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Fractal---a weird but beautiful branch of mathematics [Copy link] 中文

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Post time 2006-7-7 12:29:21 |Display all floors






By observing the natural constructions which have a very common property---self-similarity, a small part of construction is very similar to the whole one, such as above the pic of spiral shappe of conch and the pic of a part of a real cauliflower, which is really similar to the whole cauliflower, mathematicians were enlightened. They began to create some artificial constructions to imitate some very complex natural constructions by only using some simple functions that iterates by infinite times.

A fractal is a geometric shape that can subdivided into parts, each of which is a reduced-size copy of the whole. It can be used to imitate consturctions of weather for weather forecast, or imitate the quotation of stock markets, or even the universe.

Here is a website that shows how to create a very simple but remarkable  fractal image:


http://ejad.best.vwh.net/java/fractals/koch.shtml

From the images, we can suppose that math is art, and art is a genre of math.




















[ Last edited by cathay at 2006-7-7 01:00 PM ]
C contends solitude to cause madness, while S maintains meditation for solace.

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Post time 2006-7-10 07:30:11 |Display all floors

Can you post pics?

Or do you need more credits? Well, I'll put some of them so people are enticed to click on more....

Here are the first 3 and the last 4:
Sorry! They're not in order. The real pics, snowflake, shell, & cauliflower are her first 3 links. The big ones are the last 4.

[ Last edited by freakyqi at 2006-7-10 07:35 AM ]
fractal01-dolexolali.jpg
natural_cauliflower.gif
fractal23-vaalea.jpg
fractal35-levitatron.jpg
natural_snailshell.jpg
fractal33-olmekinne.jpg
natural_snowflake.jpg

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Post time 2006-7-10 11:49:31 |Display all floors

I don't know where I could upload curiosity

Originally posted by freakyqi at 2006-7-10 07:30
Or do you need more credits? Well, I'll put some of them so people are enticed to click on more....

Here are the first 3 and the last 4:
Sorry! They're not in order. The real pics, snowflake ...


Thank you very much!

No, I can not post any pix, and of posting a message, there are not any option or button that indicates that I have access to upload attachments. I don't know where I could upload, or it's just becuase my credits are not enough yet.

It seems that folks here do not have much interest about math, a pure art. Perhaps most of folks, esp in China, think math is difficult and can not make money. How disappointed what they said is! Chinese social system has been ruining people's curiosity, the extremely precious spiritual wealth!

Thank you again!
C contends solitude to cause madness, while S maintains meditation for solace.

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Post time 2006-7-10 11:50:54 |Display all floors

oh very nice!

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Post time 2006-7-11 12:23:58 |Display all floors
Very intersting artwork.

Is it art or science or both?

We learned about chaos theory in elementary school.  We learned that the way clouds swirl, and the way that cigarette smoke curls up from the ash tray, and the way that water beads as it  falls from a stream are all mathematical formulas.  They seem to repeat in some ways, but never repeat in other ways.  Very interesting.

Fractals were discovered by a mathmatician working for AT&T.  His name is French but escapes me at the moment.  He was working to solve a problem that we never see anymore, or hear anymore I should say.  Decades ago static on telephones lines would follow fractal patters -- they seemed to repeat in some ways but were never identical in other ways.  By analyzing the spaces between the clicks of static, the scientist was able to prove that the pattern was non-random, even though it never repeated itself identically.
龙年顺顺利利

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Post time 2006-7-11 16:27:10 |Display all floors
really nice
always be OK
always be Great

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Post time 2006-7-11 22:04:26 |Display all floors
Originally posted by matt605 at 2006-7-11 12:23
Very intersting artwork.

Is it art or science or both?

We learned about chaos theory in elementary school.  We learned that the way clouds swirl, and the way that cigarette ...


It's wonderful to see you!

Perhaps not we, but you in your elementary school learned about Chaos theory  which, as far as I know, is never taught by any teacher in China in elementary school, in which both teachers and pupils are not capable of studying Chaos theory, which domain includes lots of mathematical analysis, such as set theory, Calculus, advanced algebra, Topology, introduction of number theory, theory of probability, etc. If you  learned Chaos theory from elementary school, you would be a genius; or you learned about the mere beginning of Fractal.

Benoît Mandelbrot, the forefather of Fractal, what I admire him is not him, but his uncles, they guided him to study mathematics.  I wish I had such people to guide me!

Yes, those images are belonged to the domain of art since they use various and vivid colors to render the original images, nevertheless the backbone of images are totally based on iterated functions from math.  

Here is a website that has a graph to illustrate the relationship among art and Fractal and Chaos and more.


http://www.btinternet.com/~se16/mhi/

Big joy!

[ Last edited by cathay at 2006-7-11 10:10 PM ]
C contends solitude to cause madness, while S maintains meditation for solace.

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