Fibonacci spiral - The stairway has not changed size - it only appears to do so as it gets further away. The optical illusion does this in the perfect proportion of Phi, the "Golden Ratio". Artists have always know this - it is how they convey 3 dimensional perspective on a 2 dimensional canvas.
Geometry in nature // Fibonacci sequence// Golden Ratio // Phi point // The same ratio Vitruvius saw in the human body – 1 to PHI (1.618) – exists in every part of nature, from swimming fish to swirling planets. This divine ratio, or divine proportion, has been called the building block of all life.