Are fractals a dead-end area of maths?

In summary, the conversation discusses the broad topic of fractals and their various uses and applications. While they are often considered "cute" and have led to new fields of mathematics, such as measure theory, it is debated whether the study of fractals has produced any significant spin-offs. However, there are still many papers being published in the field, indicating its ongoing relevance and potential for new developments.
  • #1
nomadreid
Gold Member
1,665
203
This is not a high school question, but it seems to be too broad to fit in any of the other categories. Fractals are cute (nice pictures that can also be used to give better graphics, and also "shocking" that one can define a non-integer dimension), can be used to estimate lengths or volumes of irregular shapes (coastlines, Brownian motion or surfaces, fluid dynamics and all that), is a byword anytime anyone finds some self-similar scaling (everything from galaxies to quasi-crystals), and so forth. But do they lead to any other new mathematics? For example, the motion and logical paradoxes are also "cute", but they led to whole new and fruitful fields of mathematics being born. But, for example, are Hausdorff dimensions good for anything besides fractals? Is the study of fractals good only for itself?
 
Mathematics news on Phys.org
  • #3
Thanks, jedishrfu. Interesting papers in this link. That fractals are a vibrant field means mostly that new results in the field arise, or that one finds new applications (or hopes for new ones: Professor Lapidus has been trying for years to see if a fractal approach to the Riemann zeta function will bear fruit.) The question was however whether there has grown out of the study of fractals any new fields that then operate as independent fields of study: for example, Pascal's work on probability led to today's measure theory, Lebesgue integration, etc. That is, any "spin-offs". I shall be going through the 117 papers on that arxiv link, though, and perhaps I will find my answer. So thanks again.
 

1. What are fractals?

Fractals are mathematical patterns that repeat themselves at different scales. They are often described as "self-similar" because no matter how much you zoom in or out, the same pattern can be seen.

2. How are fractals relevant to math?

Fractals have many applications in math, including geometry, chaos theory, and computer graphics. They are also used in modeling natural phenomena, such as coastlines, clouds, and trees.

3. Are fractals a dead-end area of math?

No, fractals are not a dead-end area of math. While they may not be as heavily researched as other areas of math, they continue to have practical applications and are still being explored and developed by scientists and mathematicians.

4. Can fractals be seen in nature?

Yes, fractals can be seen in many natural phenomena, such as snowflakes, leaves, and rivers. They are also found in the human body, such as in the branching patterns of blood vessels and nerves.

5. How can fractals be used in real-world applications?

Fractals have many real-world applications, such as in image compression, creating realistic computer graphics, and predicting stock market trends. They are also used in weather forecasting, studying biological growth patterns, and designing efficient transportation systems.

Similar threads

  • General Math
Replies
7
Views
4K
  • General Math
Replies
4
Views
3K
Replies
5
Views
2K
  • Other Physics Topics
Replies
6
Views
2K
  • STEM Academic Advising
Replies
13
Views
2K
  • STEM Academic Advising
Replies
11
Views
3K
  • General Math
Replies
13
Views
9K
  • STEM Academic Advising
Replies
4
Views
2K
  • Special and General Relativity
Replies
29
Views
6K
  • STEM Academic Advising
Replies
10
Views
4K
Back
Top