In September 2018 I gave a presentation about patterns constructed using grids at the 4th International Workshop on Geometric Patterns in Islamic Art in Istanbul. For the presentation I prepared these timelapse videos demonstrating different methods for constructing grids using ruler and compass and I have posted them here to be of service to a wider audience.
Square and isometric (triangular) grids provide a rich and expansive foundation for the exploration of geometric patterns. They have arisen from the simplest regular divisions of the 2D plane. The triangle and the square are two of the three regular polygons which can tile a 2D plane by themselves. The hexagon is the third but can be seen as a combination of 6 triangles so equates directly with the isometric grid. These first two videos show the basic construction of the hexagon and square from the circle, fundamental constructions in the study of geometric art.