Via Wikipedia:

A fractal as a geometric object generally has the following features:

  • fine structure at arbitrarily small scales
  • is too irregular to be easily described in traditional Euclidean geometric language.
  • is self-similar (at least approximatively or stochastically)
  • has a Hausdorff dimension that is greater than its topological dimension (although this requirement is not met by space-filling curves such as the Hilbert curve)
  • has a simple and recursive definition.

Due to them appearing similar at all levels of magnification, fractals are often considered to be ‘infinitely complex’. Obvious examples include clouds, mountain ranges and lightning bolts. However, not all self-similar objects are fractals — for example, the real line (a straight Euclidean line) is formally self-similar but fails to have other fractal characteristics.

Personally, I could just look at them all day long….


7 thoughts on “Gaze

  1. adreampuppet says:

    These fractal posts are, admittedly, my Empress magnets….


  2. Bilquees says:

    Beatutiful!! Thanks for this feast for the eyes.

  3. Hawk Sr says:

    Mike (and others): Help me get inside these fractals. When you gaze at them, what are you seeing? What are the emotions, and what are the intellectual processes that you experience.

    Such questions probably just expose the obvious fact that my limited experience and my intellectual orientation place blocks that inhibit understanding. I see intricate beauty and form that say something about the mind that created the images. But I would enjoy and appreciate hearing what others are seeing as they gaze.

    Help this beginner!

  4. Fixer says:

    Wish I still did acid when I see shit like this. Good thing we didn’t have stuff like this way back then or I probably still would … heh. 30 years ago I’da been staring at this for hours.

  5. adreampuppet says:

    Apparently, Fixer, things had not changed that much between your high school era and mine….

  6. Amelopsis says:

    Hey, better late than never, right?

    Very attractive, fractals.
    Considering the math can admittedly make my head hurt a little, (not a proud admission, but there it is) but I am fascinated by them.

  7. adreampuppet says:

    I knew we’d get you, Amelopsis!

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