Reminds me of the conundrum of being unable to measure shoreline
Can you see it?
Submitted 1 day ago by ickplant@lemmy.world to [deleted]
https://lemmy.world/pictrs/image/92a4deec-7e36-41c5-b908-3ede6c92fd96.gif
Comments
Big_Boss_77@fedinsfw.app 1 day ago
Akasazh@lemmy.world 1 day ago
Alan Davies (of qi fame) once made a documentary where he tried to measure the length of a piece of string, the shoreline issue also comes up.
Naz@sh.itjust.works 1 day ago
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Imagine an island (e.g: Bermuda, Hook Island, Sardinia, etc)
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Draw a square or rectangle approximating all of the land not currently touching water (e.g: All pixels must not contain water)
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Draw a larger red square encompassing the smaller red square or rectangle.
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Subtract any brown, green, or “land” pixels, and add them to the total count of Box_1.
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Remove green, blue and other “water” pixels from Box_2.
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Your final result will be a red outline precisely mapping the coastline of the island in question. You can now measure distance by taking
pixelsand multiplying by the scale of the zoom-distance (parralax).
mushroomman_toad@lemmy.dbzer0.com 1 day ago
This measurement is a factor of pixel size. As resolution increases and pixel width approaches 0, the shoreline length approaches infinity.
Though I guess you’d eventually run into the problem of clearly defining the shoreline once you’re distinguishing between water molecules and grains of sand. is the water between the sand molecules part of the ocean? How concave is the boundary on the stretches between sand grains?
FishFace@piefed.social 1 day ago
Over a very broad range of scales (like, from the scale of 10km down to the scale of 1mm) the number of boundary pixels of a natural shape like an island increases according to a power law as you increase the resolution.
This means that your approach doesn’t give you an objective value because it depends so strongly on the resolution.
This way of computing the length of a boundary leads to the concept of box-counting dimension. When you increase the resolution of the pixel grid, you’ll get a larger number of pixels on the boundary. Keep refining the grid many times. Graph the log of the total number of pixels against the log of the number of boundary pixels. The box counting dimension is the slope of that graph.
Why would we call this “dimension”? Because if you do this to a line, the slope is 1, and if you do it to a square, the slope is 2.
More information: https://en.wikipedia.org/wiki/Fractal_dimension?wprov=sfla1
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stupidcasey@lemmy.world 1 day ago
Just get a small enough ruler either you’ll measure the shoreline or you’ll disprove calculus either way it’s not nothin’
marcos@lemmy.world 1 day ago
Well, if you get a small enough ruler you will already disprove quantum physics. No need to use it for anything.
Klear@piefed.world 1 day ago
At best you’ll disprove shoreline.
Aarkon@discuss.tchncs.de 1 day ago
Fractal shorelines. Always a pleasure to behold.
applebusch@lemmy.blahaj.zone 1 day ago
hmm yes this beach is made of beach
0ops@piefed.zip 1 day ago
Son of a beach
ivanafterall@lemmy.world 1 day ago
Does a nude woman jiggling down a beach not count as NSFW anymore!?
MeatPilot@sh.itjust.works 1 day ago
Raiderkev@lemmy.world 1 day ago
It took me a while, but the payoff when it finally gets there is great.
raspberriesareyummy@lemmy.world 1 day ago
No I can’t see it. Anyone willing to enlighten me?
Treczoks@lemmy.world 1 day ago
Same here.-
Makeshift@sh.itjust.works 1 day ago
This successfully hurt my brain.
Imke@feddit.org 1 day ago
You fucker
gandalf_der_12te@feddit.org 1 day ago
infinite real estate! how practical :D
pineapplelover@lemmy.dbzer0.com 1 day ago
This made me research the coastline paradox
MathiasTCK@lemmy.world 1 day ago
This made me research the coastline paradox
Admetus@sopuli.xyz 1 day ago
Infuriating but pretty cool
Zier@fedia.io 1 day ago
It's Fractal Beach, DUH!
SaltyIceteaMaker@lemmy.ml 1 day ago
damn. only found out its a gif due to other comments, for me its just a static image
Arachnidbrilliant@lemmy.dbzer0.com 1 day ago
Alright…… I fell for that.
Phantaloons@piefed.zip 22 hours ago
ENHAAAAAAAAAAA
Resonosity@lemmy.dbzer0.com 1 day ago
Thanks I hate it
melsaskca@lemmy.ca 1 day ago
Those are turtles!
Misty@lemy.lol 1 day ago
I’m still squinting to see…
helpImTrappedOnline@lemmy.world 1 day ago
Crime shows; Pull up the satilight view. Zoom in. There, what’s that spec? Enhance. There’s our guy, move out!
Glitterkoe@lemmy.world 1 day ago
Unexpected Dumpert.nl
ashenone@lemmy.ml 1 day ago
Glad I made it to the end. Totally worth it
Uebercomplicated@lemmy.ml 1 day ago
This is an evil comment