3 ms·

> 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 ag

• taneq 7y ago
  Well yeah, that's the "(statistically) selfsimilar" bit. Random fractals like this aren't self-congruent, just self-resembling.
• arketyp 7y ago
  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.
• swiley 7y ago
  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.
• benogorek 7y ago
  Yeah if you were to discretize it, then you'd get random walks with the only difference being the variance of movement from the last point. Wish I could find this one source that talked about continuous time noise processes - it was pretty interesting. If you assign a random variable to every point t on a continuum, it's not a real process (in terms of the definitions set forth in Measure Theory), so you have to use other methods to define them, like limits of discrete processes.