I guess there are two questions here, and I would answer them differently. I've seen fractal analysis applied to biomechanical data in 4-D with great success in discovering subtle differences in movement patterns. Particularly in comparing regular and irregular movement patterns. However, the interpretation of the data was very convoluted, and perhaps even completely obscured from the intended audience.

So I would say yes, fractals can help with analytics, but one might need to be cautious with visualization or interpretation. That's maybe the part where further work needs to be done?

Hi Sean Osis, Thank you for sharing the experience and insight. Can you please mention what could be those factors that made data interpretation difficult. Can it be some inherent property of fractals?

Gokul, I think you are right that fractal analysis can be inherently more difficult to understand than some other analyses. I'll admit that I am no expert in fractal analysis, but I have had experience in communicating concepts like Fourier Transforms or PCAs to others. I think that one factor that makes these concepts more difficult to translate and interpret is a general lack of context. Many simpler mathematical concepts can be explained by analogy to someone is unfamiliar, whereas something like a Fourier Transform can be tough to comprehend if you don't already know the mathematical concept behind it. So, one thing that I found valuable was to add a contextual X-axis to my FFT frequency plots. Instead of just saying frequency on the axis, I would add some context about systems that vibrate at those frequencies (car springs, tennis racquet etc). This helped a lot in providing some context to the person who was trying to understand the research.

I'm not sure exactly what this context would look like for fractal analysis, but it would probably be very helpful to figure out a sort of context for readers of this kind of research.

Herewith some examples on how fractals help in space time analytics and data visualization:

Jiang B. (2015), Head/tail breaks for visualization of city structure and dynamics, Cities, 43, 69-77, Preprint: http://arxiv.org/ftp/arxiv/papers/1501/1501.03046.pdf.

Herewith my fresh reflections on the very interesting question.

As long as you are working with real world data, if you took the right perspective and scope, the data would be fractal, so head/tail breaks applies. However, a few points for your attention:

(1) there are three definitions of fractal, but the third definition is more effective:

Article A Smooth Curve as a Fractal Under the Third Definition

(2) usually topological perspective rather than geometric perspective enables one to see the underlying scaling or fractal or living structure:

Presentation A Geospatial Perspective on Sustainable Urban Mobility in th...