Fractalettes: A Fractal Design Strategy to Color Mining and Learning through Discovery

We have just published this short article, based on The Color Miner tool:

Fractalettes: A Fractal Design Strategy to Color Mining and Learning through Discovery - Based on Fractal Geometry, fractalettes are color palettes within color palettes, where each cell contains color space information and relationships. These types of architectures engage end-users in data mining, critical thinking, and learning through discovery.

Reconstruction and Iteration of Windows 16-Color VGA Palette

With The Color Miner, we have programmatically reconstructed the classic Windows 16-color VGA palette with few basic algorithmic rules.

We also found that iterating the 16-color VGA palette, with these rules, the result converges to a 42-color palette. As given below.

Advantages?

The algorithms utilized allow one to:

• reconstruct large palettes with a small set of seed colors.
• store a small set of colors instead of a large palette file.
• build basic palette generators and color tools.
• use an initial palette to discover colors or propose new ones, then use these to expand the initial palette.

For additional information and to verify these findings, visit the The Color Miner page.

A Web-Browser Approach to the Construction of Fractals and Multifractals

We have published a new article titled:

A Web-Browser Approach to the Construction of Fractals and Multifractals

The traditional way of constructing fractal patterns is with mathematical algorithms. Some of these are based on pixel-by-pixel drawing techniques wherein the output of a recursive function is evaluated against a predefined condition. This is a slow process which requires of a large number of iterations.

Other strategies or combination of strategies have been proposed; for instance, using HTML tables, image files, VML, SVG, or the canvas tag introduced in HTML5. In most cases, implementing these strategies and techniques is not a straightforward process, involve a learning curve, or unnecessarily consume Web server resources.

None of this is necessary with our approach. We are also providing the corresponding source codes at Mi Islita.com, so others can reproduce or improve our results. These are winRAR-zipped files. An unzipped, live example for the Sierpinski Gasket is provided.

Mann Iteration Method

Here are some great papers on Mann Iteration Method.

“What does it has to do with IR, CSS or Fractals?”, you might ask. Well, I’m using it in an upcoming article.

Simpler is also better in approximating fixed points

The equivalence of Mann and Ishikawa iteration methods

The equivalence between the convergence of Mann and Ishikawa iteration methods

Fractal Art and Three-Column Iterated Layouts

I’ve uploaded a new article on fractals:

Fractal Art and Three-Column Iterated Layouts

Enjoy it.

In an upcoming article I will demonstrate how to create classic fractals as found in the literature, right on the user’s browsers, with no HTML5 canvas tag and without high-level mathematical algorithms. We only need to use CSS and HTML. Markup code will be provided for those interested in reproducing the results.

Fractaless Menus and Grids

In a recent article, we presented a fractal approach to the design of menus and grids. It was demonstrated that:

• these patterns can be emulated with CSS and division-based iterated layouts.
• by using divisions, positioning issues associated with the use of list elements (ul, ol, etc) and mentioned at this Mozilla blog are avoided altogether.
• there is no need to resource to browser hacks or css gymnastics, which often cause new issues with other browsers.

Almost immediately some asked if we could achieve same results using a fractaless approach (i.e., no iterations at all), and if so, what are the pros and cons of using one approach over the other.

In a nutshell, indeed: the above design patterns (menus and grids) can be emulated without having to use recursion. We just need to use the correct design strategy.

Last week we published the Fractaless Menus and Grids article which explains how this can be done. Both approaches, fractal and fractaless are compared.

To do what we teach, we are updating the Fractal Resources Index sub-site so some of these design patterns will be incorporated. We are also looking forward to implement changes across some pages of http://www.miislita.com.

Menus and Grid Article: An Update

I’ve updated the Menus and Grids article. CSS and markup instructions have been modified to make the iterated patterns more flexible and applicable to a variety of scenarios. Additional reference material has also been added. Wrappers generated by default by our design tool have been removed to simplify the markup.

I believe the proposed fractal approach avoids all the CSS workarounds and positioning issues raised at this Mozilla blog and in relation with the design of grid-like patterns.

BTW, a Wikipedia entry has an interesting article on CSS tableless Web design, but unfortunately goes to the extreme of including the following statement:

“Using divisions to simulate a table for the display of tabular data is as  much a design flaw as using tables to control graphic and page layout.”

According to whom? Since when achieving a given rendering through different design strategies is a “design flaw”? Evidently, Wikipedia allows biased opinions from individuals or interest groups disguised as reputable editors.

I challenge the above half-true opinion. Read my rebuttal to Wikipedia in the improved version of the Menus and Grids article.

IRW:2010-3 Fractals in IR and Web Design

The current issue of IRW is out. As mentioned before, it is dedicated to fractals and their application to Computer Sciences, in particular to Information Retrieval (IR) and Web Design.

Enjoy it.

Fractal Design: Menus and Grids

The traditional way of rendering horizontal menus and grids in Web pages is with HTML tables or by styling block level elements like dl, ol, or ul with Cascading Style Sheets( CSS). This often involves CSS workarounds for handling positioning issues.

In Menus and Grids, we present an alternate approach using fractal concepts. The article provides two examples of this approach using no images, no JavaScript, no ordered lists (ol, ul, dl), but just division elements, CSS, and a bit of fractal theory. These have been tested with the latest versions of Internet Explorer and Firefox browsers, only.

Since the only block level elements used are divisions, positioning issues and CSS workarounds associated with the use of list elements (ol, ul, li, and dl) are avoided altogether.

BTW. This month issue of the IRW Newsletter is dedicated to Fractals in IR and Web Design. It should reach subscribers’ inboxes next week.

Cheers.

CSS-only Iterated Layouts

Thank you all for visiting the recently launched sub-site on fractals. I forget to add to yesterday’s blog post a sample picture of some of CSS-only iterated fractal layouts. Here is an example: The Accordion Family. These patterns were obtained by iterating a basic two-column Web page layout.

These were created as described in the Random Patterns document and in the Fractal Movies, CSS-only Backgrounds, and Two-Column Layouts article. BTW, the later is a long PDF file (more than 800k because of the so many pictures in it). So if you initially see a broken link message, ignore it. The file should download just fine.

Don’t forget to read the disclaimer before watching the fractal movies. These run faster with Firefox than with Internet Explorer.