Pattern designs created in different cultures have been a subject of mathematical analysis and only recently they have been created (using computers) based on the new mathematical knowledge like hyperbolic geometry. Visualization of hyperbolic plane, even of the basic objects and their images under isometries, can be highly symmetrical and visually attractive .

Using Mathematica package Tess [6] different types of tessellations and all possible realizations can be generated:

• uniform (3,7,3,7) and (9,12,12)
• chiral uniform (3,3,3,3,3,4)
• chiral non-uniform (3,4,6,3,6).

There are no limits on the choice of polygons or the number of polygons around each vertex. Moreover, polygons of the same colour can be mapped on each other by isometries which do not change the tessellation, or we can obtain various “coloured” tessellations