It is a human characteristic to organize chaos of all that life represents. Yet, it is this drive that unfortunately drives us farther away from the true breakthroughs dependent on not following form and structure - breakthroughs at a fundamental level. The best example of this is Albert Einstein, the famous patent clerk.
A similar case is Benoit Mandelbrot, the inventor of fractal geometry - "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole". See what is a fractal here.
Or further simplified... Fractals are mathematical representations of geometric shapes that are "rough" or "complex".
See an excellent interview with Benoit Mandelbrot here.
See the Public Broadcasting Service's program Nova on fractals called "Hunting the Hidden Dimension" online here.In our education systems to teach geometry, we have simplified it and described it with clearly defined and recognizable shapes like circle, triangles, etc. With fractals comes understanding existing and development of new shapes both physical and virtual that mimic nature. Rather then my listing the large number of applications of fractals, see this site for fractal use. For a little more in depth mathematical understanding, see here.
What has driven me to write about fractals after having studied them for couple of decades is the application in the form of fractal antennas. See a company solely dedicated to selling fractal antennas here.See a bit more detail here.
I believe, the combination of fractal antennas and the substantial drop in manufacturing prices of RFIDs due to discoveries in cellulose based dielectric, the future is all about any and all objects being tagged, tracked and data based.
As my good friend Mr. Chris Downs of LiveWork (see my blog here) states, "It is all about the new oil called data".