Escher was an artist is the early-mid 20th century with interest for mathematics.
His infinite staircases are probably most famous among his drawings. By playing with perspective and our human intuition he is able to create the illusion that each step leads upwards. Note that there are less steps on the back right than at the front left and that each step is not just a diagonal movement but the combination of forward and up ward. The visual effect would not be possible using a ramp.
Escher is however able to recreate the illusion that water is in a perpetual cycle falling through a water wheel. This is in fact a totally different trick again using perspective. The water of course moves backwards in the picture and is nowhere near the wheel when it begins to fall, but because the drawing is on two dimensional paper it is not immediately obvious.
One final trick of perspective is this odd looking building Close one eye and put a finger infront of the ladder and you should see how this image works. The ladder is essential to ‘prove’ that the upper floor is oriented differently to the lower floor.
These hands instead of an optical illusion are a hint at infinity and paradoxes. Which hand started drawing the other? How can they both exist?
Another trick Escher liked to include was tessellations that changed from one object to another. A tessellation is made by repeating the same pattern over and over. in this case the shapes vary slightly from top to bottom but you can still vaguley see a fish outline between the birds at the top. Since the birds are given detail in the top half and fish given details in the lower half this is what stands out and it appears there is a transition between the two.
This is a circular tessellation with an infinitesimal twist. Since each shape gets smaller moving away from the centre the gaps allow for a few more to fit in and each of these is smaller with a smaller gap, and we can keep fitting in more and more of them forever.
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