1. Playful Imaginings: The Illusions of M.C. Escher Megan Rible Stanford University

2. Escher’s Inspiration “Sometimes it seems as though we are all obsessed with a longing for the impossible. The reality around us, the three dimensional world surrounding us, is too ordinary, too boring, too common. We yearn for the unnatural or the supernatural, the impossible, the miraculous.”

3. New Worlds mixture of reality and reflection Three Spheres II, Three Worlds, Still Life and Street

4. Illusion of Space the human brain insists on making two- dimensional pictures spatial Dragon, Three Spheres I

5. Perspective focusing attention on the nadir: Tower of Babel interchanging zenith, nadir, and distance points: Other World, Relativity curved lines of perspective: Up and Down, House of Stairs

6. Relativity My computer rendering of Escher’s world of staircases. There are three separate points of view depicted with the same vanishing points.

7. Rendering #2 Another, less picturesque view, but the possibilities can be seen.

8. Deep Fish Contours - thickness decreases with distance Network of Lines Rhythmic positioning Fading colors Colors go from warm - cold as water gets deeper

9. Impossible Objects “If you want to express something impossible you must keep to certain rules…The element of mystery to which you want to draw attention should be surrounded and veiled by a quite obvious, readily recognizable commonness.” quasi-spatial: only exist on a flat surface Convex and Concave, Print Gallery

10. Impossible Cube Here is the secret behind the impossible cube that Escher displays in Belvedere

11. Roger Penrose’s Triangle

12. The Endless Staircase “Yes, yes, we climb up and up, we imagine we are ascending; every step is about ten inches high, terribly tiring- and where does it all get us? Nowhere; we don’t get a step farther or higher. I’m working my fingers to the bone, believing I’m ascending. How absurd it all is.”

13. Escher’s Staircase Escher received the idea for this model from Roger Penrose.

14. Quotes “Although I am absolutely without training or knowledge in the exact sciences, I often seem to have more in common with mathematicians than with my fellow-artists.” “An understanding of the relationships between plane and space is a source of emotion for me; and emotion is a strong incentive, or at least a stimulus for making a picture.”

15. Computer Renderings

16. More Cool Stuff

17. Belvedere