Castellations

by Jglass

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 b