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General Interest:Fractals

Fractals are mathematical objects that typically have the following characteristics
  1. a fine structure (detail on abitrarily small scales)
  2. too irregular to be described in traditional geometrical language, both locally and globally
  3. has some form of self-similarity, perhaps approximate or statistical
  4. its "fractal dimension" is greater than its topological dimension
  5. is defined in a very simple way, perhaps recursively.
Fractals often are associated with natural objects, such as the branchings of a tree, or the tributaries of a stream. A great deal has been written about fractals, and there are several web sites that deal exclusively with fractals (see our list of images on the web).

Subgroups:

  • CCL
    - The cubic connectedness locus (CCL) is a four-dimensional analog of the familiar Mandelbrot set.
  • Clouds
    - Cloud simulations using spectral synthesis.
  • Henon
    - The Henon map is a 2-dimensional generalization of the logistic equation.

Images:

1. [Amoeba Fractal] 2. [An aperiodic tiling] 3. [Antoine's Necklace] 4. [Arbitrary substitution tiling]

  1. Amoeba Fractal
  2. An aperiodic tiling
  3. Antoine's Necklace
  4. Arbitrary substitution tiling
1. [Brot Cheese Fractal] 2. [DodecaFoam! First Stellation] 3. [DodecaFoam! Second Stellation] 4. [DodecaFoam! Third Stellation]
  1. Brot Cheese Fractal
  2. DodecaFoam! First Stellation
  3. DodecaFoam! Second Stellation
  4. DodecaFoam! Third Stellation
1. [DodecaFoam!] 2. [Garden at Midday] 3. [Garden at Sunset] 4. [Nebula Fractal]
  1. DodecaFoam!
  2. Garden at Midday
  3. Garden at Sunset
  4. Nebula Fractal
1. [Plants on Island in Water] 2. [Three Ring Circus] 3. [Variety of Flowering Plants]
  1. Plants on Island in Water
  2. Three Ring Circus
  3. Variety of Flowering Plants
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Created: Fri Jun 26 14:36:37 CDT 1998 --- Last modified: Fri Jun 26 14:36:37 CDT 1998

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