The baker's transformation
http://www.maths.bris.ac.uk/~majpk/papers/16.pdf
http://www.sciencedirect.com/science/article/pii/0003491689902595
baker's transformation,
n. the transformation of the unit square with Lebesgue measure that analytically is given by
T(x, y) = (2x, y/2) for 0 ≤ x < 1/2
T(x, y) = (2x - 1, 1/2[y + 1]) for 1/2 ≤ x < 1.
This corresponds to first deforming the unit square to the rectangle twice as wide and half as tall, and then cutting this rectangle along the line x = 1, and then placing the right-hand part above the left, to reform a square. This is called the baker's transformation because of its similarity to a method of kneading dough.
T(x, y) = (2x, y/2) for 0 ≤ x < 1/2
T(x, y) = (2x - 1, 1/2[y + 1]) for 1/2 ≤ x < 1.
This corresponds to first deforming the unit square to the rectangle twice as wide and half as tall, and then cutting this rectangle along the line x = 1, and then placing the right-hand part above the left, to reform a square. This is called the baker's transformation because of its similarity to a method of kneading dough.
http://www.scholarpedia.org/article/Quantized_baker_map