Cantor's comb

MathematicalPhysicist

Gold Member
4,122
146
does it have other applications in maths?
 
After doing some research in google, I found 2 results.
1) It is used to visualize the Cantor set
2) It can be put under the topic, fractals (I prefer a 2D fractal to a one-dimension one :wink:)

Besides these 2, I don't know whether it has any other application in math
 

Integral

Staff Emeritus
Science Advisor
Gold Member
7,185
55
I once did a homework assignment that started with the cantor set and ended with the binary number system. Along the way the equivalance of 1 and .999... or .111... binary fell out.
 

MathematicalPhysicist

Gold Member
4,122
146
Originally posted by KL Kam
After doing some research in google, I found 2 results.
1) It is used to visualize the Cantor set
2) It can be put under the topic, fractals (I prefer a 2D fractal to a one-dimension one :wink:)

Besides these 2, I don't know whether it has any other application in math
how is it used in fractals?
 
Originally posted by loop quantum gravity
how is it used in fractals?
The 3 properties of fractals are
1. Self-similarity
2. Fractional dimension
3. Formation by iteration

For Cantor's Comb, it has property 1. I guess it can be formed by iteration but I'm not sure. Also I'm not sure whether it has fractional dimension. I'm not an expert and I think some mathematicians here can clear it up a bit.
 
I'm in no sense an expert or even knowledgable on this issue, but wouldn't it have to have a fractal dimension? It could be 0, which is still a fractal dimension. I can't remember exactly, but I think Cantor's Dust has a fractal dimension between 0 and 1 , and Cantor's box has a fractal dimension of 0.

Here is a good website I found on fractals, but it dosn't seem to be working at the moment.

http://library.thinkquest.org/26242...torial/ch4.html
 
Last edited by a moderator:

Related Threads for: Cantor's comb

Replies
9
Views
2K
  • Posted
Replies
10
Views
2K
  • Posted
Replies
5
Views
2K
  • Posted
Replies
1
Views
4K
  • Posted
Replies
2
Views
1K
  • Posted
Replies
17
Views
4K
Replies
19
Views
729
Replies
4
Views
2K

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving

Hot Threads

Top