|
|
|
Germany2896 Posts
For a coastline you can't give a definite length, because the closer you look, the more little bumps you find. The dimension tells you how much longer the coast gets each time you zoom in.
For normal objects if you zoom in by the factor 2, lengths grow by the factor 2^1=2, areas by the factor 2^2=4 and volumes grow by the factor 2^3=8. The coastline might grow by the factor 2.3 which corresponds to a dimension of 1.2.
In a way the dimension can be used to describe how much finestructure there is. Or expressed differently how much detail is added when zooming in.
For most non artificial fractals the dimension also depends on the current scale.
But I'm not too much into fractals, just looked a little into them for procedural content creation some years ago.
|
A friend of mine worked on magnetisation zones in iron, as he thought they might have a fractal pattern. He used imaging of the zones to work out the fractal dimension. I'm guessing it wasn't too useful...
I think D is the fractal dimension of the boundries of the magnetized zones, ie they were 1D line so complicated they took up an area. I think the box counting method was used, and I think, but I'm willing to be corrected, that the method essentially slaps a grid onto the image and counts the boxes in which the boundy lies. (ie, it measures an upper limit of the 2D space the 1D line occupies). Then it does it again with a tighter grid, to see at higher detail, what volume the line takes up. The actual definition of the fractal dimension D is a defined function including the ration of those numbers of boxes. Or something like that.
|
|
|
|
|
|
EPT
