Digital Kaleidoscope: Triangular Tiling with Textures
This Demonstration tiles the plane in kaleidoscopic fashion, with textures defined from portions of images drawn from the Wolfram example data library. Controls are provided to select the location and magnification within the image for use in the tiling. You can change the shape of the triangles by clicking inside the image area. It may be more convenient to work with a small portion of the full tiling (set "tile image area" control toward the left) and then adjust the image. Increasing the "tile image area" slider retiles the image area.
The construction begins with an arbitrary triangle. The tiling reflects the triangle about each of its three sides. Each of these triangles is then similarly reflected times to fill up the whole plane, where is specified by the "tile image area" slider. The points of the triangle can be changed by dragging in the image area. Clicking close to one of the vertices causes that vertex to relocate to the mouse position; dragging the vertex causes the triangles to continuously resize. Increasing the jitter slider adds a random value to each point in the construction for a more organic feel.