interests? What roles do economic and political considerations play in creating links that nudge people in one or the other direction?

Click to read more ...

Mathematics Reveals the Artistry

Brueghel's Fall of IcarusDaniel Rockmore writes about the mathematical analysis of art in the June 2006 Chronicle (The Style of Numbers Behind a Number of Styles). In the essay Rockmore describes Richard Taylor's work in analyzing Jackson Pollock pieces, which may be forgeries. ( See my post on this topic)

The Pollock intro is a lead in to a description of stylometry - the mathematical/scientific analysis of literary texts that attempts to address issues of authorship. (See Bookish Math, an excellent intro to stylometry by Erica Klarreich for Science News Online.) Rockmore than describes a method he developed with co-workers Siwei Lyu and Hany Farid that uses wavelet analysis to determine unique "signatures" of different artists - in effect a stylometry for visual images.

The actual mathematics of the wavelet approach can be found in A Digital Technique for Art Authentication. Here the authors use examples of Pieter Bruegel and Perugino to test their model. They claim that their "techniques, in collaboration with existing physical authentication, to play an important role in the field of art forensics."

The wavelet technique is different from Taylor's fractal analysis of Pollock's works, but both are examples of stylometry applied to visual information. Both Taylor and Rockmore are attempting to quantify art, an activity that Rockmore admits is unsettling/impossible to some. According to Taylor, this quantification should be expected: "Both mathematics and art are all about pattern...it would be unusual that you would not apply mathematical analysis to the question."

Rockmore is more explicit about what mathematical categorization of art analysis does not do: "Fractal analysis doesn't diminish Pollock's athleticism and movement, nature and turbulence, chaos and beauty; it reveals and amplifies it."

For more on this topic, see Can Mathematical Tools Illuminate Artistic Style?, by Sara Robinson for SIAM.

Fractal Solar Wind

Massive solar flare starting and ending on earth's surface. Click to enlarge.Sunspot cycles are hot right now - literally and figuratively. After just posting about Cycle 24 - the about-to-begin 11-year cycle of sunspot activity, I now see a lot of references to scientists at Warwick University reporting on observed fractal nature of the solar wind, and the ramifications for prediction and understanding of sunspot cycles

The articles announcing the findings have been very exuberant about this latest finding, but so far they are short on some crucial facts. They are also woefully inadequate when it comes to reporting previous work.

Most web sites are just reproducing the press release from the University of Warwick:

The researchers, led by Professor Sandra Chapman, have also been able to directly tie these fractal patterns to the Sun's 'storm season'. The Sun goes through a solar cycle roughly 11 years long. The researchers found the fractal patterns in the solar wind occur when the Sun was at the peak of this cycle when the solar corona was at its most active, stormy and complex - sunspot activity, solar flares etc. When the corona was quieter no fractal patterns were found in the solar wind only general turbulence.

From this description it is not clear what the fractal pattern is. The New Scientist site provides more details, including a possible reason for the fractal pattern:

Click to read more ...

Visualizing Web Pages - HTML Graphs

FractaLog web graph. Click to enlarge. As an interesting follow up to my recent post on KartOO and Google Browser, check out the HTML Graphlet applet created by Sala (no last name), and posted on the Aharef blog. To use the applet, just enter the URL of the page to be graphed.

The applet constructs multi-colored graph of nodes and edges, with each color representing a different HTML tag. As the graph is produced, it grows outward, with branches sprouting - all in a very kinetic/organic way.

The color of the nodes refer to specific HTML tags:

blue: for links (the A tag)
red: for tables (TABLE, TR and TD tags)
green: for the DIV tag
violet: for images (the IMG tag)
yellow: for forms (FORM, INPUT, TEXTAREA, SELECT and OPTION tags)
orange: for linebreaks and blockquotes (BR, P, and BLOCKQUOTE tags)
black: the HTML tag, the root node
gray: all other tags 

The image at the top of this post is a map of FractaLog as of the date of this posting.

Sala asks that those with flickr accounts post a screenshot of their site tree, using websitesasgraphs for a tag. Click on this link to see a wide variety of web page graphs.

Some of these graphs are more fractal-like than the others. I can only hope that someday the FractaLog graph will look suitably fractal to deserve its name.

Update on Thursday, May 31, 2007 by R.A. DiDio

Note:  Just as I published this post, the link to the Graphlet is not working - nor is the link to Aharef.  I am getting  a "WEb Site Suspended" message.

If it is working for anyone, please let me know with a comment here. 

Web Search Visualization & Fractal Maps

KartOO fractal search. Click to enlarge.There is a growing trend in using connectivity-visualization mapping when web searching. Search engines such as KartOO and TouchGraph Google Browswer, attempt to show the linkage among web sites/pages by web-like 2-D graphics, where colors and icon-sizes indicate the strength of the site linkages. The effect can be described best as a "concept map", with nodes representing sites, and connections between nodes representing links. Of the two engines, KartOO is much more visually interesting. (I have included screen shots produced by each engine in a search for "fractal".)

Whether this enhances the search experience is debatable - at present. While KartOO's pr claims that the non-linear nature of the way information is distributed on the internet should be matched in the non-linear nature of the visualization, so far I haven't seen anything that makes me want to switch from Clusty, which does a great job of organizing themes in web searches, and provides the links/themes in a nice old-fashioned list.

I find the same lack of compelling features for the Touch Graph Google Browser. I should note that TouchGraph is a company that designs custom-tailored visual search features for other companies and projects, with a focus on "creating tools that enable decision makers to display, navigate, and analyze complex data simply and intuitively...Individuals and organizations have more vital information at their fingertips than ever before. Traditional search engines provide a way to sift through this data. However, the greatest insights can be achieved not by sifting, but by looking at the big picture to see how items are connected."

TouchGraph fractal search. Click to enlarge.I'm still underwhelmed by what the visual engines do that's better than Clusty. They do produce some fascinating, kinetic displays, because nodes and connections expand when clicking on different parts of the graphic display, and various pop-ups appear with further detail about the sites. Because clicking often produces new sets of nodes, there is a fractal-like quality to the search map. I can see the efficacy of such a search for different types of data, or business functions, but I doubt that they will become the main search option for an ordinary web search.

Playing a Mandelbrot Set - Hum a Few Iterations and I'll Fake It

Eventually by Sergio Lazo

In the annals of how-to songs one will find everything from delicate interactions with a weapon of mass destruction - e.g. How to Dismantle an Atomic Bomb by U2 - to an even more dangerous and potentially deadly situation - How to Handle a Woman from Camelot comes to mind.

(Yes I know that How to Dismantle an Atomic Bomb is not the name of an actual song! So suggest a better title to match up with How to handle a Woman.)

And now comes the ultimate how-to for the fractally-minded: Mandelbrot Set by Jonathan Coulton, the Contributing Troubadour for Popular Science Magazine and composer of "well-crafted geek folk-pop. Hilarious but heartbreaking songs about mad scientists, robot armies and self-loathing giant squids." His is the voice of "every one of us who has ever sat despairingly on the floor, surrounded by parts of an Ikea endtable, weeping over our Allen wrenches.

Coulton's work is truly unique. Check out his site for all of his tunes. And there are plenty of them: In 2005-2006 he recorded and published a new song podcast every week. All of the lyrics are there, as well as guitar tabs and videos.

Mandelbrot Set is funny, incredibly clever, and mathematically correct! Some excerpts...

Click to read more ...

The Gateway to Educational Materials

A Cantor Set on an Egyptian column. Click to enlarge.An excellent resource for any teaching, but especially K-12, can be found at the Gateway, a site run by the U.S. Department of Education and Syracuse University.  The site is  the project of  a consortium whose member institutions join what is known as GEM, the Gateway to Educational Materials.

The Gateway is an essential site, both for educators, and for anyone interested in anyone learning any topic on-line.

You will use the Gateway primarily for its very sophisticated search engine, specifically designed to search for  educational materials.  When you search for a particular topic, e.g. "fractals", you will get a nice listing of hits that describe not only online educational fractal resources, but also a categorization scheme linked to the appropriate educational setting.  This is implemented on-screen by a category list that appears in a right-hand pane following a search.  Similar to clusty, the categories allow you to instantly narrow your search into one of the categories.  The categorization is an incredibly helpful way of finding the right resource for you class.  For example, back to the fractal search:  categories include areas such as curriculum support, lesson plans, and individual categories for grades 1 through 12.

The real benefit of the categorization scheme, however,  are the categories that you probably aren't aware exist - these are the ones that allow the cross-connections across all disciplines to become evident.  One of the categories that appear when searching for "fractals" is Cultural Perspectives on Mathematics.  A click here yields 5 hits, one of which is  African fractals: modern computing and indigenous design, an article on a fractal geometric view of the " self-organized location of huts in Tanzania, art design among the Mangbetu in central Africa, and Mali windscreens."

So plan to spend plenty of time on the Gateway - learning, teaching, and marveling at the sophistication and power of a search engines designed specifically for the educational community.

The Spam Artist

Spam Plants - Click to enlargeOne of the most innovative and creative artists working today is Alex Dragulescu, a Romanian "visual" artist who heads  the Experimental Game Lab at the Center for Research in Computing and the Arts at University of California, San Diego. 

His images are absolutely fascinating.  Some of them are beautiful and organic-looking, while others appear to be views of some alien architecture.

But it's not the images that are interesting so much as the process.  Dragulescu uses spam to generate some of his images.  He does this by using words in spam mailings to trigger different structures to be digitally rendered.  The image at the top of this post comes from his Spam Plants series.

Dragulescu definitely pushes the art/mathematics interface to an extreme, with the random detritus of life thrown in for good measure.   He describes his projects as "experiments and explorations of algorithms, computational models, simulations and information visualizations that involve data derived from databases, spam emails, blogs and video game assets."

It's impossible to describe Dragulescu's work without seeing the images, so check his website for much more. 

Be sure to investigate some of the other work being created at the Experimental Game Lab , where "somewhere between media art, scientific visualization and computer gaming a new territory of expression is emerging." Sheldon Brown's Scaleable City project is one such project.

It is hard to imagine how amazing it must be to teach or go to school at a university like UCSD, where anything short of the absolute limits of creativity is viewed as abject failure.

The Most Expensive Fractal in the World

No. 5, 1948 (click to enlarge)The basic free market model of supply and demand is pushed to the limit in the case of the price of art pieces. Just how much will someone pay when the supply is only one, i.e. when the piece is one of a kind?  Especially when the artist was truly one of a kind?

Last week the Jackson Pollock painting No. 5, 1948  was sold at auction for $140 Million, the most money ever paid for an American painting. (Click here for story) 

This stunning number is now going to color the debate on the validity of the Pollock paintings discovered earlier this year and claimed to be possible frauds because they were not fractal enough.  (See my previous post on this controversy.)  Given that computer software can regularly produce fractals with the same fractal dimension as any of Pollock's paintings, determining if a painting is an original Pollock or a computer-generated image should be a concern for anyone with $140 Million to burn.

This  situation suggests that a lucrative, niche career-op exists for anyone who can discern the difference - a fractaconsulter.

Paul Santoleri: A Fractal Muralist

Philadelphia-area artist Paul Santoleri draws/paints amazing images that are evocative of fractals.  Not the Mandelbrot-class fractals that are the staple of most  fractalologists and fractal software, but reminiscent of  the fiendishly delicate and organic-looking fractals created by  Clifford Pickover.

Only Pickover does his with a computer, while Santoleri paints his.  The image at the top of this post is titled Red Spider, and is a 2' by 2'  painting using acrylic on canvas.  (Santoleri also paints on a very large scale:  he is also a muralist, and has done 70+  large murals around the world, with a few in Philadelphia.

Here's a fairly well-known Pickover creation titled From the X-Files.  See more of Picover by clicking here.

While Pickover has done an enormous amount of spreading the fractal word, and has been a great spokesman for the melding of art and mathematics, I find Santoleri's work much more interesting because its organic-like nature is truly evident, painted without any dependence on computers.  In Santoleri's own words:

In my works I erase the borders between the visible and invisible matter and create a new medium generating object and beings whose meaning, gender, and whereabouts is unclear and not important. My works should be viewed just as a part of the moving beyond their bounds whole that knows no spatial or temporal limitations.

Pickover certainly captures an artistic view of infinity with his images, but they are more of space alone and can't compete with Santoleri's temporal infinity.