Fractional Brownian Motion for Terrain Generation
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Fractional Brownian Motion for Terrain Generation
1–10 of 29 posts
Re: Fractional Brownian Motion for Terrain Generation
#2If you ever need to produce a bunch of FBM or other noise on the cpu fast, these two libraries are handy. They use SIMD instructions to make noise ~3x to ~7x faster than usual.
Re: Fractional Brownian Motion for Terrain Generation
#3> These movements define paths that are random yet (statistically) selfsimilar, ie, a zoomed-in version of the path resembles the whole path
This goes a bit against my intuition of self-similar, but I guess I should interpret "resembles" as *statistically resembles" here as well? Does it mean something like the distribution being the same at all zoom levels?
Re: Fractional Brownian Motion for Terrain Generation
#4> These movements define paths that are random yet (statistically) selfsimilar, ie, a zoomed-in version of the path resembles the whole path This goes a bit against my intuition of self-similar, but I guess I should interpret "resembles" as *statistically resembles" here as well? Does it mean something like the distribution being the same at all zoom levels?
Well yeah, that's the "(statistically) selfsimilar" bit. Random fractals like this aren't self-congruent, just self-resembling.
Re: Fractional Brownian Motion for Terrain Generation
#5> These movements define paths that are random yet (statistically) selfsimilar, ie, a zoomed-in version of the path resembles the whole path This goes a bit against my intuition of self-similar, but I guess I should interpret "resembles" as *statistically resembles" here as well? Does it mean something like the distribution being the same at all zoom levels?
There is a visual resemblence between zoom levels because of the statistical self-similarity across zoom levels. I suppose the word resemblence was chosen by the author as a less strict variation of the concept. But even the self-similarity of for instance the convergence border of the Mandelbrot set isn't completely self-same either.
Re: Fractional Brownian Motion for Terrain Generation
#6> These movements define paths that are random yet (statistically) selfsimilar, ie, a zoomed-in version of the path resembles the whole path This goes a bit against my intuition of self-similar, but I guess I should interpret "resembles" as *statistically resembles" here as well? Does it mean something like the distribution being the same at all zoom levels?
You should read Mandelbrot’s book “the fractal geometry of nature.” He talks quite a bit about ideas like this. It’s written with the intention that non mathematicians can read and understand the ideas too which is kind of neat.
Re: Fractional Brownian Motion for Terrain Generation
#7I'm surprised that he does not mention that, if you can compute FFT really fast, then you can implement all these textures without a loop along the octaves, by simply specifying the spectral decay and using random phases.
Re: Fractional Brownian Motion for Terrain Generation
#8I feel like a terrible adult for chuckling at the appropriateness of BM as the abbreviation for Brownian Motion.
Re: Fractional Brownian Motion for Terrain Generation
#9If anyone isn't aware of who Iniqo Quilez is, then explore the entire site and follow it up by looking at his work over at Shadertoy (username: iq) and any of his demoscene contributions at http://www.pouet.net and maybe read this fascinating article about his work with Pixar on Brave: http://www.cgw.com/Publications/CGW/2012/Volume-35-Issue-4-J...
Re: Fractional Brownian Motion for Terrain Generation
#10For 1-d time series analysis, the Autoregressive Fractionally Integrated Moving Average is the apparent analog: https://en.wikipedia.org/wiki/Autoregressive_fractionally_in.... "In a fractional model, the [differencing] power is allowed to be fractional, with the meaning of the term identified using the ... formal binomial series expansion"