Good fractals to draw/doodle?

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Xutar
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Good fractals to draw/doodle?

Postby Xutar » Sun Mar 15, 2009 11:01 pm UTC

One of my hobbies in class has been doodling fractals in empty spaces on worksheets and in my notebook. So far I've drawn the popular ones like Koch snowflake/curve, Sierpinski's triangle, and couple space filling ones. If anyone has any links to fractals that are fun to draw or to some sort of guide to drawing fractals/self-similar shapes that'd be appreciated. All I use to draw is a pencil, ruler, and maybe a compass If I'd need one.

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Oort
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Re: Good fractals to draw/doodle?

Postby Oort » Mon Mar 16, 2009 5:44 am UTC

I like the Hilbert curve. Learned about it on xkcd in fact.

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Re: Good fractals to draw/doodle?

Postby phlip » Mon Mar 16, 2009 6:36 am UTC

Luthen's avatar. (Also known as the Heighway dragon curve.)

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Re: Good fractals to draw/doodle?

Postby runa » Mon Mar 16, 2009 8:07 am UTC


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Re: Good fractals to draw/doodle?

Postby ConMan » Mon Mar 16, 2009 11:17 am UTC

I like to do dot Sierpinskis. By which I mean, take a grid of somewhere between 2x2 and 5x5 squares. Choose some of the squares to be filled in. Now, on your page, make a small pattern of dots that matches your filled-in pattern. Then, take that pattern and repeat it in the same pattern. Repeat until paper is filled.

That wasn't a particularly good explanation, so I will give you a simple example, in the form of a right-angled Sierpinski triangle:
Spoiler:
generating pattern.png
The pattern of squares for the Sierpinski triangle
generating pattern.png (48.85 KiB) Viewed 3078 times

iteration 1.png
Just turning the filled-in squares to dots gives this.
iteration 1.png (1.4 KiB) Viewed 3077 times

iteration 2.png
Using the first dot-pattern as the base for a redrawing of the original pattern gives this.
iteration 2.png (2.79 KiB) Viewed 3076 times

iteration 3.png
Do the same thing again, but with the second iteration ...
iteration 3.png (6.9 KiB) Viewed 3076 times

iteration 4.png
And repeat ...
iteration 4.png (15.92 KiB) Viewed 3077 times

iteration 5.png
For as long as you like.
iteration 5.png (48.97 KiB) Viewed 3077 times
That one turned out a little messy, but hopefully you can see the process. The next spoiler has some 3x3 examples.

Spoiler:
generating pattern 2.png
If you take some 3x3 patterns, you have a bit more room for ideas.
generating pattern 2.png (41.74 KiB) Viewed 3078 times

x.png
x.png (9.39 KiB) Viewed 3076 times
k.png
k.png (12.51 KiB) Viewed 3077 times
c.png
c.png (19.67 KiB) Viewed 3076 times
d.png
d.png (18.25 KiB) Viewed 3079 times
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Re: Good fractals to draw/doodle?

Postby Indon » Mon Mar 16, 2009 4:04 pm UTC

Morse-thue maps out well to a graphical representation, after selecting two colors:

Spoiler:
1001011001101001
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1001011001101001
0110100110010110
1001011001101001
1001011001101001
0110100110010110
0110100110010110
1001011001101001
1001011001101001
0110100110010110
1001011001101001
0110100110010110
0110100110010110
1001011001101001
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Re: Good fractals to draw/doodle?

Postby Cheese » Mon Mar 16, 2009 5:23 pm UTC

ConMan wrote:I like to do dot Sierpinskis. By which I mean, take a grid of somewhere between 2x2 and 5x5 squares. Choose some of the squares to be filled in. Now, on your page, make a small pattern of dots that matches your filled-in pattern. Then, take that pattern and repeat it in the same pattern. Repeat until paper is filled.

That wasn't a particularly good explanation, so I will give you a simple example, in the form of a right-angled Sierpinski triangle:
Spoiler:
[stuff in spoilers]

interesting idea, I might try that sometime. Looks like an interesting way to kill some time.
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Re: Good fractals to draw/doodle?

Postby Xutar » Mon Mar 16, 2009 8:05 pm UTC

The Dragon Curve was an excellent Idea. So far I've drawn up to the eighth iteration on graph paper (see here).

I'll need to start over and position it better if I want to get to the ninth.

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Re: Good fractals to draw/doodle?

Postby DonChubby » Tue Mar 17, 2009 12:47 am UTC

Yeah, I had that same problem. It's hard to anticipate how much space to each side you're going to need.
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Re: Good fractals to draw/doodle?

Postby Luthen » Tue Mar 17, 2009 4:05 am UTC

phlip wrote:Luthen's avatar. (Also known as the Heighway dragon curve.)
I come here out of duty to my avatar and it's already done. Thanks!

DonChubby wrote:Yeah, I had that same problem. It's hard to anticipate how much space to each side you're going to need.
Xutar wrote:The Dragon Curve was an excellent Idea. So far I've drawn up to the eighth iteration on graph paper (see here).
I'll need to start over and position it better if I want to get to the ninth.
I wrote a spreadsheet to graph it. If you'd like a copy: Openoffice version (definitely should work), Excel version (sometimes doesn't).
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Re: Good fractals to draw/doodle?

Postby ConMan » Tue Mar 17, 2009 5:04 am UTC

Cheese wrote:
ConMan wrote:I like to do dot Sierpinskis. By which I mean, take a grid of somewhere between 2x2 and 5x5 squares. Choose some of the squares to be filled in. Now, on your page, make a small pattern of dots that matches your filled-in pattern. Then, take that pattern and repeat it in the same pattern. Repeat until paper is filled.

That wasn't a particularly good explanation, so I will give you a simple example, in the form of a right-angled Sierpinski triangle:
Spoiler:
[stuff in spoilers]

interesting idea, I might try that sometime. Looks like an interesting way to kill some time.

As you might be able to tell, the trickiest bit is keeping everything even. I was rushing a bit when I drew those, so you can see where I had to fudge a little to make things line up (and particularly the lower edge of the triangle drifted a lot).
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Re: Good fractals to draw/doodle?

Postby Phen » Tue Mar 17, 2009 4:25 pm UTC

I think fractals are kinda cool, but all those goddamn exotic names are deterring me from reading about more about it at wikipedia. I don't mind math, but srsly.
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