Benoit Mendelbrot described the coastline as fractal in 1967, it is interesting to see how many people have picked up on this in 43 years...

- Wikipedia quotes an exact length (11072.76 miles), then somewhat as an add on states that it is also fractal, but without any citation and no fractal dimension given. (see

http://www.ben-daglish.net/mapping.shtml for why they chose the quite arbitrary figure).

- Wikianswers gives 2400 miles, Encyclopaedia britannica 1960 gives 2336 miles

- The British cartographic society correctly describe the coastline as fractal, but still give the figure of 11072 miles and fails to give a fractal dimension.

- Another website gives the value 6000 miles.

- The CIA factbook has it as 7723 miles.

So the idea of fractal dimensions really isn't well appreciated, despite it being essential in this question. The above values are all correct and all incorrect depending on your resolution. 11072 miles is too short if you are using a pedometer. Or if you measured it by hand with a measuring tape it might be 15000 miles long.

I think the problem is that Mandelbrot correctly showed that you can model the coastline as having a fractal dimension of about 1.2. But

*we have all forgotten to do the final step*... 1.2 is not the amount of coastline, it is the dimension of the amount. So just as an area has units m^2, Britain's coastline has units m^1.2... but how many m^1.2 is it???

Let's say it is 20,000,000m^1.2, that means that at a resolution of 1 metre it passes through 20 million squares, and at 1/n metres it passes through 20,000,000*n^1.2 squares.

This should be how we measure coastlines, e.g. South Africa's is 4,700km^1.02. Note we are not measuring their 'length' but the 'amount' or 'size' of coastline.

This is a better way to define the size of coastlines, as people can use it appropriately, e.g. if you are planning on circumnavigating a country on 4x4 you can interpret the amount differently than if you just want to know how much string to use to mark out the coast with on a map.

We should all be using this convention right? and we could start with simple fractals. For example, Wikipedia states that the fractal dimension of a Koch snowflake is 1.2619, but what is the size of the snowflake border of diameter 1m? 3m^1.2619? 100m^1.2619?

Is there 'more' Koch curve than 2d cantor dust (which has the same fractal dimension) of the same diameter? We can know the answer to this.