Designing Symmetric Peano Curve Tiling Patterns with Escher-esque Foreground/Background Ambiguity

Douglas McKenna
Bridges Leeuwarden: Mathematics, Music, Art, Architecture, Culture (2008)
Pages 123–130


By generalizing Peano’s original space-filling curve construction, one can design out of simple square tiles modular, two-color tiling patterns whose foreground and background are “self-negative” under 180° rotation. The resultant abstract geometric tiling patterns have an “Escher-esque” quality due to the attendant ambiguity that arises when the visual system cannot tell which connected area is foreground and which is background.