Are fractals a dead-end area of maths?

[nomadreid]

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?

 

[jedishrfu]

If you check arxiv.org:

http://arxiv.org/find/all/1/all:+AND+fractal+math/0/1/0/all/0/1

You'll see that there are a lot of papers still being published in the area so I would say its still a vibrant field.

 

[nomadreid]

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.