Escher-like mosaics

M.C. Escher is well known by his artistic regular plane divisions and artworks of impossible constructions. But he also created several artworks with irregular mosaics, which consist of shapes of various animals. Two of them you can see below. As you can see every animal in mosaics are fit all its neighbours without any gaps.

Today may artists follow the way of Escher in creating complex mosaics. Images of Bobby Bogl are worthy, which you can see below. Take a notice of how all parts of his images accurate match to each other.

Escher's building in origami

Some people redraw Escher's artworks with computer, the others create woodcarvings based on Escher's lithographs, but Ingrid Siliakus crates Escher's buildings using paper. I don't know how this kind of art can be called. I think it's a branch of origami.

UPDATE (thanks to lispnik):

This kind of art is called kirigami that is variation of origami, where the artist is allowed to make small cuts in the paper.

Below you can see some Escher-like kirigami works with respective originals.

Balcony

Relativity

Convex and concave

These images are close to originals by M.C. Escher. More such style origami constructions can be seen here http://haha.nu/amazing/unique-paper-cut-artworks/

Platonic solids with Escher's mosaics

With Escher's mosaics we can cover not only flat plane but also surfaces of platonic solids. Some Escher's tessellations can be divided into simple shapes such as triangle and square. Using these simple shapes we can cover facets of polyhedrons. Below, you can see several examples of covering of Platonic solids with Escher's mosaics.

These images was found at http://www.math-inf.uni-greifswald.de/mathematik+kunst/polyeder.html

Printgallery

M.C. Escher "Printgallery" (1956)

Printgallery is one of the most fascinating image of M.C. Escher. We see a young man which stands before print on the wall in print gallery. We see ships and seaside town with many houses on it. One house is closer to us than others and there's print gallery on the first floor. Then we look through the window of the print gallery and see young man looking at print. So we returned to beginning. It's a looped image, and we can infinitely look on it and never find the end.

But artist leaved center of the image empty and placed his sign there. What is under this blank spot? We don't know if Escher knew it. In 2002 this puzzle was solved and it's proved that reduced and rotated copy of the source image should be behind the spot.

A reptile from Escher's artwork

A very interesting object was found at Google Maps near Ciudad Juárez in Mexico. It represents a single reptile from Escher's artwork "Smaller and smaller" (1956). Below you can see the original Escher's artwork and part of it with reptile in similar position.

This artwork is an artistic illustration of hyperbolic space. Due to properties of such kind of hyperbolic space you can infinitely go towards the center of the square but never reach it. Also Escher illustrated hyperbolic space in his artworks "Snakes", "Circle limit IV" etc.

Möbius strip

Möbius strip a surface with only one side and only one boundary. It was first described in 1858 by German mathematician August Ferdinand Möbius and co-discovered by Johann Benedict Listing in the same year.

The most known illustration of the surface was created by M.C. Escher in his lithograph "Möbius band II" where read ants crawl by the Möbius strip.

Also it frequently being used in logos. The most famous is international symbol of recycling.

Introduction

There are many artists which are use various mathematical principles in their art. Frequently various polygons and solids are used but there'smany other themes in mathematics for art.

The most common themes in mathematical art are polyhedrons,fractals,tessellations,gold section, impossible figures, strange surfaces.

The most known mathematical artist is M.C. Escher from Holland. Many mathematical laws laid down in his lithographs such as tessellations, polyhedrons and impossible figures.