# Simple tessellation

## combining sequences

An array can be generated as a single list by combining sequence commands as shown below:
sequence[sequence[translate[poly1, m*u+n*v], m, -3, 3], n, -3, 3]
In the algebra view, there is only one list (which is list3) created by this command, which contains 7X7=49 copies of poly1.

## figure 17

## adjust the vectors

The vectors are rearranged to make them equal to the diagonals of poly1. The result shows a tessellation with the given quadrilateral. (The space enclosed by 4 quadrilaterals can be covered by an inverted copy of the quadrilateral.)

## figure 18

## redefine the vectors

In figure 19, the vectors are redefined in terms of the vertices of the quadrilateral, forming two diagonals. Drag the 4 vertices to see how the vectors change and the tessellation pattern maintains. The short video below shows how the vectors are redefined. (Double each vector to edit its definition.)