When a quadrilateral with no two opposite edges equal in length, is extended along its two shorter edges by copying a scaled copy of the same over and over, they converge to a single point in plane. However, in general, the quadrilaterals do not coincide when the clockwise and counter-clockwise arms meet. This paper searches for the conditions under which such coincidence is possible and hence provides a method to construct such spirals. The paper further explores how these quadrilateral spirals can be used to create Escheresque tessellations and convert some of Escher’s planar tilings into spiral ones.