Penrose Stairs
An impossible staircase where ascending and descending are the same thing. A small figure walks endlessly, never reaching a higher or lower level — the paradox that inspired Escher’s Ascending and Descending.
About this lab
The Penrose stairs (also called the impossible staircase) were first described by Lionel Penrose and his son Roger Penrose in their 1958 paper “Impossible Objects: A Special Type of Visual Illusion.” The figure depicts a staircase that makes four 90-degree turns, forming a continuous loop. A person walking the stairs would ascend (or descend) forever without ever getting higher (or lower).
M.C. Escher encountered the Penroses’ paper and used the concept as the basis for his famous 1960 lithograph Ascending and Descending, which shows monks walking endlessly around the top of a building on an impossible staircase.
The illusion works because an isometric (or specific axonometric) projection eliminates depth cues. The staircase is drawn so each flight of steps consistently ascends, but the fourth flight connects back to the starting point at the same level. In three dimensions, this requires a hidden discontinuity — a gap in the staircase that only becomes visible from a different viewing angle. The “reveal” button above shifts the perspective to expose this gap.
Impossible objects like the Penrose stairs, the Penrose triangle (tribar), and the Necker cube exploit the brain’s tendency to interpret 2D line drawings as 3D objects. Each local region of the drawing is geometrically consistent, but the global configuration is contradictory. These objects exist as 2D drawings but cannot exist as coherent 3D structures — they are visual paradoxes.