Wow! This is absolutely brilliant explanation! I just finished reading Per Bak’s Self Organized Criticality, where he mentions the coastline example, but without deriving it. Your explanation made it obvious! Many thanks!
The coast is a fractal. A fractal is when the Hausdorff dimension (what's being shown in the video) is larger than the topological dimension (what you typically think of as a dimension). Fractal does not imply self similarity, but self similarity does imply fractal. You can think of something being a fractal if it's rough (the perimeter is always changing directions even when you look really close), and most natural things are fractals because of that.
If you went to the 'coast' and drew what you could see at your feet (assuming you are at the water's edge); would the drawing be (self)similar to the large coast? Yes. Same but different at all scales - fractal.
..."Coastline," not "Border." Read the definition of "Border" in the Devil's Dictionary by Ambrose Bierce: "In political geography, an imaginary line between two nations, separating the imaginary rights of one from the imaginary rights of the other." That definition doesn't apply here. However, to be fair, another historical example I could have used is the border between Portugal and Spain. Surveyors from Portugal and Spain used different size intervals to do this kind of measurement and came out with different lengths for the boundary. This seeming paradox is one of the historical precursors to this topic.
I had always thought that natural selection produced this, until I saw the Nova video about fractal geometry. So, who "created" Loren Carpenter? Just as people did not see what Benoit Mandelbrot saw, the creators of this video are not seeing WHO created them and everything else in the universe using, among other things, this concept of geometry.
So firstly that Alpha sign (looks like a fish) is not a proportional sign (~) and secondly: proportional doesn’t means equal. In a linear graph, the numbers are proportional to each other, but they aren’t equal. So you can’t transform this one formula into this other when you are calculating the dimension of the British coast. The second formula may be right, but this isn’t the way to get there.
Wow! This is absolutely brilliant explanation! I just finished reading Per Bak’s Self Organized Criticality, where he mentions the coastline example, but without deriving it. Your explanation made it obvious! Many thanks!
I bought a book by Mandelbrot himself, but his style was not educational. This video clarified the math so perfectly.
You did not include links.
sir, will you tell me which software allows me to present a subject like you did in this video, i mean drawing and recording it..
In 24:18, why log 200 = 5.3 and etc? Isn't it with base 10, therefore resulting in 1.7?
+Irene Vega He's using the natural logarithm.
Natural log = base 2.71...
What drawing software do you use for your videos?
Nice approach. Just that you're missing a minus sign. (1/r)^(-1)=N, not ^1. Analogously, (1/r)^(-D)=N. Cheers.
Can you please explain how this works??
How will it become G^(1-D) at the end?
Thanks a lot, would be lovely to see more videos on fractal. :)
Thank you! This video helped me a lot :)
Awesome video, cheers!
thank you so much, it helps me a lot in my investigation of fractal dimension. thank you.
btw I'm not sure about the (1/r)^D = N if r>1
Thank you so much! This really helped
Great video
The coast could be a fractal, but it doesn't look self-similar in smaller scale
The coast is a fractal. A fractal is when the Hausdorff dimension (what's being shown in the video) is larger than the topological dimension (what you typically think of as a dimension). Fractal does not imply self similarity, but self similarity does imply fractal. You can think of something being a fractal if it's rough (the perimeter is always changing directions even when you look really close), and most natural things are fractals because of that.
If you went to the 'coast' and drew what you could see at your feet (assuming you are at the water's edge); would the drawing be (self)similar to the large coast? Yes. Same but different at all scales - fractal.
i was promised no borders on this channel, i feel cheated
..."Coastline," not "Border." Read the definition of "Border" in the Devil's Dictionary by Ambrose Bierce: "In political geography, an imaginary line between two nations, separating the imaginary rights of one from the imaginary rights of the other." That definition doesn't apply here.
However, to be fair, another historical example I could have used is the border between Portugal and Spain. Surveyors from Portugal and Spain used different size intervals to do this kind of measurement and came out with different lengths for the boundary. This seeming paradox is one of the historical precursors to this topic.
@@davidschandler48 IT IS A JOKE YOU DIDNT HAVE TO PULL UP WITH THE WIKIPEDIA ARTICLE
@@CeleryBruh My reply was also a joke. Look up "The Devil's Dictionary."
@@CeleryBruh LMAOO
Thanks!
I had always thought that natural selection produced this, until I saw
the Nova video about fractal geometry. So, who "created" Loren
Carpenter? Just as people did not see what Benoit Mandelbrot saw, the
creators of this video are not seeing WHO created them and everything
else in the universe using, among other things, this concept of
geometry.
THIS WAS 10 YR AGO HELLO FUTURE!!!😅😊😂😅🎉😅😂😅😂😂😊
So firstly that Alpha sign (looks like a fish) is not a proportional sign (~) and secondly: proportional doesn’t means equal. In a linear graph, the numbers are proportional to each other, but they aren’t equal. So you can’t transform this one formula into this other when you are calculating the dimension of the British coast. The second formula may be right, but this isn’t the way to get there.