THIS is cool!!

[chilehed]

SUMMARY:
What’s the connection between a dripping faucet, the Mandelbrot set, a population of rabbits, thermal convection in a fluid, and the firing of neurons in your brain? It’s this one simple formula: Xn+1=rXn(1-Xn). The logistic map connects all these and so much more!

 

[Strathos]

Don't post videos without a summary please.

 

[The IbanezerScrooge]

super interesting!

 

[FrumiousBandersnatch]

Don't post videos without a summary please.

It's Veritasium revisiting chaos and non-linear dynamics to introduce universality - well worth watching IMO.

 

[essentialsaltes]

I can remember programming my Apple //e to make that graph in the still image and estimate the Feigenbaum number.

 

[Oaktree125]

The presenter actually states the right idea- a deterministic computer generates it....This is important to Christianity because= Can - in the midst of this- a deterministic fractal actually also be expressed that does provide a viable structure and create predictable you-ness even to the number of hairs on your head, that you will exist, and all the other children of God, even prophecy despite complexity, selecting out a Chosen people, etc coming to be throughout history??? When you attach fractal driven behavior to the actual agency of the fields and particles of nature you get divine synchronicity inside of chaos right? It is not acausal it is emergent behavior when all interactions are ex frangere. I mean it is not merely a good model of what we see but the guide by which nature unfolds itself intrinsically. When nature unfolds certain creases and intersections are predictable even in very very very complex systems.
Does anyone here know if that is a correct assessment?

 

[AV1611VET]

I can remember programming my Apple //e to make that graph in the still image and estimate the Feigenbaum number.

Watch the language please.

 

[sjastro]

I can remember programming my Apple //e to make that graph in the still image and estimate the Feigenbaum number.

I recall many years ago generating the Mandelbrot set on an Amstrad computer running at the breathtaking speed of around 4 MHz.
It took days where as on a single core of a 16 x 3.6 GHz processor it now takes less than 3 minutes.

 

[FrumiousBandersnatch]

... Can - in the midst of this- a deterministic fractal actually also be expressed that does provide a viable structure and create predictable you-ness...

... When nature unfolds certain creases and intersections are predictable even in very very very complex systems.
Does anyone here know if that is a correct assessment?

No, it's not correct. You may have missed that the characteristic feature of deterministic chaos is unpredictability.

 

[FrumiousBandersnatch]

I recall many years ago generating the Mandelbrot set on an Amstrad computer running at the breathtaking speed of around 4 MHz.
It took days where as on a single core of a 16 x 3.6 GHz processor it now takes less than 3 minutes.

Ever used Fractint? It's still around... I remember chugging through Mandelbrot & Julia sets on my old IBM PC at work (I think it was a dual-floppy). Happy days

 

[Oaktree125]

No, it's not correct. You may have missed that the characteristic feature of deterministic chaos is unpredictability.

I guess Im going to still be confused for awhile....

Chaos.
Professor James Yorke, an applied mathematician at the University of Maryland, is often credited with associating the word "chaos" with these particular mechanisms, in the late 1970s. While it has helped the field of nonlinear dynamics to have a simple, handy word like "chaos", the word itself is a bit of a misnomer. In fact, the word is downright confusing, if one interprets it in the nontechnical sense of common language--"lack of order". In fact, deterministic chaotic systems are quite ordered and even predictable on short time scales. In many ways modern dynamicists study deterministic chaotic systems to understand the interplay between order and "utter chaos". The goal is to find the hidden order in the apparent chaos.
And while I think I understand the 3rd/4th sentence in the way you mean :
Instead, through the rule's repeated application the long-term behavior becomes quite complicated. In this sense, the unpredictability "emerges" over time.
as a constructible of system elements and collective UMPFH!(effort) from each equals a fractal
but..
I think Im saying something inside that that determines certain future characteristics of a data set without defining the entirety...but I will pursue my education.
Thanks

 

[FrumiousBandersnatch]

I think Im saying something inside that that determines certain future characteristics of a data set without defining the entirety...

Not sure what you mean by that - mathematical determinism implies that the entire data set is defined.

Sensitive dependence on initial conditions means that very similar initial parameters define very different data sets - although they may follow the same attractor.

 

[sjastro]

Ever used Fractint? It's still around... I remember chugging through Mandelbrot & Julia sets on my old IBM PC at work (I think it was a dual-floppy). Happy days

I'm not familiar with it.
I decided to write a program in Basic not only for the fun of it but to also familiarize myself with the bounded properties of the Mandelbrot set.
For example the number of iterations used to determine whether a point in the complex plane remains bounded or not varies from point to point.
By colour coding each point against the number of iterations a psychedelic version of the Mandelbrot set can be generated.
This is centered around (-0.761574, -0.0847596i) "zoomed" to around 10000X.

 

[FrumiousBandersnatch]

I'm not familiar with it.
I decided to write a program in Basic not only for the fun of it but to also familiarize myself with the bounded properties of the Mandelbrot set.
For example the number of iterations used to determine whether a point in the complex plane remains bounded or not varies from point to point.
By colour coding each point against the number of iterations a psychedelic version of the Mandelbrot set can be generated.

This was one of the features of Fractint - it allowed you to pick a colour range and could then cycle the colours over the various escape values so rainbows of various hues would sweep out from the cycloids and around the various curves. Like this:

Very psychedelic for the time!

This is the most amazing zoom I've seen so far:

 

[Oaktree125]

Not sure what you mean by that - mathematical determinism implies that the entire data set is defined.

Sensitive dependence on initial conditions means that very similar initial parameters define very different data sets - although they may follow the same attractor.

Well Im not entirely sure how to put my finger on it - Im scratching my head -perhaps the attractor is the thing drawing my attention as the recurring factor that should be divisible. I think I need to understand that first. Thanks

My thinking is more to the line that the observables relate to the invariant distances between fractal features and akin to a fixed lattice. Change can happen but i.e there will be something that happens here at x point which is a continuation of some underpinned reccurence. The proponents of the event can be from different areas each iteration and not subject to ray tracing a specific causal chain, but ultimately the collective behavior trace out the same end shape. It could be the carrier reason for scale invariance and conservation.
Scripturally i would add: Ecc 1:9 What has been will be again, and what has been done will be done again; there is nothing new under the sun.
And ultimately trying to understand how that works with different employees.

 

[sjastro]

This was one of the features of Fractint - it allowed you to pick a colour range and could then cycle the colours over the various escape values so rainbows of various hues would sweep out from the cycloids and around the various curves. Like this:

Very psychedelic for the time!

This is the most amazing zoom I've seen so far:

Quite a remarkable video although I didn't sit through the 1hr+ presentation.
Is there any information on the maximum zoom factor?

 

[FrumiousBandersnatch]

Quite a remarkable video although I didn't sit through the 1hr+ presentation.
Is there any information on the maximum zoom factor?

The numbers in the description are: Zoom: 3.4e¹⁰⁹¹, Iterations: Almost 17 million. It took over a week to render.

 

[SelfSim]

This was one of the features of Fractint - it allowed you to pick a colour range and could then cycle the colours over the various escape values so rainbows of various hues would sweep out from the cycloids and around the various curves. Like this:

Very psychedelic for the time!

This is the most amazing zoom I've seen so far:

Reminds me of the Hubble Ultra Deep field ..

 

[sjastro]

One of the advantages of writing your own programs is being able to generate Multibrot sets which are iterations of the function f(z) = zⁿ + c where z and c are complex numbers and n > 2.
For n=2 is the familiar Mandelbrot set.

For n =3 is a symmetrical Multibrot set.

 

[Nithavela]

Hmm, fast toasts.