How Monument Valley Uses Impossible Figures to Redefine Puzzle Game Design

Last week a department sharing session introduced the popular game Monument Valley , a creative puzzle title from USTWO that employs impossible‑figure parallax illusion, exquisite design, and music, earning global praise on iOS and later on Android as a free download.

The designers used extensive mathematical thinking to craft pay‑walls and a scalable story space, delivering a complete narrative within three hours while maintaining a unique market‑defying approach.

Despite its minimalist and occasionally pixel‑style aesthetics, the game’s visuals are striking, the story engaging, and the controls smooth; hidden mechanisms and impossible routes serve as the secret to clearing each level.

Monument Valley heavily utilizes the concept of “impossible figures,” creating visual depth through differing reference points, a technique also popular in painting and street art, such as works in Beijing’s 798 Art District.

Impossible figures, also called undecidable or impossible objects, are optical illusions where a two‑dimensional drawing is perceived as a three‑dimensional object that cannot exist in reality, unlike the Möbius strip which is geometrically feasible.

The earliest example is the “Impossible Cube” designed by M. C. Escher for his work Belvedere , where a near edge is mysteriously blocked by a far edge.

The concept later evolved into the “Penrose triangle,” first created by Swedish artist Oscar Reutersvärd and popularized by mathematician Roger Penrose in the 1950s; Escher incorporated similar figures into his art, and variations like the Penrose square and pentagon also exist.

Roger Penrose, also known for contributions to geometry and black‑hole singularities, co‑created the “Penrose stairs” with his father Lionel Penrose—a four‑cornered staircase that loops endlessly without rising or descending.

In the game, the Penrose stairs are adapted to create looping pathways, sometimes resembling a Möbius‑like continuous surface.

Earlier games such as the PlayStation title Infinite Corridor employed similar designs, though its mathematical model was more complex yet less engaging.

Another visually stunning title, Tengami , presents a paper‑crafted world where players flip pages to solve puzzles, offering a silent, immersive storybook experience.

Polytron’s award‑winning PC game FEZ also uses perspective shifting to blend 2D and 3D platforming, showcasing creative gameplay and retro aesthetics.

Beyond games, impossible‑figure concepts appear in literature, such as the “ghost tomb” scene in the novel Ghost Blows Out the Light , and in film, Christopher Nolan’s Inception visualizes a real‑world Penrose staircase.

Overall, Monument Valley’s success stems not only from its design philosophy but also from integrating cutting‑edge visual‑magic concepts, offering a vivid lesson in innovation for designers seeking to bridge art, mathematics, and interactive storytelling.