Impossible Structures






Jean-François COLONNA
www.lactamme.polytechnique.fr
jean-francois.colonna@polytechnique.edu
CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641, Ecole Polytechnique, CNRS, 91128 Palaiseau Cedex, France
france telecom, France Telecom R&D

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[en français/in french]


Abstract: How to build impossible structures?


Keywords: Picture Synthesis, Impossible Structures.



One simple way to build impossible structures is to define a library of elementary tridimensional symbols:



Some elementary symbols used to built impossible structures
.



Then, their arbitrary bidimensional assembly will reveal impossibilities:



Periodical impossible structure
.


Periodical impossible structure
.


Periodical impossible structure
.


Periodical impossible structure
.


Periodical impossible structure
.



Then, colors can be added:



Impossible structure
.


Double impossible staircase and a paradoxal structure
.


Double impossible staircase painting a paradoxal structure
.


Double impossible staircase built by means of a paradoxal structure -a tribute to M.C. Escher-
.


and/or transformations can be made:



Autostereogram -using a periodical paradoxal structure as a desguise texture- with an hidden gaussian mountain
.


Paradoxal structure
.


Paradoxal black hole
.


Paradoxal structure
.


Paradoxal structure -from Order to Disorder-
.


Paradoxal structure
.


Paradoxal structure in the sky
.


Paradoxal structure based on the geometry of the sphere
.


Paradoxal structure based on the geometry of the Bonan-Jeener's triple Klein bottle
.


Paradoxal structure based on the geometry of the Boy surface
.


Paradoxal structure based on the geometry of the plane
.


Paradoxal structure based on the geometry of the sphere
.


Paradoxal structure based on the geometry of the Bonan-Jeener's triple Klein bottle
.


Paradoxal structure based on the geometry of the Boy surface
.




Finally, here are some of my oldest impossible structures:



No Title 0032
.


No Title 0079
.



Copyright (c) Jean-François Colonna, 1998-2014.
Copyright (c) France Telecom R&D and CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / Ecole Polytechnique, 1998-2014.