Fractal Gears | Hacker News Reader

Fractal Gears

brm.io

89 pointscolinprince22 comments

This would be an awesome screensaver

+1 while really cool, this isn't really a fractal. More like a 'gear cloud'

Thinking of the negative space generated by the space-filling algorithm rather than the individual shapes might help see the fractality. This link uses a similar algorithm and discusses measuring fractality of the output http://paulbourke.net/texture_colour/randomtile/

I see, that makes sense now. Thanks

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

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

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.

"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.

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!

Just for nitpicking, there are "fractals" with integer fractal dimension.

Example: https://en.wikipedia.org/wiki/Dragon_curve

The boundary of the dragon curve got a fractional dimension, therefore it qualifies.

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).

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.

Can you make it keep an arrangement up for longer?

I don't have time to properly think about any one arrangement before it's disappeared and moved on to the next one.

untick autoShuffle in the controls.

Not available on mobile.

Thanks!

Agreed - in addition to wanting more time to look at it, the sudden change while i'm trying to focus on it is giving me motion sickness. Looks pretty cool apart from that though.

The fact that I cannot zoom is infuriating!

Author must be still editing it, I can zoom in now (Android).

Cool. If the author is viewing this, could you set a min threshold for the tooth count?

And a max threshold - make really thin gear teeth, allowing a greater range of scaling.

any way one can save the animation?

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