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.)

figure 19

figure 19a