This is a tiling of a Hyperbolic surface made famous by MC Escher. Each region bounded by black lines--actually an artifact in the way the image is constructed--is identical to all the other regions.

What is essentially going on is we are looking at a point of this hyperbolic surface with our regular Euclidean vision, and this point is moving to the right.

From our point of view: shit looks freaky yo.

But from the point of view of a person living in this hyperbolic surface, all they are doing is moving to the right in a straight line.

You will notice that the image seems to be less distorted toward the middle upper center. This is the point where our Euclidean vision is centered, where the local picture is not too far from distorting Euclidean space. As you get further away from this point, distances become more and more distorted. Like if you fill up a balloon, draw on it, and then deflate it, the drawing will become distorted.

For example: every single fish in this gif, from the point of view of a person living inside the hyperbolic space, is the same size and shape.

For more info/related topics:

http://euler.slu.edu/escher/index.php/Hyperbolic_Geometry#Hyperbolic_Space http://en.wikipedia.org/wiki/M%C3%B6bius_transformation http://euler.slu.edu/escher/index.php/Math_and_the_Art_of_M._C._Escher

/r/math, /r/puremath, /r/learnmath, etc.