< p >其实比你想象的更复杂,因为风景大约< a href = " https://en.wikipedia.org/wiki/Fractal_landscape " rel = " nofollow noreferrer " > < / >分形表面。一个模拟< a href = " https://en.wikipedia.org/wiki/Coastline_paradox " rel = " nofollow noreferrer " >海岸线悖论< / >。基本上,问题是衡量一个海岸线的长度。简单,是吧?但是,事实证明,这完全是依赖于所使用的分辨率。量尺越小,越小入口你测量,周长生长在小的极限测量棒无穷测量在每个小砂粒和岩石。这样的线路,据统计,分形,在这个意义上,看着越来越小的尺度上你会看到大约相同数量的循环本身。这些都是常见的自然;一个更好的例子(因为它是一个分形小得多的尺度上)是一个云。< / p > < p >同样,没有特定的规模看风景时,因为大型山脉看起来大约像山(山在同一区域,统计在世界各地是不一样的)。 The way to measure the roughness of these surfaces is by their fractal or Hausdorff dimension. Of course, however, all of these things are not perfect fractals and are really only fractals for a certain size range. Big mountains look like little mountains, but rocks under your shoe look different. And in my explanation above, it's questionable to compare the sand grains to the coast as you would see it on a map. And, finally, I don't have expertise regarding what actual geographers use as their measure of roughness, but they certainly have to contend with fractal statistics.