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.

aperiodic flowers with bird

"Oasis"
Aperiodic tiles Penrose P1 (Tribute to Sir Roger Penrose)

aperiodic fish & seaweed

"Exuberance & Aridity"
Aperiodic tiles Penrose P1

large aperiodic tessellation

"Mural Flowers & Bird"
Aperiodic tiles Penrose P1

aperiodic rose with birds

"Pentagonal rose with birds"
Aperiodic tiles Penrose P2

aperiodic rose with fishes

"Greeny & Rosy the aperiodic fishes"
Aperiodic tiles Penrose P3

aperiodic starfish & shells

"Aperiodic Isle"
Aperiodic Starfish, Ivy leaf & Hex Tiles

aperiodic flowers

"Pentagonal Flowers"
Aperiodic Starfish, Ivy leaf & Hex Tiles

aperiodic tessellation with birds

"Bunch of Birds"
Aperiodic tiles Danzer triangles (Tribute to Ludwig Danzer)

aperiodic tessellation with fishes

"4 Fishes 4 Directions"
Aperiodic modified Robinson tiles (Tribute to Raphael Robinson)

aperiodic tessellation with sea shell

"5 Fishes 4 Directions"
Aperiodic modified Ammann A1 tiles (Tribute to Robert Ammann)

aperiodic tessellation with houses

"Robert's Little House"
Aperiodic Ammann A5 tiles

aperiodic cat

"Mistigri & the magic Y"
Aperiodic Nicolas tile

aperiodic stem flowers

"Stems & Flowers"
Aperiodic Nicolas tile

aperiodic butterflies

"Springtime"
Aperiodic Nicolas tessellation

spiral with aperiodic set of 2 x 36° lozenges

"Spiral"
Non-periodic tessellation

sunrise with aperiodic set of 2 lozenges

"Sunrise"
Non-periodic tessellation

star with set of 2 lozenges aperiodic

"Seven-pointed star"
Non-periodic tessellation

non-periodic happy man tessellation

This "Happy Man" opens the gallery
Non-periodic tessellation

non-periodic cat cube tessellation

"Cats & Cubes"
Non-periodic tessellation

non-periodic rebel ducks tessellation

"Three Rebel Ducks"
Non-periodic tessellation

non-periodic triton tessellation

"Tritons"
Non-periodic tessellation

non-periodic birds with stars tilings

"Stars Birds"
Non-periodic tessellation

non-periodic snakes tilings

"Snakes"
Non-periodic tessellation

non-periodic duck tilings

"Duck diamond"
Non-periodic tessellation

non-periodic tilie goose tessellation

"Tilie, the magic goose"
Non-periodic tessellation

non-periodic looping birds tessellation

"Looping"
Non-periodic tessellation

non-periodic lion cub tessellation

"Lion Cub"
Non-periodic tessellation

non-periodic bird in hexagon tessellation

"3 Birds in a hexagon"
Non-periodic tessellation

non-periodic goose tessellation

"2 Gooses in a Rhomb"
Non-periodic tessellation

non-periodic toucan tessellation

"Toucan 2 Profiles"
Non-periodic tessellation

non-periodic birds 2 in a square tessellation

"2 Birds in a Square"
Non-periodic tessellation

non-periodic ghosts & fishes tessellation

"Ghost of the Fish"
Non-periodic tessellation

non-periodic dog tessellation

"Sitting Puppy?"
Non-periodic tessellation

non-periodic dog tessellation

"For Whom the Sugar?"
Non-periodic tessellation

aperiodic infinity

"Non-periodic Infini (Infinity in French)"
Non-periodic tessellation

non-periodic fishes tessellation

"Nightmare"
Non-periodic tessellation

aperiodic flowers tessellation

"Non-periodic Flowerbed"
(Tribute to Josh Socolar)

non-periodic spiral tessellation

"Triangulated Whirlpool"
Non-periodic tessellation

non-periodic 4 directions tessellation

"Four Horizons"
Non-periodic tessellation

non-periodic hexagon tessellation

"Miss Fish"
Non-periodic tessellation

non-periodic rabbit tessellation

"Cairo Little Rabbit"
Non-periodic Cairo tessellation

non-periodic human tessellation

"Boules Player"
Non-periodic tessellation

non-periodic cats tessellation

"Cranky Cats & Joyful Cats"
Non-periodic tessellation

non-periodic animals tessellation

"Disappearance of a Goose on a Cats Background"
Non-periodic tessellation

non-periodic fishes

"Fishes’ Eyes Grid"
Non-periodic tessellation

curvilinear perspective

"Child's Eye View #2"
Same birds as "Pentagonal Convergence"

non-periodic chicken

"Chicks & Chickens"
Non-periodic tessellation

non-periodic fishes

"Pentagonal Swimming"
Non-periodic tessellation

non-periodic pentagonal birds

"Pentagon with Birds"
Non-periodic tessellation

non-periodic hexagonal birds

"Profile Bird"
Non-periodic tessellation

non-periodic cats

"Tidy & Untidy Kittens"
Periodic & non-periodic tessellations

pentagram with lizards tessellation

"Pentagram with lizards"
Non-periodic tessellation

non-periodic fishes

"Different"
Non-periodic tessellation

aperiodic birds

"Pentagonal Convergence"
Non-periodic tessellation

non-periodic human

"The Blues of Clown"
Non-periodic tessellation

non-periodic ghost

"The Ghosts of Decagone"
Non-periodic tessellation

non-periodic human

"Pentagonists Order"
Non-periodic tessellation

non-periodic symmetric birds

"Attraction"
Non-periodic tessellation

non-periodic elephant

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

non-periodic birds

"Pentagonal Flight"
Same birds as "Pentagonal Convergence"

non-periodic bird pyramid

"Birds Pyramid"
Non-periodic tessellation

non-periodic gooses

"Twin Gooses Assembly"
Non-periodic tessellation

non-periodic tiling

"Quadrilaterals and fireworks"
Non-periodic tessellation

non-periodic umbrella

"Umbrella with Birds"
Non-periodic tessellation

non-periodic rainbow

"Rainbow Birds"
Non-periodic tessellation

non-periodic fish

"Square with Fishes"
Non-periodic tessellation

non-periodic ducklings

"Ducklings & Little Fishes"
Non-periodic tessellation

non-periodic cats

"Hexagon with Cats"
Non-periodic tessellation

non-periodic rays

"Ornithological Rays"
Same birds as "Attraction"

non-periodic sun

"Sun"
Non-periodic tessellation

non-periodic fishes tiling

"Whirpools"
Non-periodic tessellation

non-periodic fish tiling

"Who Eats Who?"
Non-periodic tessellation

non-periodic bird tiling

"Hexagon with Birds"
Non-periodic tessellation

non-periodic hexagons tiling

"Fishes in Hexagons"
Same fishes as "Whirpools"

non-periodic ducks tessellation

"The Square of the Twin Ducks"
Non-periodic tessellation

non-periodic fishes tessellation

"Affluence"
(Tribute to John A.L. Osborn)
Non-periodic tiles type Osborn

non-periodic isosceles birds tessellation

"Isosceles Birds"
Non-periodic tiles type Osborn

MORE TO COME

Alain NICOLAS