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Fractals
Topic Started: Jan 12 2011, 05:31 PM (1,329 Views)
Michelle
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This video's for CJ:




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CJ
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A very minor case of serious brain damage

Looks good. I'll definitely watch it when I have time.
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Michelle
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Yeah you should, it is a good show.
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CJ
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Well, that was excellent!

It really does get me thinking, where else can this be applied?
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Michelle
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I know! It's so cool.

I've kinda figured out how to make them.
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CJ
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Ah, nice.

Could you help me, please? I can't even work out how to get started :( .
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Michelle
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I suggest going to the little white sheet thing: that's a new fractal. Go to "Parameters" if you want to change the shape, go to formula (if you don't want the Mandelbrot). The only way I could figure out how to change the background colour is under the "Colorcycling" window. I would put it on 3.7, since anything higher is too fast.

To save it, click SHIFT + I. I suggest saving it as a PNG, because it generally looks better. (Save it under "My Pictures" because for life of me, I cannot find the original folder it's saved under!!)

Ta-da!
Posted Image
Edited by Michelle, Jan 13 2011, 02:48 PM.
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CJ
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A very minor case of serious brain damage

Nice!

Thanks for the help. Is there any way to generate fractals of your own, though, rather than using a pre-existing one? There probably is, but do you know what it is?
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Michelle
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No... wouldn't know how.
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CJ
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Oh, OK. It'd be useful if either of us could work that out, since I wouldn't want to use the same background over and over.
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Michelle
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I did figure out how to change the background colour.
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CJ
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I saw, but what I meant was, I wanted completely different fractals, not just re-coloured versions of existing ones.
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Michelle
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Oh okay. I'm not that smart.
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CJ
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What about Cantor dust? This is similar to the Cantor set (which is constructed at the beginning of part 2 of that video), but in multiple dimensions:

Posted Image
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Michelle
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Whoa... friggin weird....
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CJ
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Yeah. The construction's pretty simple, though: it's one cube divided into 8 smaller ones, which are themselves divided into 8 smaller ones, which are divided into into 8 even smaller ones....and so on infinitely many times.
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Michelle
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I know, I saw that... O.O mind*censored*ed me.
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CJ
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A fractal a bit like the Cantor dust is the Menger sponge. Here's how to construct one:

1) Start with a cube.
2) Punch a hole right through the centre of each face.
3) Punch 8 smaller holes around each of these holes.
4) Punch 8 smaller holes around each of these.

And so on, ad infinitum. What you're left with at the end is the Menger sponge.

Here's a picture of one three steps into the construction:

Posted Image

Here's one four steps in:

Posted Image

Notice that they have an extremely large surface area compared to the original cube (be
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Michelle
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WHOA *censored*. That's amazing.
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CJ
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I know! I'd love to play Hide and Seek in the last one :P .
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Michelle
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Me too! I doubt if you could find me in that.
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CJ
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LOL :P

It almost looks like it's made out of Meccano.
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Michelle
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What is that?
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CJ
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It's a construction toy:

Posted Image
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Michelle
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Oh cool, maybe it could be a fractal
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CJ
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I'm not sure you could make a fractal out of Meccano. They don't make it that small :P !
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Michelle
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That sounds really cool! LOL!
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CJ
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Going back to fractals, here we have the starting cube, plus the first four steps in the construction of the Menger sponge:

Posted Image
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Michelle
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That's really cool!
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CJ
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I know. The fourth one has around 200,000 individual faces.
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