5 ms·

Is this quasi-fractal? The gears are not made of gears so it's not exactly fractal.

trymas 11y ago
+1 I do not get it either. Gears by themselves are just gears and those gears barely form a fractal structure, though once there was something a little bit resembling third/fourth iteration of a Sierpinski triangle[0]. [0] https://en.wikipedia.org/wiki/Sierpinski_triangle https://en.wikipedia.org/wiki/Sierpinski_triangle
JimmyM 11y ago
Quasi-fractal makes sense to me, I'm assuming that the gears are created from generic fractal-generating code (pass a basic geometric pattern, draw a portion of a self-similar fractal) that's been modified to create finite gears instead. Or I could easily be talking nonsense. The page itself is really cool, and I love the effect. I wonder if I would be able to use screenshots from it for personal projects? I assume not. As the most minor point that could possibly be made – never seen · before, seems like it could be quite useful.
munificent 11y ago
"Fractal" has always meant "self-similar" not "self-identical". There are subtle and some not-so-subtle differences within all of the repeating shapes in a Julia or Mandelbrot set.
- deleted 11y ago
  [deleted]
- sklogic 11y ago
  In the most classical meaning, "fractal" stands for "an object with a fractional fractal dimension". Since there is a clear cut on the level of details, the fractal dimension of this image is integer (i.e., precisely 2). Nevertheless, it's totally cool!
  - leni536 11y ago
    Just for nitpicking, there are "fractals" with integer fractal dimension. Example: https://en.wikipedia.org/wiki/Dragon_curve https://en.wikipedia.org/wiki/Dragon_curve
    - sklogic 11y ago
      The boundary of the dragon curve got a fractional dimension, therefore it qualifies.
  - evanpw 11y ago
    I don't think there's much agreement about the exact, formal definition of fractal, but "Hausdorff dimension greater than the topological dimension" is probably a better one than "Hausdorff dimension is not an integer". Otherwise, not even the boundary of the Mandelbrot set is a fractal! (It has Hausdorff dimension 2).
ctdonath 11y ago
It's fractal a la the Apollonian Gasket, to wit place a large circle within a space, then repeatedly fill all available outside-a-circle spaces with the largest possible circle. Interestingly in this case, the limiter is the number of gear teeth - when down to two, stop. It's a fractal if you start your first gear with an infinite number of teeth. That being problematic, when down to 2 teeth scale back up to resume filling space with the largest gear possible ... making the real trick determining whether a gear should be placed such that it does not immobilize the chain.

+1 I do not get it either. Gears by themselves are just gears and those gears barely form a fractal structure, though once there was something a little bit resembling third/fourth iteration of a Sierpinski triangle[0]. [0] https://en.wikipedia.org/wiki/Sierpinski_triangle https://en.wikipedia.org/wiki/Sierpinski_triangle

JimmyM 11y ago

Quasi-fractal makes sense to me, I'm assuming that the gears are created from generic fractal-generating code (pass a basic geometric pattern, draw a portion of a self-similar fractal) that's been modified to create finite gears instead. Or I could easily be talking nonsense. The page itself is really cool, and I love the effect. I wonder if I would be able to use screenshots from it for personal projects? I assume not. As the most minor point that could possibly be made – never seen · before, seems like it could be quite useful.

munificent 11y ago

"Fractal" has always meant "self-similar" not "self-identical". There are subtle and some not-so-subtle differences within all of the repeating shapes in a Julia or Mandelbrot set.

deleted 11y ago
[deleted]
sklogic 11y ago
In the most classical meaning, "fractal" stands for "an object with a fractional fractal dimension". Since there is a clear cut on the level of details, the fractal dimension of this image is integer (i.e., precisely 2). Nevertheless, it's totally cool!
- leni536 11y ago
  Just for nitpicking, there are "fractals" with integer fractal dimension. Example: https://en.wikipedia.org/wiki/Dragon_curve https://en.wikipedia.org/wiki/Dragon_curve
  - sklogic 11y ago
    The boundary of the dragon curve got a fractional dimension, therefore it qualifies.
- evanpw 11y ago
  I don't think there's much agreement about the exact, formal definition of fractal, but "Hausdorff dimension greater than the topological dimension" is probably a better one than "Hausdorff dimension is not an integer". Otherwise, not even the boundary of the Mandelbrot set is a fractal! (It has Hausdorff dimension 2).

ctdonath 11y ago

It's fractal a la the Apollonian Gasket, to wit place a large circle within a space, then repeatedly fill all available outside-a-circle spaces with the largest possible circle. Interestingly in this case, the limiter is the number of gear teeth - when down to two, stop. It's a fractal if you start your first gear with an infinite number of teeth. That being problematic, when down to 2 teeth scale back up to resume filling space with the largest gear possible ... making the real trick determining whether a gear should be placed such that it does not immobilize the chain.