Pentagonal, triangular, hexagonal and other cool geometric tilings

One of the possible things to do in Filter Forge is to make geometric tilings and grids and here I want to share many different examples found on Wikipedia and other places showing the many and varied different possible ways that it can be done

Many of these are already available as filters in the FF library or forum, especially the ones done very well by Rick Duim ( see below)

These below are the descriptions and examples found on wikipedia, but there are many more websites about these different tilings and with even more examples

To start, a list of some of them

List of convex uniform tilings

Regular and semi-regular tilings

Tessellations by Polygons

And now some specific ones

Pentagonal tilings

Triangular tilings

Hexagonal tilings

Heptagonal tiling of regular hyperbolic tiling

Uniform tilings in hyperbolic plane

List of isotoxal polyhedra and tilings

Penrose tilings

Quote
A Penrose tiling is a non-periodic tiling generated by an aperiodic set of prototiles.

Rep-tile tiling

Quote
In the geometry of tessellations, a rep-tile or reptile is a shape that can be dissected into smaller copies of the same shape.

Pinwheel tiling

And there are more in this following one

All the above and the one below here are from wikipedia

TESSELLATION

Tessellation on wikipedia

Quote

A tessellation of a flat surface is the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps.  A periodic tiling has a repeating pattern. Some special kinds include regular tilings with regular polygonal tiles all of the same shape, and semi-regular tilings with regular tiles of more than one shape and with every corner identically arranged. The patterns formed by periodic tilings can be categorized into 17 wallpaper groups. A tiling that lacks a repeating pattern is called "non-periodic tiling". An aperiodic tiling uses a small set of tile shapes that cannot form a repeating pattern.

Rick Duim have done already an awesome, amazing and excellent work reproducing the 17 wallpaper groups in a easy way to use in FF

Also in the FF forum there is a very good hyperbolic tiling filter

And there is many other filters that cover many of these tilings shown above

Fractal tessellation


There are other kind of tilings that will not fill a plane and are based on fractal distribution

Compendium of fractal tiling

INCREDIBLE ART MADE WITH TESSELLATIONS

Now that is shown the basics, will see how it was applied by some great artists

Art Tessellations - Everything You Ever Wanted to Know - Incredible Art Department

As shown in this above link, M.C. Esher designed a tessellation that is not based in any geometric shape ànd uses his own shapes as shown in the official website here

And another art tiling

Random fractal tiling plane vine videos

Will put more on another post

Hope this may be useful