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Topic review (newest first)

bunman00
2012-12-19 21:43:39

Why is a mountain a fractal?

Agnishom
2012-12-18 23:07:35

Okay neutral Zero

anonimnystefy
2012-12-18 05:44:01

It does. And if you reduce something infinitely times, what do you get?

Agnishom
2012-12-18 03:16:54

Hi anonymnystefy;

Doesn't the volume get reduced by 20/27 in every step

bunman00
2012-12-18 02:54:18

Can you explain to me how to measure the root of a plant using fractal geometry.

anonimnystefy
2012-12-17 03:14:51

Try calculating the ratio of two steps in getting the menger sponge...

Agnishom
2012-12-17 02:58:16

Prove that the volume of the menger sponge is zero.

bobbym
2012-12-15 19:45:47

Hi bunman00;

You asked for a little bit more.

I was actually looking for a detailed one although your explanation helped a lot.

Okay, you got it. After all what do Barnsley and Mandelbrot know anyway? The essence of fractals begins Isaac Newton and Arthur Cayley. Take a look at the drawing.

When Newton's method is applied to the equation x^3 - 1 = 0, the fractal in the image is created. See the x's those are the roots of equation. Now the red areas are all the initial conditions that converge on that root in the red. Same for the blue and yellow. No one ever imagined such structure in such a simple system until Arthur Cayley first tried to answer the question.

He had already solved it for x^2 - 1 = 0 and assumed that the cubic would only be slightly harder.

bunman00
2012-12-15 18:19:15

What is a non-integer dimension.

bob bundy
2012-12-15 17:57:26

hi bunman00

A look at a map shows the coastline as a line that winds about apparently at random.  If you view the map at increasing magnifications it still looks like that.  You are perhaps expecting that the shape is exactly the same at all magnifications but I don't think that was what was meant when Benoit Mandlebrot first introduced the idea.  I don't know the underlying math but you could make a start by looking at

http://en.wikipedia.org/wiki/Benoit_Mandelbrot

I couldn't find much math  theory there and it seems you might have to read his book.  Maybe you can get it from a library.

As for a fern, take a look at this picture.  Each fern leaf is made up of minature ferns which are made up of even more minature ferns .......

http://1.bp.blogspot.com/-PuB07ZVgHds/TgADEK0skUI/AAAAAAAAAas/LIr0gD8y-gE/s1600/fern+fractal.png

Bob

bunman00
2012-12-15 16:58:16

And just to make sure a fractal is an image that has the same shape as the base when zoomed. I got that from library.thinkquest when I googled koch snowflake.

bunman00
2012-12-15 16:49:10

Can you explain to me how a cloud, pineapple and fern resemble fractals and how a coastline is a fractal.
Thank you

bobbym
2012-12-15 09:46:48

Hi;

bunman00 wrote:

Doess anything on earth resemble a ideal fractal which infinitely repeats itself.

bob bundy wrote:

My brother argues that the coastline is an example of a fractal.

According to Benoit your brother is correct.

There's a book written by bobbym for example called "My Age and Other Interesting Facts" that doesn't exist.  It weighs nothing as well as having zero volume.

Yes and it is equally interesting.

anonimnystefy
2012-12-15 09:08:50

The Apollonian gasket is also a nice one, but a bit less three dimensional...

http://upload.wikimedia.org/wikipedia/commons/thumb/e/e6/Apollonian_gasket.svg/220px-Apollonian_gasket.svg.png

bob bundy
2012-12-15 08:54:36

Oh how disappointing.  You take a photo of one and show it to me, and then it turns out it doesn't exist.  That's a great camera you've got there.

Come to think of it, I can think of lots of things that don't exist and also have zero volume.

There's a book written by bobbym for example called "My Age and Other Interesting Facts" that doesn't exist.  It weighs nothing as well as having zero volume.

Then there's the snowman I made last year.  That was made from all the ice I could find when the temperature was 20 degrees C.

And the gin and tonic I make when I've got no tonic.  Oh yes, I've got no gin either.

Bob

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