Real world tiling  
Appearance  Links 
Brief Remarks  Appearance  Links  Brief Remarks  
Copenhagen  Link  Bruges  
Savador Dali, playing with a classical deterministic tessellation involving squares and equilateral triangles.  The definitive collection of regular (deterministic) tessellations: http://www.tilingsearch.org/ It features over 2000 different tiling patterns, many crowdgathered from Islamic art, others from mathematical theory.  
Link/Explanation Allied Link History of the Cairo Tiling (from David Bailey)  Bev
Dunbar and Chrissy Monteleone's photo of "pentagon used to
decorate steps on a veranda in Earlwood, Sydney, Australia, dated about
the 1960s." From David Bailey's extensive site containing many deep analyses of interesting tessellations and their histories. 
Dailey's work with tiling (hosted at ello.co/ddailey and on cs.sru.edu/~ddailey)  
Generally, in the majority of these, at least, a single tile (shape) is used, but its various orientations are all differently colored. So for example, the concave equilateral pentagon shown in the first row below, has 10 different orientations (each 36 i for 0 ≤ i < 360 degrees). I find this makes it easier to identify subtle differences between tessellations.  
Appearance  Links 
Brief Remarks  Appearance  Links 
Brief Remarks  
Link/explanation Allied link Allied link 
Concave equilateral pentagon: an animated introduction Explore these, here, at your own pace (using scrollbars and zoom) 
Concave equilateral pentagon: animated gallery of options  
Link Allied link 
Experiments with clusters of the above concave equilateral pentagon. (It turns out there are 422 options for tetraominoes.)  Link Allied link Allied link 
Fanciful arrangement of clusters of these.  
Link  Link  Concave Equilateral Heptagon.  
Link  One of three quadrilateral segments of an equilateral triangle.  Link  Ways of partitioning hexagons into shapes which tile (ideally in ways other than the classical honeycomb/hexagonal tessellation).  
Link  Quadrilateral halfhexagons.  Link  Snowflakelike clusters of halfhexagons. (Pretty!)  
Link  Showing how to tessellate in an outward spiral (avoiding all but a few hexagonal dominoes) and then replicating the resultant teardroppentagon from there.  The clustered teardrop pentagon make some nice patterns, but I'm not sure if it can continue nondeterministically.  
Link  More experiments with a (larger) clustered spiral teardrop.  Link  This particular cluster of halfhexagons forms an 18sided polygon, which itself tessellates deterministically.  
Link/explanation  Demonstrating how the Ltriomino forms a "reptile"  i.e., makes successively larger but similar (same shaped) versions of itself.  Link Explanation 
Triangle adjoining smaller rhombus. 1/24th of an equilateral triangle. 1/12th of a hexagon. "reptiles" fractally. See also below (Another way of joining a large triangle with a smaller rhombus.) 

Link  Double rhombuses aka sixths of a hexagon  Link  V's and faultlines. To what extent can a periodic tiling be completely characterized by its partial faultlines? I don't know the answer. 


explanation link  Gallery: Big and little triangles sharing an edge and a vertex to make a concave pentagon.  explanation
link allied link 
Explorations: Big and little triangles sharing an edge and a vertex to make a concave pentagon. 

Link Explanation 
Parallelograms: clusters of 3 x 4 and 4 x 3. Same tile as above but in curiously heterogeneous, though extensible arrangement. Note that it consists of differently oriented parallelograms, each composed of the same four basic orientations.  Explanation Link 
Same as at left but with animated gradients (for fun)  
Link Explanation 
Sliced pentagons. Take an equilateral triangle and a square. Hook them together to make a pentagon. Then cut that in half.  Link Explanation 
One of many tessellations involving the sliced pentagons seen at left.  
Link Explanation 
Castile and Leon come to Teotihuacan  eLink SVG Link 
Sshaped tile used radially.  
Link Explanation 
Heptagonal Hexatriominoes Closeup (1  5) Closeup (6  11) Closeup (12  18) Closeup (19  22) 
Link Explanation 
Funky Mandala  
Link  Asterisks made of double halfhexagons.  SVG
Link Elink 
Deconstructed asterisk using dominoes made of halfhexagons.  
Link Explanation 
Gallery of tilings made with double halfhexagons.  Link Explanation 
Nonagonal Heptatriominoes: Seven triangles hooked together into a nonagon.  
Link Explanation Link 
Tiling with thirds of a hexagon (Part I)  Link other colors 
Heptagonal thirds of a hexagon. A slightly different shape than seen at left. It is also three of the double half hexagons seen above left (e.g., here).  
Explanation Link 
Tiling with sixths of a hexagon. Part 1.  Link Explanation 
Tiling with sixths of a hexagon, Part 2. This shows that most of the ways that one might try to tessellate with this shape, simply don't work.  
Explanation Link 
Tiling with sixths of a hexagon. Part 3.  Explanation Link 
Tiling with sixths of a hexagon. Part 4. I think I need to write a Part 5.  
Link  Reptiling with sixths of a hexagon, by making successively larger hexagons.  Explanation Link Explanatory link 
Nice tiling with ektohexagons. It's fourcolored (meaning using four orientations) and faultless (meaning having no continued faultlines  unlike 'most' tesselations using this tile).  
Link Explanation 
An idea based on the Ltetramino. I tried to replicated it along a baseline and to extend upward from there. Unsure if it can continue.  Link  
Link  Dented octagons  Link  Octagonal crescents  
Link  A concave equilateral pentagon with interior angles of 60, 90, 60, 300 and 30.  Link  Another way of joining a large triangle with a smaller rhombus.  
Explanation Link Link Link  A fourth of a square with a bit of family history.  Link Allied link  Squares with equilateral triangles.  
Link Explanation  Guangdongese Cell Phone Towers. Tiling with Vshapes, made of six equilateral triangles. I don't remember if these tile any way other than as dominoes made into parallelograms. 
Tessellationlike things (packings, knot tilings, paradoxes, etc)  
Appearance  Links  Brief Remarks  Appearance  Links  Brief Remarks  
Link Explanation 
Superstrong carbon mesh with quinary memory. (Simple nondeterministic paradoxical tessellation). See here for more on paradoxical tiling.  Link  Deforming a square tessellation (using SVG animate)  
Making moirelike patterns out of overlayed and animated squiggles.  Link  Dynamic tessellations formed from shapemorphing animations.  
Link Explanation Allied Link Allied Link Allied Link 
Positron emission tomography  Animated
Explanation Scrollable Explanation Link/Explanation Allied Link 
Systematic enumeration of Knottiles  
Explanation Link 
Paradoxical tiling  




Animations of tessellations (already studied by others) including morphs.  
Hooking squares and equilateral triangles together, replicating and animating (just for fun)  Link Allied Link 
Twirling the SVG pattern space of the (3,4,3,3,4) tessellation of squares and triangles.  
Link Allied link 
More work with the (3,4,3,3,4) tiling, showing that it tiles nondeterministically.  Explanation  The (3,4,3,3,4) tiling is the first nondeterministic tiling I worked with, some forty years ago. I need to develop something deeper to show some of my investigations.  
Link  A fun concave decagon that hooks with itself. Also this demonstrates how to make a rectangular segment that can be used as an SVG <pattern> block to avoid having to replicate or re<use>, hence allowing largescale animations that are faster than the equivalent built of numerous vectors.  Same as at left, but making the SVG <pattern> space visually obvious.  
Link  Morphing between two tessellations by expanding the borders (the grout) and celebrating them as full partners in tiling.  Link  Bistable rotation of SVG pattern space  
Link  Link Allied Link Allied Link 
Fun use of animated gradients in simple triangular tiling.  
Link  Explanation  
Link Allied Link Allied Link Allied Link  Clock tiles  