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The Altgeld Collection Project | Quasi Crystals | The Julia Set
Benign Orthanc, Boy Surface, Corrupt, Regel, and Twirl, works by Abby Watt, are part of The Altgeld Collection Project. Please visit The Altgeld Collection Project website for more information.
The illiMath Collective, 2004-2007
immersive interactive environment
From Matthew Gregory:
The application generates quasicrystals, are 3D shadows of 6D objects. More specifically, it is showing a 3D projection of a 6D hypercube. The effect of this turns out to be an aperiodic tiling of 3D space.
The easiest way to describe a tiling is to first imagine a checkerboard, a square filled completely by multiple smaller squares. Now, this is an example of a periodic tiling of the 2D plane because a pattern (just one square in this case is applied repeatedly and could cover a board of any size. To imagine this in 3D, simply imagine a cube of arbitrary size. It too can be filled completely by a number of repeated cubes of a smaller size, just as the checkerboard is filled by smaller squares.
Now we can think about aperiodic tilings. One aperiodic tiling of the 2D plane is the Penrose tiling, which uses two rhombi of different proportions to cover the plane with no repeating patterns. It may look like there are pattern at first due to the rotational symmetry, but there is in fact no pattern of tiles that can be repeated to cover an infinitely sized plane.
Finally, the application draws the 3D analogue of this. It creates an aperiodic tiling of the 3D space in a similar way to the Penrose tiling, by using two rhomboids of different proportions to fill the space without repeating patterns, and it also has rotational symmetry.
When the program runs, it should show the object as each of the cells are being drawn. Also, each of the cells has a color which has mathematical significance. Cells of different colors form various higher level polyhedra with nearby cells of the same color.
Nicholas Duchnowski, 2007
UltraChrome K3 on Piezo Pro Matte Canvas media
Visit Nicholas Duchnowski's math blog entry on Quaternion Julia Set Fractials for more information on quaternion Julia Set fractals.
|The Traveling CANVAS is developed by the ISL at the Beckman Institute at the University of Illinois at Urbana Champaign.|