The Mandelbrot Set – The only video you need to see!
Good video, other than the title.
I have a question though:
Considering the widespread occurrence of fractal-like properties in real things, why is it often said that classical (i.e. non-quantum) mechanics defines the future exactly, when every single interaction would involves a calculation to literally infinite precision?
The Rev Dodgson said:
The Mandelbrot Set – The only video you need to see!Good video, other than the title.
I have a question though:
Considering the widespread occurrence of fractal-like properties in real things, why is it often said that classical (i.e. non-quantum) mechanics defines the future exactly, when every single interaction would involves a calculation to literally infinite precision?
It is a good question.
won’t let me watch the video in my country, been blocked, what it tells me
told me twice, I tries again in case was a blip, told me same, again
transition said:
won’t let me watch the video in my country, been blocked, what it tells metold me twice, I tries again in case was a blip, told me same, again
apparently, the info is copyrighted?
transition said:
won’t let me watch the video in my country, been blocked, what it tells metold me twice, I tries again in case was a blip, told me same, again
That’s strange.
I watched that just an hour ago on my pad, but on my computer I get the blocked messag
The Rev Dodgson said:
transition said:
won’t let me watch the video in my country, been blocked, what it tells metold me twice, I tries again in case was a blip, told me same, again
That’s strange.
I watched that just an hour ago on my pad, but on my computer I get the blocked messag
youtube have a new set of terms and conditions.
transition said:
won’t let me watch the video in my country, been blocked, what it tells metold me twice, I tries again in case was a blip, told me same, again
VPN Europe.
The Rev Dodgson said:
transition said:
won’t let me watch the video in my country, been blocked, what it tells metold me twice, I tries again in case was a blip, told me same, again
That’s strange.
I watched that just an hour ago on my pad, but on my computer I get the blocked messag
Does your tablet have a VPN set up? I was able to get the video to play via Opera with the inbuilt VPN enabled and set to America…
furious said:
The Rev Dodgson said:
transition said:
won’t let me watch the video in my country, been blocked, what it tells metold me twice, I tries again in case was a blip, told me same, again
That’s strange.
I watched that just an hour ago on my pad, but on my computer I get the blocked messag
Does your tablet have a VPN set up? I was able to get the video to play via Opera with the inbuilt VPN enabled and set to America…
Opera VPN on americas got blocked but europe didn’t.
furious said:
The Rev Dodgson said:
transition said:
won’t let me watch the video in my country, been blocked, what it tells metold me twice, I tries again in case was a blip, told me same, again
That’s strange.
I watched that just an hour ago on my pad, but on my computer I get the blocked messag
Does your tablet have a VPN set up? I was able to get the video to play via Opera with the inbuilt VPN enabled and set to America…
I don’t know, but I just checked the pad and it’s being blocked on there as well now, so looks like just bad timing.
OK, so here’s another one:
Very different from the first one, but also interesting.
That Geogebra program looks good. Hadn’t heard of it.
The Rev Dodgson said:
furious said:
The Rev Dodgson said:
That’s strange.
I watched that just an hour ago on my pad, but on my computer I get the blocked messag
Does your tablet have a VPN set up? I was able to get the video to play via Opera with the inbuilt VPN enabled and set to America…
I don’t know, but I just checked the pad and it’s being blocked on there as well now, so looks like just bad timing.
imagine living in a country where you had to VPN to access videos you want to watch
The Rev Dodgson said:
The Mandelbrot Set – The only video you need to see!Good video, other than the title.
I have a question though:
Considering the widespread occurrence of fractal-like properties in real things, why is it often said that classical (i.e. non-quantum) mechanics defines the future exactly, when every single interaction would involves a calculation to literally infinite precision?
Fair enough question. It was discussed in the 1950 book “First lensman” by E.E.Smith for example, before fractal-like behaviour was discovered. People who say this don’t understand “strange attractors”, which is not too surprising as it’s a bit esoteric.
Not only does classical mechanics not define the future exactly, it has been proved that the Navier-Stokes (fluid flow) equations cannot be solved for turbulent flow at all. Similarly, Einstein’s equations of General Relativity for conservation of mass and momentum give us 4 equations in 10 unknowns, leaving the result 6-fold unpredictable.
The unsolvability of the classical equations for fluid flow is why no-one can predict climate change.
mollwollfumble said:
The Rev Dodgson said:
The Mandelbrot Set – The only video you need to see!Good video, other than the title.
I have a question though:
Considering the widespread occurrence of fractal-like properties in real things, why is it often said that classical (i.e. non-quantum) mechanics defines the future exactly, when every single interaction would involves a calculation to literally infinite precision?
Fair enough question. It was discussed in the 1950 book “First lensman” by E.E.Smith for example, before fractal-like behaviour was discovered. People who say this don’t understand “strange attractors”, which is not too surprising as it’s a bit esoteric.
Not only does classical mechanics not define the future exactly, it has been proved that the Navier-Stokes (fluid flow) equations cannot be solved for turbulent flow at all. Similarly, Einstein’s equations of General Relativity for conservation of mass and momentum give us 4 equations in 10 unknowns, leaving the result 6-fold unpredictable.
The unsolvability of the classical equations for fluid flow is why no-one can predict climate change.
Why it can’t be predicted precisely anyway, so it might be very much worse than current “worst case” predictions suggest.
I can’t watch the video, but I got myself into trouble when I was at Uni in 1988 trying to program a Mandelbrot zoom set of images. I tried it with the brand new 80286 processor in the labs PS2, but it took too long to provide an image even as low resolution as 320×240.
My bright idea was to check out the brand new intranet of PCs in the University, and test to see how many processors were connected to it. I found dozens, not only in the room, but also many that had just been connected elsewhere in the Uni. This was great, I sent a packet of code to each of them to run one single Mandelbrot image overnight and return the result to my own terminal.
The next day, with a smile on my face, I was collating the images that were returned during the night when I felt a hand on my shoulder…
“I was wondering who it was. Your little project has stopped all of the salary payments, exam results, and background processes.”
At that point I was asked to leave the uni. :(
Mandelbrot animation created in Excel:
Mandelbrot x 2^48
The Mandelbrot set is based on the iterative expression 
where z is a complex number of the form 
. If the same expression is applied to the quaternions of the form 
, where the 
are each real numbers and 
, 
, the result is a 4-dimensional image. I wrote a program a while ago to generate just such images (it’s interactive, so once the calculations are done the user can rotate the image, zoom in and out, change viewports, sweep across any of the real or complex axes, etc.); here’s an example image (this one’s a 2-D representation of a 3-D cross-section of a hyperjulia set with 
I made some movies of sweeping through the different spaces, too, but I can’t put them here.
btm said:
The Mandelbrot set is based on the iterative expression
I made some movies of sweeping through the different spaces, too, but I can’t put them here.
Bloody show-off :)
But seriously, that’s impressive. Anything available online?
On the discovery of the quaternion:
The Rev Dodgson said:
On the discovery of the quaternion:
And a link linked from the link above:
The Rev Dodgson said:
btm said:
The Mandelbrot set is based on the iterative expression
I made some movies of sweeping through the different spaces, too, but I can’t put them here.
Bloody show-off :)
Yes :)
The Rev Dodgson said:
But seriously, that’s impressive. Anything available online?
Nothing from me, though there may be others who have had the same idea. I don’t have much of an online presence (deliberately), no youtube or facebook accounts. I’ll look into finding somewhere to host them.
As to the octionions, I haven’t tried to expand the software to look at octonions, sedenions, or higher-order Cayley-Dickson algebras; as the number of imaginary dimensions increases, so does the level of abstraction. Complex numbers are commutative and associative under multiplication:
The quaternions are non-commutative, though they’re still associative:
The octonions lose associativity, though they retain alternativity:
The sedenions lose all those properties, and things start to get complex :)
btm said:
The Rev Dodgson said:
btm said:
The Mandelbrot set is based on the iterative expression
I made some movies of sweeping through the different spaces, too, but I can’t put them here.
Bloody show-off :)
Yes :)
The Rev Dodgson said:
But seriously, that’s impressive. Anything available online?Nothing from me, though there may be others who have had the same idea. I don’t have much of an online presence (deliberately), no youtube or facebook accounts. I’ll look into finding somewhere to host them.
As to the octionions, I haven’t tried to expand the software to look at octonions, sedenions, or higher-order Cayley-Dickson algebras; as the number of imaginary dimensions increases, so does the level of abstraction. Complex numbers are commutative and associative under multiplication:
The quaternions are non-commutative, though they’re still associative:
The octonions lose associativity, though they retain alternativity:
The sedenions lose all those properties, and things start to get complex :)
I meant to add that there some interesting information about C-D algebras and the fun you can have with them here: https://math.ucr.edu/home/baez/week59.html; this page is part of a series by the American mathematical physicist John Baez.