Fractals in mathematics

[D'Nalor]

I have an assignment on Fractals, but I am unable to find much helpful info on them (research based assignmnet, it wasn't that I wasn't paying attention in class). just a brief deffinition will be sufficient. Thanks if you can help. info on mandelbrot sets and julia sets would be nice too if you can give me some.

Edited August 4, 2009 by D'Nalor

[DJBruce]

Here is the the MathWorld article that gives the basic discriptions of fractals. PBS' Nova did a video called "Fracatals: Hunting the Hidden Dimension" it is gives a brief history of fractals and then covers topics like the coastline paradox, Mandelbrot Sets, and possible uses of fractals I would suggest trying to find it at a local library.

 

Here is an article on Mandelbrot Sets.

[D'Nalor]

I looked at the sites, but the first site wasn't particullary helpful (I want to know what a fractal actually is), and the second isn't very friendly for High School students(which I am). I appreciate the help, but it isn't really what I need.

[iNow]

DJBruce mentioned it in his post, but didn't link to it. You should poke around this site for a while. It will help:

 

http://www.pbs.org/wgbh/nova/fractals/about.html

 

 

Also, you can watch the program which is worth the 50 minutes. It's split into five chapters, and is super informative, and super easy to follow.

http://www.pbs.org/wgbh/nova/fractals/program.html

[ajb]

Roughly a fractal is a geometric figure that has the self-similarity property. That is is looks the same at different scales.

 

There are plenty of objects in nature that are (approximately) fractal. Think about a fern and a cauliflower or broccoli.

 

More formally a fractal has a dimension that is not a whole number. For example, the plane has dimension 2 as where the Sierpinski triangle has dimension 1.58.....

 

I suggest you read the wiki article on fractal dimension and take it from there.

[D'Nalor]

Thanks, the info was helpful, but the video wouldn't let mewatch it because I don't livein the US. I still need a bit of info on Julia sets as well, the sites haven't given any info on them.

[DJBruce]

Julia sets are a specific type of fractal named after Julia Gaston in the early 20th century. Bellow are some links that I hope might help:

 

Wiki on Julia Set

 

Basic Information on Julia Sets

 

A Site that lets you zoom in on a Julia Set

MathWorld on Julia Sets

 

I hope this helps give you the general understanding you need. If you have a more specific question just ask.