Favorite Fractals?

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applepi
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Favorite Fractals?

Postby applepi » Sat Oct 17, 2015 5:44 pm UTC

I'd say my favorite is Sierpinski's Triangle - probably because I'm a fan of triangles, and it's easy to draw. Though I will say the Dragon Curve is pretty groovy.

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measure
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Re: Favorite Fractals?

Postby measure » Thu Oct 22, 2015 2:07 am UTC

I personally like the Koch Snowflake and the Thue-Morse Sequence. I think my favorite though is the Conway Triangle fractal.

Related, a Fractal Program I made for drawing them.

Spoiler:
Image


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applepi
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Re: Favorite Fractals?

Postby applepi » Fri Oct 23, 2015 9:18 pm UTC

I had heard of the Koch Snowflake before, but I hadn't heard of the others! Wow. Props to you on the fractal program, the screenshot is beautiful.

The Mandelbrot is fascinating. I feel enlightened... Thank you :shock: I could stare at the second link for awhile and still be in awe by those spirals.

Derek
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Re: Favorite Fractals?

Postby Derek » Fri Oct 23, 2015 9:42 pm UTC

I've always been partial to the dragon curve.

suriya
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Re: Favorite Fractals?

Postby suriya » Tue Nov 10, 2015 5:05 pm UTC

The Mandelbrot set rocks!

Mike Rosoft
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Re: Favorite Fractals?

Postby Mike Rosoft » Wed Jan 13, 2016 7:59 pm UTC

How about the space-filling curves - continuous (though self-intersecting) curves that fill the entire interval [0,1]^2 (^3, ..., ^n, ...)

[ETA:]
suriya wrote:The Mandelbrot set rocks!

Nice, and now I am looking for Mandelbrot set-shaped rocks.

Lothario O'Leary
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Re: Favorite Fractals?

Postby Lothario O'Leary » Fri Feb 05, 2016 11:21 pm UTC

Derek wrote:I've always been partial to the dragon curve.

This, and the Levy C curve (which is similar in idea but very different in result).

I agree that the Sierpinski triangle is easy to draw (though, to be fair, I don't recall ever actually trying). My Koch snowflakes always end up bunched up on one side. And I like the Hilbert curve, but it's a bit tedious when you try to do too many iterations (more than 3 or 4, say), and it's too easy to mess up and have to start over.
Also, ever tried to draw a blancmange curve? It's a bit complicated without graph paper, but very pretty; and if you do have graph paper, it can be easily drawn to smaller scale (and more iterations) than most other fractals, because its structure it fairly simple, and its Hausdorff dimension is very tiny (so you don't have to drag your pen that much longer).


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