_{}** NON-PERIODIC TESSELLATIONS **_{}

Another extraordinary possibility regarding the tessellations, and never explored by Escher, is that of non-periodic tiles and tessellations.

A periodical tessellation is a set of tiles that pave the plan to infinity by reproducing by translations.

A non-periodic tessellation is a set of tiles that pave the plan to infinity, but without translations.

Its tiles can be either periodic or aperiodic.

Some periodic tiles can pave the plan non-periodically.

A set of aperiodic tiles can only paves the plan non-periodically.

You can take any part of an aperiodic tessellation, however large it is, you will not be able to translate it.

You will find them first. Click on the constructions to see the tessellations.

Then you will find non-periodic tiling.

For good clarity, the values of the interior angles are shown on the outside.

All the drawings are copyright Alain Nicolas, all rights reserved. You must get my permission to reproduce any of my work.

"Oasis"

Aperiodic tiles Penrose P1 (Tribute to Sir Roger Penrose)

"Exuberance & Aridity"

Aperiodic tiles Penrose P1

"Mural Flowers & Bird"

Aperiodic tiles Penrose P1

"Pentagonal rose with birds"

Aperiodic tiles Penrose P2

"Greeny & Rosy the aperiodic fishes"

Aperiodic tiles Penrose P3

"Aperiodic Isle"

Aperiodic Starfish, Ivy leaf & Hex Tiles

"Pentagonal Flowers"

Aperiodic Starfish, Ivy leaf & Hex Tiles

"Bunch of Birds"

Aperiodic tiles Danzer triangles (Tribute to Ludwig Danzer)

"4 Fishes 4 Directions"

Aperiodic modified Robinson tiles (Tribute to Raphael Robinson)

"5 Fishes 4 Directions"

Aperiodic modified Ammann A1 tiles (Tribute to Robert Ammann)

"Robert's Little House"

Aperiodic Ammann A5 tiles

"Mistigri & the magic Y"

Aperiodic Nicolas tile

"Stems & Flowers"

Aperiodic Nicolas tile

"Springtime"

Aperiodic Nicolas tessellation

"Spiral"

Non-periodic tessellation

"Sunrise"

Non-periodic tessellation

"Seven-pointed star"

Non-periodic tessellation

This "Happy Man" opens the gallery

Non-periodic tessellation

"Cats & Cubes"

Non-periodic tessellation

"Three Rebel Ducks"

Non-periodic tessellation

"Tritons"

Non-periodic tessellation

"Stars Birds"

Non-periodic tessellation

"Snakes"

Non-periodic tessellation

"Duck diamond"

Non-periodic tessellation

"Tilie, the magic goose"

Non-periodic tessellation

"Looping"

Non-periodic tessellation

"Lion Cub"

Non-periodic tessellation

"3 Birds in a hexagon"

Non-periodic tessellation

"2 Gooses in a Rhomb"

Non-periodic tessellation

"Toucan 2 Profiles"

Non-periodic tessellation

"2 Birds in a Square"

Non-periodic tessellation

"Ghost of the Fish"

Non-periodic tessellation

"Sitting Puppy?"

Non-periodic tessellation

"For Whom the Sugar?"

Non-periodic tessellation

"Non-periodic Infini (Infinity in French)"

Non-periodic tessellation

"Nightmare"

Non-periodic tessellation

"Non-periodic Flowerbed"

(Tribute to Josh Socolar)

"Triangulated Whirlpool"

Non-periodic tessellation

"Four Horizons"

Non-periodic tessellation

"Miss Fish"

Non-periodic tessellation

"Cairo Little Rabbit"

Non-periodic Cairo tessellation

"Boules Player"

Non-periodic tessellation

"Cranky Cats & Joyful Cats"

Non-periodic tessellation

"Disappearance of a Goose on a Cats Background"

Non-periodic tessellation

"Fishes’ Eyes Grid"

Non-periodic tessellation

"Child's Eye View #2"

Same birds as "Pentagonal Convergence"

"Chicks & Chickens"

Non-periodic tessellation

"Pentagonal Swimming"

Non-periodic tessellation

"Pentagon with Birds"

Non-periodic tessellation

"Profile Bird"

Non-periodic tessellation

"Tidy & Untidy Kittens"

Periodic & non-periodic tessellations

"Pentagram with lizards"

Non-periodic tessellation

"Different"

Non-periodic tessellation

"Pentagonal Convergence"

Non-periodic tessellation

"The Blues of Clown"

Non-periodic tessellation

"The Ghosts of Decagone"

Non-periodic tessellation

"Pentagonists Order"

Non-periodic tessellation

"Attraction"

Non-periodic tessellation

"Elephant"

Non-periodic tessellation. The outer contours are periodic, but not the interior designs

"Pentagonal Flight"

Same birds as "Pentagonal Convergence"

"Birds Pyramid"

Non-periodic tessellation

"Twin Gooses Assembly"

Non-periodic tessellation

"Quadrilaterals and fireworks"

Non-periodic tessellation

"Umbrella with Birds"

Non-periodic tessellation

"Rainbow Birds"

Non-periodic tessellation

"Square with Fishes"

Non-periodic tessellation

"Ducklings & Little Fishes"

Non-periodic tessellation

"Hexagon with Cats"

Non-periodic tessellation

"Ornithological Rays"

Same birds as "Attraction"

"Sun"

Non-periodic tessellation

"Whirpools"

Non-periodic tessellation

"Who Eats Who?"

Non-periodic tessellation

"Hexagon with Birds"

Non-periodic tessellation

"Fishes in Hexagons"

Same fishes as "Whirpools"

"The Square of the Twin Ducks"

Non-periodic tessellation

"Affluence"

(Tribute to John A.L. Osborn)

Non-periodic tiles type Osborn

"Isosceles Birds"

Non-periodic tiles type Osborn