Castellations

thingiverse

A sandy beach is essentially an infinite plane; a canvas waiting for patterns that can be created, modified, erased, and washed away instantly. Relationships are formed and destroyed with a shovel, a bucket, a hand, or a wave. The space available for exploration is vast and practically endless. A beach can naturally be filled with dunes, children, or sun. Can math fill a beach? Can small shapes, ones we can hold in the palm of our hands, cover wide sandy planes? Let's find out together by exploring tessellations. The tessellation is an 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), can be carried out infinitely, filling all space on a plane. 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 project, I aim to develop basic sand sculpting tools to explore 2D geometry and tessellations 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 with common, adjustable properties for iteration. Project published. -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 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