Beach Inspirations

A sandy beach is essentially an infinite, maleable, instantly-erasable, reshape-able plane; a whiteboard on which patterns can be created, modified, erased, and washed away. Relationships can be formed and destroyed with a shovel, a bucket, a hand, or a wave. And the space available for exploration is vast, practically infinite.

A beach can naturally be filled with dunes, with children, with sun. But can math fill a beach? Can small shapes, ones we can hold in the palm of our hands, be made to cover wide sandy planes? Let's find out together by exploring tessellations.

The tessellation is a type of infinite pattern that completely covers a plane in one or more shapes. The squares of a checkerboard, carried out to infinity, are one basic type of tessellation, as are the cells of a honeycomb. These patterns, made of basic shapes (squares and hexagons, respectively), can both be carried out to infinitely, filling all the space on a plane, much as the sandy shore covers the water's edge.

But checkerboards and beehives are simple tessellations; each uses only one shape, in one scale, with no rotations; the mathematics of covering a plane run much deeper. In this thing, I aim to develop a basic set of sand sculpting tools to explore 2D geometry, and tessellations in particular, using sand.

Current Status

-July 25 - Parameterized the mold-making via OpenSCAD. Now, any 2D geometric shape that's describable can be turned into a sand-mold, and all molds will have common, adjustable properties for iteration. Published Project.

• July 24 - Changed name of project to Castellations. Couldn't pass up the Portmanteau
• July 23 - Start of project and first upload - a set of square sand stencils with varying profiles, to see if any are suitable for making shapes in sand

Shapes

-Square
-Equilateral Triangle
-Regular Hexagon
-Regular Octagon
-Rhombus (60/120 Degree)
-Rhombus (30/150 Degree)

Future Goals/Problems to Solve

• Make these bits into, well, castles! They're no fun if they're not castles...
• What vertical profile is best for engraving a design into sand? Are stamps or cutters better/more durable?
• Is there a way to enforce only edge-to-edge tessellations through design? (Notching, labeling?)
• Find a way to connect stencils/stamps together along edges, to create more complicated shapes.
• 3D Tessellations?
• Put the name/angle of each shape on a stamp?

The tessellation tiles are crafted programmatically in OpenSCAD, then combined into a single print using the MakerbotDesktop software.

Unfortunately, OpenSCAD doesn't quite have the math acument to programmatically determine the verticies of a regular polygon, so the basic shapes are created manually in code. A wrapper function then ensures that all finished prints have similar physical parameters (height, depth, labeling, etc.)