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Last year, I became interested in voronoi patterns. These patterns are found in nature (ex., soap bubbles, butterfly wings, giraffe spots, etc). In addition, these patterns are applied in economics, math, and computational geometry as well. They are referred to as a "Voronoi Diagram". Other Machine Co. has a great definition for Voronoi Diagram:

A Voronoi diagram is a mathematical method of dividing space into regions. Seed spots are spread along a field, and polygons are generated around these seed spots. The polygons are every point in space around a seed spot that are closer to that seed spot than any other (here's a little more about them if you are curious).

As a computational designer, I am constantly searching for new algorithms to help create new and novel forms. After much research on voronoi patterns I started sketching with code (openFrameworks).

I then created an application which allowed me to analyze the cell sites of the voronoi diagram and to understand how these 2D diagrams evolve over time. The application also allowed me to see the 3D forms created by the 2D cell slices stacked over time. You can see some of what I am referring to in the video above; note how the 3D forms evolve over time as the cell sites move.

Individually, these 3D shapes are out of this world. They create a challenging, but fun, puzzle to put together. I extended the application in order to 3D print the puzzle. In this Instructable, I'll be describing how to generate and print the puzzle shown above.

Step 1: Generate 3D Voronoi Puzzle

The puzzle was generated by the previously described application. This application uses a particle system to control cell site position. These particles were given several behaviors to vary their positions over time. These behaviors represent forces used to influence particle positioning.

The application has the ability to generate millions of unique puzzles. It's user interface exposes variables that control the particle system (which then control how the cell sites move over time). This interface also controls puzzle dimensions and resolution of the 3D forms (number of time slices). Check out screenshots from the application.

<p>Each piece looks like a cool faceted crystal. Really beautiful work.</p>
<p>Thanks Audrey! :)</p>
<p>I want one. I want to make one. Making it and solving it both look fun.</p><p>I think I will experiment with paper first.</p>
<p>Reallly very good, no, excellent. I wonder what the acoustic vibration looks like?</p>
<p>Wow!</p>
Amazing! I see next Christmases hot gift idea.
<p>*jaw drops* :O whaaaaaaaaaaaaaaaaaaaaaaaaaaaa?</p><p>(I think I was gonna say somthing but now I'm only gonna say ) HOW??????</p>
<p>Very cool, I know the terminology from a resource estimation methodology (2D and now defunct), but I've never seen such a pretty touchable representation. Very clever! </p>
Awesome! I love Voronoi and what you've done with them :)
that's really cool
<p>Thanks Livichris!</p>

About This Instructable

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Bio: Reza is a computational designer & creative engineer. He uses code to express himself, and creates tools and libraries to help others create. He is the ... More »
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