**There is a form of spatial plot known as a Voronoi plot.** A diagram is shown here. The picture was borrowed from the brilliant people at Wolfram research. they make mathematica. Stephen Wolfram is behind the firm. If you get a chance take a look at his book A new kind of science. I will make some comments on it later. It is profound and a peak into a fascinating future of math, physics and complex systems understanding, that we have just started to understand.

The Voronoi tessellation or plot has many applications. If you have a look at the diagram to the left, you will notice points and vertices which create closed spaces or cells. This optimal (packing) plot is found in many places in natures and natural phenomenae where physical spaces and points of growth grow to define "boundaries".

Like many things in nature that are beautiful, the beauty emerges from a set of rules, governing symmetry, growth and pattern while allowing for diversity, strength and emerging complexity across scales. Imagine if you will each point to be the nucleus of a cell and the edges to be cellular walls.

One of the best sites to explore the Voronoi concepts is The Voronoi website. the Voronoi concept is used not only in small physically bounded regions such as biological cells but also in astronomy to identify likely galactic clusters (see paper here) and here as well

The concept also lends itself to many forms of optimization and problem solving for crude or abstract bounded set problems. The nature of an auto clustering algorithm on a 2d plane is very powerful. It is my belief that using iterative resolution voronoi plots, will be a way in the future for image recognition as it is the most logical to way to detect variance without use crude spectral analysis.

These 2 images are an example of high noise dataset reduced using a Voronoi map see here. The feature set is reduced significantly. My guess is that the delta of various plot resolutions would very effective for measuring and detecting crude sets or image identification. This is far more effective and probably efficient than edge detection and then spectral mapping.

As a clustering approach, something feels right to me about the Voronoi approach and I wouldn't be surprised to see it showing up in a lot of places in the future. As more analog data needs to be compared and contrasted in complex sets, this approach makes sense. Now that is all good and well for understanding "static" data matches or comparing static data over a dynamic range.

The other interesting application will be Voronoi plots involving Cellular Automata. Most CA models use simple regular boundaries, typically 2-dimensional squares. Wolfram's first work involved this. However, most phenemonae exhibit radial irregular boundary conditions that don't work for traditional lattice models etc. The Voronoi method of modeling things allows for "noise" within the micro boundary and positioning of elements, but gives a quick solution to synthesis and modeling. As of today no, language of Voronoi plots has evolved. My belief is it will. This is a rich field for exploration, Voronoi dynamics, fractal metrics and perhaps even a voronoi excited state model yielding something equivalent to a Feigenbaum constant remain to be discovered.

And here for a big finish is a really cool app call the Bubble Harp Scott Snibbe has made some fascinating works here. They aren't toys, they are windows on a rich and fascinating world. For fun install the bubble harp app and hold down your mouse as you create vertices. the resulting action almost looks like a beating heart :). The Voronoi concept is beautiful and will be profoundly revealing for years to come.