a strait line segment is self. if i zoom in on a strait line segment i will find that at all scales it looks perfectly like the whole. is a strait line a fractal? i was under the impression the definition for a fractal was to have a fractional fractal dimension at either all scales or all practical scales.
Yes but the perimeter has (Hausdorff) dimension > 1, so it is somewhat space-filling. Arguably, it does have a little thickness. Of course, the line segments used to construct it do not!
nah, he is actually right with that one. fractal dimension has a fractional value for fractals. that's where the name fractals comes from. notably this is a different definition of 'dimension' then the commonly used one. so, no, being 1.26D does not imply thickness. also, what do the line segments dimensionality matter? the generating rule is applied infinitely there are no lines left once it is done they've all been replaced with the koch curve.
firstly, no, it certainly does not. secondly, there are 4 segments of length 1/3 the original. this is why perimeter is infinite, and why (Hausdorff) dimension is greater than one.
Ch in german is pronounced like the sound you make, when you want to clear your throat very softly with an continuing stream of air. It's like a guttural "H" sound. Kinda like the hissing of a cat.
I love this, I always foung that fascinating that an object with a finite area can have an infinite perimeter!
The fact that I love math probably increases how much I enjoyed this video but it was excellent.
Very well explained! You make it easy to understand something that, at first, seems unbelievable.
Wow man your vids are awesome!
Im not that much of a maths brain but you make it both much more fun to learn and also much easier to learn.
You can't just throw out that there is such thing as 1.26 dimensional and just leave it there! Glad to see more fractal videos!
Found myself looking at the infinite area outside of the snowflake! Fun!!!!!
Please make more videos man
I love this stuff.
Okay, this is super interesting
the patern continues on for ever great
As much as I love the Sierpinski, that's a really nice Koch
I DEMAND MOAR!
a strait line segment is self. if i zoom in on a strait line segment i will find that at all scales it looks perfectly like the whole. is a strait line a fractal?
i was under the impression the definition for a fractal was to have a fractional fractal dimension at either all scales or all practical scales.
that is really interesting keep making vids like this
the area of the koch snowflake is s^2 * √0.48 where s is the original side length.
great video, but does n't perimeter needs to be constant on the fractals?? the line can be divided into 3*(1/3+1/3+1/3)=3.
How would a four dimensional fractal look in 3d?
@fractalmath in the snow flake on part 3 you have 6 not 3.
I just... love you
How would one prove this?
I meant like a guttural, deeper cat hiss. Anyway you are probably right.
With your crazy letters which don't sound at all. :D
Yes but the perimeter has (Hausdorff) dimension > 1, so it is somewhat space-filling. Arguably, it does have a little thickness. Of course, the line segments used to construct it do not!
nah, he is actually right with that one. fractal dimension has a fractional value for fractals. that's where the name fractals comes from. notably this is a different definition of 'dimension' then the commonly used one. so, no, being 1.26D does not imply thickness. also, what do the line segments dimensionality matter? the generating rule is applied infinitely there are no lines left once it is done they've all been replaced with the koch curve.
that has to mean that there are particals smaller than atoms??
firstly, no, it certainly does not. secondly, there are 4 segments of length 1/3 the original. this is why perimeter is infinite, and why (Hausdorff) dimension is greater than one.
or any infinite amount of area, for the matter!
As the video approaches 6:22 my mental confusion approaches infinity. Just joking, infinity is great to ponder.
3:51 smiley face
3:51
Triforce within a triforce... That's some inception shit
MEH IS CONFUZZLED! :D
1:16 TRIFORCE OF TRIFORCES OF TRIFORCES OF TRIFORCE!!!!
1:16
Thank You at time 4:29 think i am is it at proportion from Golden Cut 1,6..... 777³ *#*#*
Ch in german is pronounced like the sound you make, when you want to clear your throat very softly with an continuing stream of air.
It's like a guttural "H" sound. Kinda like the hissing of a cat.
@kyleisreallycool To infinity and BEYOND!
you could, but it would be incorrect.
Whats that 298.311.997 to nearli at the light speed !!! 777³ *#*#*
Oh!! sorry! i don't know that speak :)
Don't tell Ganon.
.insipring...
First.
Yay!
Thanks for showing the perimeter sans units. Fail.