 |
Algebra: Abstract and Concrete
Frederick M. Goodman
The following images were created using algorithms from Michael
Field and Martin Golubitsky, Symmetry in Chaos, Oxford
University Press, 1992.
To create the images, one runs several million iterations of a two dimensional discrete dynamical system. The probability density for the location of the dynamical particle is encoded in colors. The dynamical system is chaotic, but possesses inherent symmetry.
For more information, and many more examples, of images created in this manner, follow this link to
Martin Golubitsky's home page.
The following are color versions of 2-dimensional images from the text. To see dynamic 3-dimensional images, follow this link.
|
Tetrahedron: Cube: Dodecahedron: |
|
|
Octahedron-cube: Dodecahedron-Icosahedron:
Tetrahedron-Tetrahedron:
|
|
Some imbeddings of regular polyhdra:
|
Tetrahedra in the cube: tetrahedron in cube Cube in the dodecahedron: cube in dodecahedron 1 |
|
