Do Fractals have anything to do with Brownian motion?

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SUMMARY

Fractals and Brownian motion are interconnected concepts in mathematics and physics. While Brownian motion was established prior to the formal study of fractals, fractional Brownian motion serves as a bridge between the two. The discussion highlights the potential for using fractals to explain the complexities of Brownian motion, referencing the Wikipedia page on fractional Brownian motion for further exploration.

PREREQUISITES
  • Understanding of Brownian motion and its mathematical foundations
  • Familiarity with fractal geometry and its properties
  • Knowledge of fractional Brownian motion and its applications
  • Basic grasp of stochastic processes and their significance in physics
NEXT STEPS
  • Research the mathematical properties of fractional Brownian motion
  • Explore the relationship between fractals and stochastic processes
  • Study applications of fractals in modeling natural phenomena
  • Investigate historical developments in the study of Brownian motion
USEFUL FOR

Mathematicians, physicists, and students interested in the relationship between fractals and stochastic processes, particularly those studying Brownian motion and its applications in various fields.

Herricane
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I watched a show on Fractals and it sort of remind me of Brownian motion. So my question is has anyone ever used fractals to explain Brownian motion?
 
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Herricane said:
I watched a show on Fractals and it sort of remind me of Brownian motion. So my question is has anyone ever used fractals to explain Brownian motion?

I believe that Brownian motion was successfully explained before fractals were solidified as an object of study.
 

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