Welcome to the new exhibition at the museo interactivo mirador (mim) in Santiago de Chile
    Bienvenido a la nueva exhibición del museo interactivo mirador (mim) en Santiago de Chile
      Bienvenue à la nouvelle exposition du museo interactivo mirador (mim) de Santiago de Chile

[ English | Goal | Look at the exhibition running | Early tries | How does it work? | Opening | Related links | Credits | Contact | Back home ]

  Goal / Objectivo / But

  • Having fun interacting with beautiful mathematical objects (these are finally real!)
  • Bring home a mathematical souvenir (an awesome picture of your meeting with infinity)
  • Discover that infinity can fit in finite space
  • Discover the complexity of conformal maps (i.e. maps that preserves the angle)
  • Discover that constructions that looks impossible may indeed be possible
  • Push everyone ask itself questions just by looking at beautiful things
  • Proving that we can do math experiments as physicists do physics experiments, i.e., without annoying people with
     interesting but afterall boring proofs or equations ;-)

  Look at the exhibition running / Mire la exhibición en marcha / Visitez l'exposition

  • Direct link to the video
  • Realtime Droste effect: Escher brought to life!
  • Note that there is a 15 sec. time offset between two consecutive iterations, allowing interactions with yourself to the infinity
     and beyond!

  Early tries / Primeros intentos / Premiers essais

  How does it work? / ¿Como funciona? / Comment ça marche ?

    All the mathematical details can be found on Jos Leys's Droste effect web page
    or on the web page dedicated to the completion of Escher's work by B. de Smit & H. W. Lenstra Jr

    But since we are here to have fun interacting with math beauty, here is a series of pictures that tells you everything you need to know:

  The frame will join in a spiral when the frame is rotated and scaled in the logarithmic space so that its corners are one above the
  other at distance 2π exactly:

Low quality - Google video	High quality - GIF (slow, 12.3MB)

  Now, let's play with the golden frame and have it rotating and scaling up and down and look at what is going on.

Low quality - Google video	High quality - GIF (slow, 53.1MB)

  Note that all the angles are preserved (the transformation is a conformal map).
  Now let's just look at the volcán Parinacota (North of Chile) in the style of Escher.

Low quality - Google video	High quality - GIF (slow, 53.4MB)

  Opening / Inauguración / Inauguration

  • The slides of the talk
  • Some pictures: [ 1 | 2 | 3 | 4 | 5 | 6 | 7 ]

  Related links / Enlazos relajados / Liens

  • Jos Leys's Mathematical imagery and its Droste effect web page
  • the web page dedicated to the completion of Escher's work by mathematicians B. de Smit & H. W. Lenstra Jr
  • the flickr Droste effect gallery
  • the museo interactivo mirador web page (the announcement web page)
  • the openCV project web page
  • the gphoto library web page
  • the red de fundaciones web page (the annoucement web page)
  • the anillo en redes web page

  Conceived and directed by: Nicolas Schabanel (url)
  Software (to be released soon as an Ubuntu package under (cc) licence):
  • Image processing: Nicolas Schabanel (url)
  • Computer engineering: Karol Suchan (url)
  Hardware design: Karol Suchan (url)
  Steampunk design: Atomo diseño (Chile)
  Voice: Camillo Larota
  Location: Museo Interactivo Mirador (Santiago de Chile)

  Operating system: Linux Ubuntu 8.04 (url)
  Webcam management: openCV (url)
  Camera management: gphoto 2.2 (url)
  Sound management: Alsa player (url)
  Display management: Freeglut 3 (url) & Qt4 (url)
  File directory sharing: Nautilus (url)
  Sound processing: GarageBand (url)
  Web site animations: ImageMagick (url)

  Contact: nicolas.schabanel:infinito _a_ gmail.com