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The coastline paradox relies on the assumption that the coast is equally “jagged” at all levels. Is this actually true? I mean, if I go to the beach and look at

The coastline paradox relies on the assumption that the coast is equally “jagged” at all levels. Is this actually true? I mean, if I go to the beach and look at the line where the water meets the land it doesn’t really seem like a fractal to me. The outer boundary of land masses gets smoothed out by erosion from the water, right?

groestl 3y ago
> it doesn’t really seem like a fractal to me. That's because you don't look close enough.
- infradig 3y ago
  The Wikipedia article states it's not really fractal.
  - ravi-delia 3y ago
    It actually bottoms out pretty low though. The apparent fractal dimension changes over scales, but is sufficient that ruler length really does make a huge distance in coastline length
meheleventyone 3y ago
Sure but the quantity that’s important is your sampling accuracy. Even on a visually smooth beach there is enough variation for that to significantly impact the results. This closely relates to numerical integration where often you’re dealing with fixed sized steps and for example can simulate significantly stiffer materials with a smaller timestep.
paulddraper 3y ago
If the coast is a sandy beach, then it is usually pretty smooth. But in other cases ... https://www.nps.gov/articles/images/acad-ship-harbor-rocky-coast_web.jpg https://www.nps.gov/articles/images/acad-ship-harbor-rocky-c...
- pjerem 3y ago
  > If the coast is a sandy beach, then it is usually pretty smooth But it underlines another issue in this problem. What is defining the coastline ? If it’s water touching the land, it’s always moving, if it’s land at sea level, it’s eight always moving or approximated depending on your definition. And billions of billions of billions of billions of … of grains of sand seems like very near to fractal that could arguably add billions of coastline kilometers depending on your max definition.
DonsDiscountGas 3y ago
Rocks and boulders have all kinds of different sizes in general. If the coast/beach area is all smooth and uniform small particles (ie sand) then it would be easy to measure as long as you use a ruler larger than ~10 grains of sand. If there are ranges of particles from 1cm (pebbles) to 10 cm (rocks) to 10 meters (boulders) to 100 meters (rock outcroppings) then the effect kicks in.
pugworthy 3y ago
You're taking the term "Coastline" literally. It's an abstract idea, and a coastline is a good way to conceptualize it as a real thing.
bee_rider 3y ago
If you look close enough the sand is pretty jagged I guess.

groestl 3y ago

> it doesn’t really seem like a fractal to me. That's because you don't look close enough.

infradig 3y ago
The Wikipedia article states it's not really fractal.
- ravi-delia 3y ago
  It actually bottoms out pretty low though. The apparent fractal dimension changes over scales, but is sufficient that ruler length really does make a huge distance in coastline length

meheleventyone 3y ago

Sure but the quantity that’s important is your sampling accuracy. Even on a visually smooth beach there is enough variation for that to significantly impact the results. This closely relates to numerical integration where often you’re dealing with fixed sized steps and for example can simulate significantly stiffer materials with a smaller timestep.

paulddraper 3y ago

If the coast is a sandy beach, then it is usually pretty smooth. But in other cases ... https://www.nps.gov/articles/images/acad-ship-harbor-rocky-coast_web.jpg https://www.nps.gov/articles/images/acad-ship-harbor-rocky-c...

pjerem 3y ago
> If the coast is a sandy beach, then it is usually pretty smooth But it underlines another issue in this problem. What is defining the coastline ? If it’s water touching the land, it’s always moving, if it’s land at sea level, it’s eight always moving or approximated depending on your definition. And billions of billions of billions of billions of … of grains of sand seems like very near to fractal that could arguably add billions of coastline kilometers depending on your max definition.

DonsDiscountGas 3y ago

Rocks and boulders have all kinds of different sizes in general. If the coast/beach area is all smooth and uniform small particles (ie sand) then it would be easy to measure as long as you use a ruler larger than ~10 grains of sand. If there are ranges of particles from 1cm (pebbles) to 10 cm (rocks) to 10 meters (boulders) to 100 meters (rock outcroppings) then the effect kicks in.

pugworthy 3y ago

You're taking the term "Coastline" literally. It's an abstract idea, and a coastline is a good way to conceptualize it as a real thing.

bee_rider 3y ago

If you look close enough the sand is pretty jagged I guess.