## Favorite Fractals?

For the discussion of math. Duh.

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applepi
Posts: 19
Joined: Sat Oct 17, 2015 2:30 am UTC

### Favorite Fractals?

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.

measure
Posts: 126
Joined: Sat Apr 04, 2015 4:31 pm UTC
Location: Time-traveling kayak

### Re: Favorite Fractals?

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:

cyanyoshi
Posts: 389
Joined: Thu Sep 23, 2010 3:30 am UTC

### Re: Favorite Fractals?

applepi
Posts: 19
Joined: Sat Oct 17, 2015 2:30 am UTC

### Re: Favorite Fractals?

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 I could stare at the second link for awhile and still be in awe by those spirals.

Derek
Posts: 2179
Joined: Wed Aug 18, 2010 4:15 am UTC

### Re: Favorite Fractals?

I've always been partial to the dragon curve.

suriya
Posts: 5
Joined: Sat Nov 07, 2015 8:44 pm UTC

### Re: Favorite Fractals?

The Mandelbrot set rocks!

Mike Rosoft
Posts: 63
Joined: Mon Jun 15, 2009 9:56 pm UTC
Location: Prague, Czech Republic

### Re: Favorite Fractals?

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
Posts: 35
Joined: Fri Feb 05, 2016 3:39 pm UTC

### Re: Favorite Fractals?

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).