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**General Science / How are fractals affected/changed by entropy?**

« **on:**18/12/2013 05:37:00 »

Hi all,

Can someone give me a simple explanation for how entropy affects the fractal dimensions of things in the natural world? For example, I've just been reading about how the coastline of Britain has an approximate fractal dimension of 1.26 (1 being not fractal, and heading towards increasing fractal complexity, shown mathematically as 2). Due to the book I am reading, I am only assuming that this number was found by Felix Hausdorff in the early 1900s. According to the same book, a typical cloud has a fractal dimension of 1.35, so a bit more fractal.

So, taking the coastline example (but it could also apply to mountains and trees), my question is, if we can give fractal dimensions, as a number (1.26), to natural edges like this, how do we posit this against changes in the landscape due to things like ocean levels and wind erosion? Does this mean that something like a coastline would become less fractal with time? Or will these things (and entropy in general) actually make no difference to the fractal nature of the world? In other words, will things change, but remain as fractal as they ever were, even when the phenomena that is changing it is something other/outside of itself? (eg the sea or the wind). - Sorry, that last sentence sounded a bit silly, I guess I am having trouble articulating this when I don't yet know very much about it, which is why I am here.

I'm sure there are a number of articles that may explain this connection between fractals and entropy, however I have no formal training in any of this, so I would really super duper appreciate a more accessible and practical explanation.

Cheers,

Alinta

PS. Not sure what subheading to put this under (physics or the environment) so I'm just going to put it here...

Can someone give me a simple explanation for how entropy affects the fractal dimensions of things in the natural world? For example, I've just been reading about how the coastline of Britain has an approximate fractal dimension of 1.26 (1 being not fractal, and heading towards increasing fractal complexity, shown mathematically as 2). Due to the book I am reading, I am only assuming that this number was found by Felix Hausdorff in the early 1900s. According to the same book, a typical cloud has a fractal dimension of 1.35, so a bit more fractal.

So, taking the coastline example (but it could also apply to mountains and trees), my question is, if we can give fractal dimensions, as a number (1.26), to natural edges like this, how do we posit this against changes in the landscape due to things like ocean levels and wind erosion? Does this mean that something like a coastline would become less fractal with time? Or will these things (and entropy in general) actually make no difference to the fractal nature of the world? In other words, will things change, but remain as fractal as they ever were, even when the phenomena that is changing it is something other/outside of itself? (eg the sea or the wind). - Sorry, that last sentence sounded a bit silly, I guess I am having trouble articulating this when I don't yet know very much about it, which is why I am here.

I'm sure there are a number of articles that may explain this connection between fractals and entropy, however I have no formal training in any of this, so I would really super duper appreciate a more accessible and practical explanation.

Cheers,

Alinta

PS. Not sure what subheading to put this under (physics or the environment) so I'm just going to put it here...