Patterns - Tiling Patterns

Definition of Tiling: Tiling, or tessellation, is a way of covering a flat surface using geometric shapes so that there are no gaps and no overlaps. Imagine a bathroom floor where every tile sits perfectly next to the others.

The Unit Shape: Every tiling pattern is made of a basic 'unit shape' that repeats over and over. For example, in a brick wall, the unit shape is a rectangle, and in a honeycomb, the unit shape is a hexagon.

No Gaps or Overlaps: For a pattern to be a valid tiling, the space between shapes must be $0$. If you can see the floor through the shapes (a gap) or if one shape sits on top of another (an overlap), it is not a tiling pattern.

Regular Tiling: This occurs when the pattern is made using only one type of regular polygon, such as all squares, all equilateral triangles, or all hexagons. A checkerboard is a perfect visual example of regular tiling using squares.

Patterns and Colors: Tiling often uses alternating colors to create a visual pattern. In a sequence of tiles, if the first is Red and the second is Blue, the pattern usually continues as Red, Blue, Red, Blue.

Tiling with Multiple Shapes: Patterns can also be created using two or more different shapes that fit together. For instance, an octagon (8-sided shape) and a small square can be placed together to cover a floor perfectly.

Symmetry in Tiling: Many tiling patterns are symmetrical, meaning if you draw a line through the middle, both sides look like mirror images. Visualizing a grid of squares, any horizontal or vertical line through the center of the tiles represents an axis of symmetry.