The Hurst Fractal Generator is a tool that allows users to generate fractal landscapes using the Hurst exponent and iterative refinement. By adjusting the Hurst index and the number of iterations, you can control the appearance and complexity of the generated fractal terrain, ranging from jagged and rugged landscapes to smooth and rolling hills.
Hurst Index in Mathematical Terms
Mathematically, the Hurst index is used to characterize the self-similarity and long-range dependence of a fractal process. The value of HH typically ranges between 0 and 1:
H=0.5H=0.5: Represents a random walk, where the fractal has no clear trend and behaves like white noise.
H<0.5H<0.5: Indicates anti-persistence, where an increase is likely to be followed by a decrease, and vice versa.
H>0.5H>0.5: Implies persistence, suggesting that an increase is likely to be followed by further increases.
By selecting the appropriate Hurst index, users can model a wide range of natural phenomena, from turbulent seas to calm landscapes.