 Many Islamic designs are built on squares and circles , typically repeated , overlapped and interlaced to form intricate and complex patterns . A recurring motif is the 8 @-@ pointed star , often seen in Islamic tilework ; it is made of two squares , one rotated 45 degrees with respect to the other . The fourth basic shape is the polygon , including pentagons and octagons . All of these can be combined and reworked to form complicated patterns with a variety of symmetries including reflections and rotations . Such patterns can be seen as mathematical tessellations , which can extend indefinitely and thus suggest infinity . They are constructed on grids that require only ruler and compasses to draw . Artist and educator Roman <unk> argues that such constructions are in effect algorithms , making Islamic geometric patterns forerunners of modern algorithmic art . 
