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

aperiodic infinity

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

non-periodic cats

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

pentagram with lizards tessellation

"Pentagram with lizards"
Non-periodic tessellation

aperiodic rose with birds

"Pentagonal rose with birds"
(Tribute to Sir Roger Penrose)
Aperiodic tiles Penrose P2

aperiodic rose with dogs and birds

"Nosy & Tubby, the aperiodic pals"
(Tribute to Robert Ammann)
Aperiodic tiles Ammann A5

aperiodic rose with fishes

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

aperiodic rose with lizards

"The family of aperiodic lizards"
Aperiodic divided tiles Ammann A5

non-periodic fishes

Non-periodic tessellation

non-periodic birds

"Pentagonal Flight"
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 rays

"Ornithological Rays"
Non-periodic tessellation

non-periodic elephant

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

aperiodic birds

Non-periodic tessellation