Calculating fractal dimensions

In this video I briefly describe what a fractal dimension is and how to calculate it.

[maximilianopoblete]

I agree, this is the best video on the subject, ive researched for HOURS and cracked my head trying to understand, and i felt so frustrated, but you.. you saved my life, it was so simple all the time... Thank you, i really mean it.

[draknagar]

A complex subject explained in so unbelievably simple way. And most of all, with a little effort one can dive in divine world of Fractals

[blackice]

these are very good times indeed, because you can find high quality videos by such math geniuses, as Perelman

[sonugeorgealex]

Gone to so many places to understand fractals and finally found a man who could explain it easily in 10 min.

[johneagle]

Thank you so much. A very clear and understandable explanation.

[revali]

great video, simple, clear, quick !

[raghav_somani]

Bruh you explained it so nicely, i directly skipped aorund 6:00 at the square thing you were teaching and am watching in 2x still get everything

[DeathByMetal]

Hello Ashley, I was wondering if you know how to calculate the fractal dimension of an asset, say the Apple stock in the stock markets. I understand there are different ways to calculate the fractal dimension of an object and I've found there's something called Correlation Dimension, which is used when the points of the fractal are putted randomly in a plane. Which is the method to calculate the fractal dimension of such a fractal as a stock from the stock market?

Thanks in advance! I need this information for my undergraduate thesis.

[ProtoG]

Great job, I love your teaching style. Keep it up!

[funnymyth]

beautiful video. Thank you! You've gained a subscriber with this.

[MrCarmen]

very easy to understand!may save my coming exam

[VinBhaskara_]

hey Ashley. .Fantastic video! I just had one confusion at the end. The last example with the triangle: you had 4 (not 3) similar smaller pieces of triangle, right? Wouldn't that be then log(4)/log(2) again? Why did you count 3 for the last example, while you counted 4 when you had 4 similar square pieces in a previous example? When you say similar do you also mean rotation-wise similar too instead of only shape-wise? Thanks a bunch

[Jacqt]

Hey, does anyone know of an official site to get the formula? I would like to use this method in my research but I can’t cite YouTube 🤦🏾‍♀️

[flapafloupas]

So the triangle is noyt 2d? It is 1.58d?
Plz tell me if im wrong i want to know

[tabether]

At 9:00, why do you say that the triangle has been broken into 3 similar pieces, when it's actually 4 - the middle triangle, and the three outer triangles?

[dailynewsgrind]

its interesting that the main triangle(s) is pointing up but the rest of the smaller triangles all point down. Anything to do with polarity/magnitism?
Or the strong & weak forces?

[tinkeringtim]

Hi Ashley, I have a question about the definition of self-similarity and your (the usual) calculation of the dimension of the Sierpinsky triangle. The definition of self-similarity I know is that there exists an anisomorphic affine transformation (among other things, preserving parallel lines) from one to another. In order for the inner triangle to be similar to the outer triangle, it also has to be rotated or (worse) flipped around its center before scaling. I think the dimension calculation works out by happy accident because you get the same result (check?) if you call the seed the outer plus the inner inverted triangle, and each iteration adds both (but this is not the usual construction).

Do you have any comments on this? has it been studied and perhaps some equivalence shown? Can the definition of self-similarity be relaxed? Or is there just something I've missed?

[djosko]

I like your easy-going approach to the subject, but I have a followup question... how would you do this for an assymmetric set?

[Alkelism]

Hi mate, bit of useless information for you on fractals, As kids me and my brothers used to roll with greg sams to the shops in his spare wheelchairs when we stayed at his house, probably 27 years ago . getting babysat by him, He came to a few of the carry on regardless parties my dad organised after our cottage burned down in wales . A very clever and a very nice man .

[manoleioan]

Does a fractal have 0 dimensions if N is 1 and R is any natural number except 0 (and 1)?