Escher created the following tessellation "Pegasus" with this method.

What is required is a more in-depth, extensive account of the intricacies; of which the following essays sets out in detail the how's and why's. By so doing, I hope to encourage further development of the subject, having laid out solid foundations from which to proceed. Essentially, people who approach the subject have to start from scratch, in effect the equivalent of reinventing the wheel each time. As I demonstrate, one's mathematical limitations are not a hindrance or barrier in the subject. Not by no means has Escher exhausted the subject, as may have been thought due to inferior examples produced by his (few) successors. For instance, he missed a whole type, of what I consider my own speciality, ‘geometric outlines', whereby the tile is simply awaiting the addition of a motif. Even amongst individual creatures, quality examples exist of those that he missed, for example the rabbits of Makato Nakamura and kangaroos of Bruce Bilney. Developments since the time of Escher have involved the use of the computers in the drawing and design of tessellation. However, again, use of such technology is shown to be unnecessary. Therefore, demonstrably, the field is still open to anyone, whatever their background, who simply has the desire to attempt such things.

And some people allow curved shapes (not just polygons) so we can have tessellations like these:

It was David Brewster, ‘the father of modern experimental optics’, who founded the sci­ence of optical mineralogy and first annotated these patterns. Knowing all too well of the allure of the prismatic figures he discovered during his polarisation experiments he invented the Kaleidoscope in 1816. This most famous of all optical toys encodes the laws and properties of light for amusement, as well the mechanics of symmetry and tessellation. Polariscopes and Conoscopes, the more serious utilitarian siblings of the Kaleidoscope, were the optical devices used to view and annotate the interference figures found in this post.

Essays about Tessellations - Is Your Art "Good enough" …

A tessellation is created when a shape is repeated over and over again covering a plane without any gaps or overlaps.

There are an infinite number of tessellations that can be made of patterns that do not have the same combination of angles at every vertex point. There are also tessellations made of polygons that do not share common edges and vertices. You can learn more by following the links listed in .

How to Make a Translation Tessellation. Do you love those cool pictures that seem to shift before your eyes? Are you fascinated by the shapes blending into each other?

Aside from tessellations, Escher also explored the idea of unlimited spaces. With these drawings, he was able to compliment the notion of infinity that he portrayed with tessellations. In drawings such as Depth (see ), Escher depicted a never-ending line of geometrical, torpedo-like fish fading off into nothingness. This was another one of the ways that he shared his concept of endlessness. Escher focused on this style in the mid 1950's, just after his peak work with tessellations.

Tessellate!: Create a tessellation by deforming a triangle, rectangle or hexagon to form a polygon that tiles the plane. Corners of the polygons may be dragged, and corresponding edges of the polygons may be dragged.

Escher was a great master of tessellation (the regular divisionof the plane, or tiling). He created symmetrical designs and planar tesselations,which he described as congruent, convex polygons joined together."

Escher, however, was fascinated by every kind of tessellation - regular and irregular - and took special delight in what he called "metamorphoses," in which the shapes changed and …

Tessellations are very difficult to create because of the geometrical preciseness needed to interlock the patterns. Yet, Escher did not just simply draw basic tessellated patterns; he incorporated them into much of his artwork and even went as far as morphing tessellations together. He enjoyed experimenting with them to show his own philosophies and theories as in Whirlpools (see ), where he created two swirling tessellations bound together by an s-shaped spiral, or as in Circle Limit III (see ), where the tessellated pattern diminishes in size as it stretches outward towards the edge of the circle. Designs like these were repeated often in Escher's work and through these pieces, he was able to reveal some of his ideas about the concept of endlessness.