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Inigo Quilez :: computer graphics, mathematics, shaders, fractals, demoscene and more

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Inigo Quilez :: articles :: fBM - 2019 Intro fBM stands for Fractional Brownian Motion. But before we talk about nature, fractals and procedural terrains, let's get a bit theoretical for a moment. A Brownian Motion (BM), without the "fractional" part, is a motion where the position of a given object over time changes in random increments (imagine a sequence of "position+=white_noise();"). Formally, BM is the integral of white noise. These movements define paths that are random yet (statistically) self similar, ie, a zoomed-in version of the path resembles the whole path. A Fractional Brownian Motion is a similar process in which the increments are not completely independent from each other, but there's some sort of memory to the process. If the memory is positively correlated, changes in a given direction will tend to produce future changes in the same direction, and the path will then be smoother than a vanilla BM. If the memory is negatively correlated, a positive change wi

--> Inigo Quilez :: computer graphics, maths, shaders, fractals, demoscene Inigo Quilez :: :: Intro fBM stands for Fractional Brownian Motion. But before we talk about nature, fractals and procedural terrains, let's get a bit theoretical for a moment. A Brownian Motion (BM), without the "fractional" part, is a motion where the position of a given object over time changes in random increments (imagine a sequence of "position+=white_noise();"). Formally, BM is the integral of white noise. These movements define paths that are random yet (statistically) self similar, ie, a zoomed-in version of th

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