Relativity by M. C. Escher

http://en.wikipedia.org/wiki/Relativity_(M._C._Escher)

In the world of Relativity, there are actually three sources of gravity, each being orthogonal to the two others (in Wikipedia)

In the Futurama episode “I, Roommate“, Fry and Bender go apartment-hunting and visit a room that resembles the lithograph. Fry claims that he does not want to pay for a dimension he isn’t going to use; Bender then trips down one of the stairs and continues to fall (in Wikipedia)

Escher greatest expression came from his intuitive and visual concept of mathmatics, although he never had any formal training on that subject. He explored the infinity. Created images right out of his mind instead of directly from observation (surrealism). he re-invented tessellation (mosaic or tilling) by using this techinque on his art (plane figures filling the plane without gaps).

He wrote his first paper in 1936, called Regular Division of the Plane with Asymmetric Congruent Polygons, which detailed his mathematical approach to artwork creation. Escher developed a system of categorizing combinations of shape, color and symmetrical properties.

 (Wikipedia)

In Metamorphosis I, he transformed convex polygons into regular patterns in a plane to form a human motif. This effect symbolizes his change of interest from landscape and nature to regular division of a plane

Escher uses in The “Waterfall” the “bi dimensional” Penrose Triangle (“impossibility in its purest form” – Mathmatician Roger Penrose). Waterfall depicts a watercourse that flows in a zigzag along the long sides of two elongated Penrose triangles, so that it ends up two stories higher than it began

Ascending and Descending (1960).

Escher: ‘recalcitrant individuals refuse, for the time being, to take part in the exercise of treading the stairs. They have no use for it at all, but no doubt, sooner or later they will be brought to see the error of their non-conformity.’

“Convex and Concave” (1955)

One can view these features as concave by viewing the image upside-down.

Note that all additional elements and decoration on the left are consistent with a viewpoint from above, while those on the right with a viewpoint from below: hiding half the image makes it very easy to switch between convex and concave. (in Wikipedia)

“Still Life and Street” (1937)

Atrani, Amalfi Coast, Italy