The concept of fractals being neither one nor two dimensions seemed to me quite odd, but after this explanation it appears to be logical. Even though, I still can not grasp the whole concept of fractals, the videos helped to deepen my understanding of it. Thank you for the amazing content!
Thank you for this excellent lecture! Every year I have my algebra students make Koch snowflakes before our winter holiday break. I always need to review this math before I present it to them
Nice explanation. BTW, unlike your examples with "regular dimensions", at Koch & Sierpinski you didn't "magnify the length by the factor R" but repeated the shortened base segment R times.
I have a great passion for mathematics. Can I, as a doctor, study fractal geometry alone? If the answer is yes, what are the prerequisite mathematics to understand fractal geometry?
An oval is just one path with no fuzziness to it, so it's just dimension 1. Same with a spiral. In general, lines (straight or curved) have dimension 1. Fractal dimensions only come into play when they have an infinite number of turns (causing the fuzziness).
We use 3 instead of 2 or some other number, because in the construction of the Koch curve, we're taking away the middle 1/3 of each segment. So a multiplication by 3 makes sense. In general, try to stay consistent with the way the figure is constructed.
What would a Pi dimensional space be like? I've looked up Fractal dimensions and it only goes up to about 3. This is so frustrating. I think many things might have Pi dimensions.
To have a dimension of 3.14159... you need to start with something 4 dimensional and start taking things away that's almost 1 full dimension but not quite. I'm sure if you search the academic materials you'll find some, but if just google, probably not, because popular sources don't tend to start with a 4-dimensional object
Hi, I was just wondering something. If u apply the formula to a disk instead of a square and to a circle instead of a line, what fractal dimension do u obtain? Is it 2 and 1 or something else?
Hi. If you apply the formula to the disk and circle you would get 2 and 1 as usual. The fractal formula is consistent with the "usual" dimensions for non-fractal figures.
Best explanation of the topic!
Thanks
Incredibly clear. Great examples, to the point. Thank you very much.
Thanks for watching
thankyou so much. I had to go through too many unclear toutorials to find this and I finally understand.
Your video is beyond the words of gratitude
The concept of fractals being neither one nor two dimensions seemed to me quite odd, but after this explanation it appears to be logical. Even though, I still can not grasp the whole concept of fractals, the videos helped to deepen my understanding of it. Thank you for the amazing content!
Super clear video. Thanks for helping me understand what’s unique about fractals beyond the fact that they are self-similar!
Wonderful explanation. Thank you very much for putting in the time to do this
Thank you. Your explanation is very clear and helpful.
Thank you for this excellent lecture! Every year I have my algebra students make Koch snowflakes before our winter holiday break. I always need to review this math before I present it to them
Awesome
Quick and easy explanation. Thank you.
Incredibly helpful
Thank you this helped me a lot! Reading a fractal book for fun and got stuck early on when it discusses Hausdorff dimension
Hausdorff dimension is another word for fractal dimension. Now if your book goes into Hausdorff measures, though, then it's way beyond this video.
Nicely explained, thank you very much!
This is helpful! Well even though I’m not taking any test on this or learning this in class
Very good explanation. Tqvm!
Excelent explication!
Very clear for a beginner on this topic
Thanks
Parfaitement expliqué. Good job. thank you
De rien!
Nice explanation.
BTW, unlike your examples with "regular dimensions", at Koch & Sierpinski you didn't "magnify the length by the factor R" but repeated the shortened base segment R times.
You're correct. Very true. But at infinity, the two are the same. As soon as you magnify everything gets repeated, and vice-versa.
Really great video.
Great explanation! Thank you
thanks! interesting discussion; Mandelbrot wrote about that in reference to Felix Hausdorff's conception of topological space;
Very interesting, thanks for sharing this
Excellent explanation
THANK YOU SO MUCH
thanks a lot
Thank you
I have a great passion for mathematics. Can I, as a doctor, study fractal geometry alone? If the answer is yes, what are the prerequisite mathematics to understand fractal geometry?
Oh yes. If you remember Math from before med school, you can learn fractal geometry on your own.
Thank you for this. I have a question tho, how is the fractal dimension of an oval and spiral calculated?
An oval is just one path with no fuzziness to it, so it's just dimension 1. Same with a spiral. In general, lines (straight or curved) have dimension 1. Fractal dimensions only come into play when they have an infinite number of turns (causing the fuzziness).
Can someone explain to me, why the length of the koch-curve is multiplyied by 3 to get the dimension? I didnt get it (5:28)
We use 3 instead of 2 or some other number, because in the construction of the Koch curve, we're taking away the middle 1/3 of each segment. So a multiplication by 3 makes sense. In general, try to stay consistent with the way the figure is constructed.
Hi sir,thanks for ur great explosion, I want know what is the dimention of phytagorian tree
The answer is log(2) / log(sqrt(2)) = 2.
What would a Pi dimensional space be like? I've looked up Fractal dimensions and it only goes up to about 3. This is so frustrating. I think many things might have Pi dimensions.
To have a dimension of 3.14159... you need to start with something 4 dimensional and start taking things away that's almost 1 full dimension but not quite. I'm sure if you search the academic materials you'll find some, but if just google, probably not, because popular sources don't tend to start with a 4-dimensional object
Hi, I was just wondering something. If u apply the formula to a disk instead of a square and to a circle instead of a line, what fractal dimension do u obtain? Is it 2 and 1 or something else?
Hi. If you apply the formula to the disk and circle you would get 2 and 1 as usual. The fractal formula is consistent with the "usual" dimensions for non-fractal figures.
@@vudomath all right ty very much
Thank you