/sci/ - Science & Math » Thread #11755678

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chaos theory & computer math

Anonymous Tue 02 Jun 20:53:28 2020 No.11755678 View Reply Original Report

Quoted By: >>11756178 >>11758198 >>11758314 >>11758439

Post anything interesting about chaos theory or mathematical programming. Anyone study chaos theory? Pic is my attempt to make an escape-time fractal out of a 3 variable quadratic Sprott attractor.

Anonymous

View Same Google iqdb SauceNAO 100x.jpg, 857KiB, 1920x1080

Anonymous Tue 02 Jun 2020 20:58:17 No.11755694 Report

Quoted By: >>11758439

dumping more images for anyone interested

Anonymous

View Same Google iqdb SauceNAO Screenshot (17).jpg, 1MiB, 3840x2160

Anonymous Tue 02 Jun 2020 20:59:25 No.11755698 Report

Quoted By: >>11758439

Anonymous

View Same Google iqdb SauceNAO Screenshot (2).jpg, 742KiB, 1920x1080

Anonymous Tue 02 Jun 2020 21:00:31 No.11755703 Report

Quoted By: >>11758439

Anonymous

View Same Google iqdb SauceNAO Screenshot (15).jpg, 1MiB, 3840x2160

Anonymous Tue 02 Jun 2020 21:01:35 No.11755710 Report

Quoted By: >>11758439

Anonymous

View Same Google iqdb SauceNAO Attractor 2016-09-02 00-51-08-39.png, 788KiB, 1920x1080

Anonymous Tue 02 Jun 2020 21:05:21 No.11755722 Report

Quoted By: >>11757561

this is what a sprott attractor normally looks like

old but still relevant doc on chaos theory:
https://www.youtube.com/watch?v=6BvTKBYBMFY

Anonymous

View Same Google iqdb SauceNAO zeta.jpg, 559KiB, 1920x1080

Anonymous Tue 02 Jun 2020 21:09:52 No.11755738 Report

Quoted By: >>11755751

numerical calculation of the riemann zeta in 150 lines:
https://pastebin.com/xfCAkrjx

Anonymous

View Same Google iqdb SauceNAO Attractor 2016-09-01 22-36-58-73.png, 948KiB, 1920x1080

Anonymous Tue 02 Jun 2020 21:12:48 No.11755751 Report

Quoted By:

>>11755738
was based on this doc if anyone wants to know how to calculate numerically:
http://numbers.computation.free.fr/Constants/Miscellaneous/zetaevaluations.pdf

Anonymous

Anonymous Tue 02 Jun 2020 23:23:10 No.11756178 Report

Quoted By: >>11758404

>>11755678
nigga you just summoned a demon

Anonymous

View Same Google iqdb SauceNAO attractors.io.png, 240KiB, 673x673

Anonymous Tue 02 Jun 2020 23:48:31 No.11756276 Report

Quoted By:

Been wanting to do this kind of stuff lately but haven't had the time. In the meantime, I've dug up some resources. Some of them are a bit old though:

https://softology.com.au/tutorials/tutorials.htm
http://www.chaoscope.org/index.htm
http://sprott.physics.wisc.edu/sa.htm
https://softologyblog.wordpress.com/2017/03/04/2d-strange-attractors/

If you want to fiddle around without installing any software nor understanding the maths behind it, there's this cute HTML5 app (pic related): http://attractors.io/

Anonymous

View Same Google iqdb SauceNAO 440px-Logistic_Map_Bifurcations_ (...).gif, 3MiB, 440x440

Anonymous Wed 03 Jun 2020 02:33:21 No.11756675 Report

Quoted By: >>11756701

https://www.youtube.com/watch?v=ovJcsL7vyrk

Anonymous

Anonymous Wed 03 Jun 2020 02:42:54 No.11756701 Report

Quoted By:

>>11756675
There's a few interesting proofs related to logistic map and chaos in general. One is that there are infinitely many periodic windows. I've done some experiments slewing Sprott attractors between one another and I see similar patterns as the log map, such as period multiplying and periodic windows in the chaotic areas.

Anonymous

View Same Google iqdb SauceNAO Attractor 2016-08-31 22-50-10-71.png, 585KiB, 1920x1080

Anonymous Wed 03 Jun 2020 03:10:01 No.11756776 Report

Quoted By:

penis attractor

Anonymous

View Same Google iqdb SauceNAO the-spore.png, 34KiB, 1908x1001

Anonymous Wed 03 Jun 2020 10:57:39 No.11757556 Report

Quoted By:

all are regular mandelbrot

Anonymous

View Same Google iqdb SauceNAO fract423420.png, 74KiB, 1908x1001

Anonymous Wed 03 Jun 2020 10:59:04 No.11757558 Report

Quoted By:

Anonymous

View Same Google iqdb SauceNAO fract20.png, 821KiB, 1908x1001

Anonymous Wed 03 Jun 2020 11:00:42 No.11757561 Report

Quoted By: >>11758047

>>11755722
whats program is that?

Anonymous

View Same Google iqdb SauceNAO fract2220.png, 1MiB, 3816x2002

Anonymous Wed 03 Jun 2020 11:01:48 No.11757562 Report

Quoted By:

funny, one of my images got "image contains malicious code" from the upload

Anonymous

View Same Google iqdb SauceNAO fract450.png, 2MiB, 3816x2002

Anonymous Wed 03 Jun 2020 11:03:06 No.11757565 Report

Quoted By:

Anonymous

View Same Google iqdb SauceNAO fract330.png, 502KiB, 1908x1001

Anonymous Wed 03 Jun 2020 11:04:32 No.11757571 Report

Quoted By:

Anonymous

View Same Google iqdb SauceNAO fract880.png, 771KiB, 3816x2002

Anonymous Wed 03 Jun 2020 11:05:50 No.11757573 Report

Quoted By: >>11758150

Anonymous

View Same Google iqdb SauceNAO Base Profile Screenshot 2020.06. (...).jpg, 1MiB, 3840x2160

Anonymous Wed 03 Jun 2020 15:51:20 No.11758047 Report

Quoted By:

>>11757561
It's my own program made in visual studio.

Anonymous

View Same Google iqdb SauceNAO chaos2.jpg, 1MiB, 4000x3000

Anonymous Wed 03 Jun 2020 15:59:09 No.11758056 Report

Quoted By: >>11758188 >>11758269

from http://www.dvq.com/oldcomp/analog/comdyna.htm

Anonymous

Anonymous Wed 03 Jun 2020 16:48:26 No.11758150 Report

Quoted By: >>11758171 >>11758221

>>11757573
what is this?
is this the mandelbrot set zoomed out?

Anonymous

Anonymous Wed 03 Jun 2020 16:57:19 No.11758171 Report

Quoted By: >>11758221

>>11758150
Looks to be zoomed in on the thin spindle

Anonymous

Anonymous Wed 03 Jun 2020 17:08:54 No.11758188 Report

Quoted By: >>11758200

>>11758056
interesting. Got schematics for those?

Anonymous

Anonymous Wed 03 Jun 2020 17:13:31 No.11758198 Report

Quoted By: >>11758217

>>11755678
Chaos firmly is largely about probability and boundaries when cool, and statistics when ice cold. True chaos math is low-key magic.

Anonymous

Anonymous Wed 03 Jun 2020 17:13:56 No.11758200 Report

Quoted By:

>>11758188
Nope, no clue, you can try to deduce from the panel and general info about analog computers.

Anonymous

Anonymous Wed 03 Jun 2020 17:24:27 No.11758217 Report

Quoted By:

>>11758198
I've heard chaos being described as systems that have non-linear stability but linear instability. All of the interesting things happen in the chaotic region. Control systems in nature like brains can be described in the same way too. Sprott attractors can be described this way too, the non-linear terms overpower at large values so push it back into the basin, while the linear terms are stronger close to the basin and keep it from converging at a single point.

Anonymous

Anonymous Wed 03 Jun 2020 17:26:19 No.11758221 Report

Quoted By:

>>11758150
>>11758171
zoomed in, somewhere, i didn't keep the coords

Anonymous

Anonymous Wed 03 Jun 2020 17:46:13 No.11758269 Report

Quoted By: >>11758331

>>11758056
>analog computer
Fascinating. Why did we abandon this in favor of digital?

https://www.youtube.com/watch?v=CO0lzOm2o80

Anonymous

Anonymous Wed 03 Jun 2020 18:09:45 No.11758314 Report

Quoted By:

>>11755678
I started going through a book that is an introduction to complexity theory. If I ever go back to school for grad school when my start up takes off and I become a millionaire, I'll focus on graph theory & complexity theory. CS grad.

Anonymous

Anonymous Wed 03 Jun 2020 18:17:57 No.11758331 Report

Quoted By: >>11758361

>>11758269
performance

Anonymous

Anonymous Wed 03 Jun 2020 18:27:44 No.11758361 Report

Quoted By: >>11758374 >>11758381 >>11758386

>>11758331
when moore's law proves false and digital reaches it's peak performance, will we ever go back and try advancing analog technology? I fear there is wasted potential here.

Anonymous

Anonymous Wed 03 Jun 2020 18:28:01 No.11758363 Report

Quoted By: >>11758633

chaos theory sounds comfy, is it ok for me to learn it concurrently with ODE? a textbook seems to imply it could be used for either subject

Anonymous

Anonymous Wed 03 Jun 2020 18:32:26 No.11758374 Report

Quoted By:

>>11758361
afaik the predicted state of hardware advancement seems to be
>different materials (gallium or carbon based computers?)
>different transistor layout (stack transistors together or some shit?)
>different architecture (less monolithic, organize your hardware to be more "spread out" since the biggest bottleneck right now is accessing memory)
>quantum?
>optical?

Anonymous

Anonymous Wed 03 Jun 2020 18:35:12 No.11758381 Report

Quoted By:

>>11758361
something something diode recovery/amplifier settling time, was what I read last. Also, they require a lot of manual balancing, tuning, and thermal compensation, which is expensive.
Vastly underappreciated, though

Anonymous

Anonymous Wed 03 Jun 2020 18:36:23 No.11758386 Report

Quoted By: >>11758391

>>11758361
But transistor computers are analog computers at the lowest level.

Anonymous

Anonymous Wed 03 Jun 2020 18:38:15 No.11758391 Report

Quoted By:

>>11758386
they try REALLY hard not to be

Anonymous

Anonymous Wed 03 Jun 2020 18:42:36 No.11758404 Report

Quoted By:

>>11756178
>Implying mathematics isn't the deranged gospel of an alien deity

Anonymous

Anonymous Wed 03 Jun 2020 18:53:55 No.11758439 Report

Quoted By:

Here's the code for:
>>11755678
>>11755694
>>11755698
>>11755703
>>11755710
https://pastebin.com/B8rJbUK7
The pics are only showing a 2d slice of an image that could be 30 dimensional. I could expand the images to be 3d but I haven't found a good way to render a 3d slice yet.

Anonymous

View Same Google iqdb SauceNAO Screenshot (13).jpg, 119KiB, 1344x756

Anonymous Wed 03 Jun 2020 19:07:11 No.11758468 Report

Quoted By:

>printing Lorenz calculated with analog computer
https://www.youtube.com/watch?v=ZpvZ3DDrb4E

Anonymous

View Same Google iqdb SauceNAO nonlinear-dynamics-and-chaos.jpg, 35KiB, 300x450

Anonymous Wed 03 Jun 2020 20:12:01 No.11758633 Report

Quoted By: >>11759592

>>11758363
should i brush up on ODEs since i literally don't remember any of it at all since i took it 4 years ago? is it assumed that you know it before reading pic related?

Anonymous

Anonymous Thu 04 Jun 2020 01:21:53 No.11759592 Report

Quoted By: >>11760341 >>11760355

>>11758633
this book is easy mode if you did odes.
You need these skills:
Know how to plot functions and find intersections.
Know how to do single integrals.
Know how to solve 2x2 linear systems.
Know how to find eigenvalues and eigenvectors.
Some basic analysis and topology notions like: continous function, open/closed set, boundary of a set.

Most important thing is to understand how polynomial functions change when you change the sign of a parameter:

Like knowing intuitively these types of functions:

ax + b
ax^2 + bx + c
ax^3 +bx^2 +cx +d

You'll usually see these in bifurcations which are equations like

dx/dt = ax -x^2 , where a is some parameter.
You plot this as (x,x_dot) then see how the curve changes as the parameter a<0 a=0 a>0.

That's the basic idea behind most of the book.

Anonymous

Anonymous Thu 04 Jun 2020 05:38:06 No.11760341 Report

Quoted By:

>>11759592
>this book is easy mode if you did odes.
i don't remember ODEs at all

Anonymous

Anonymous Thu 04 Jun 2020 05:45:24 No.11760355 Report

Quoted By: >>11760398

>>11759592
Not him but I am familiar with lin alg, intro analysis, solving systems of equations, basics of separable diff eq, vector calc and basic topological concepts. would it be possible to jump into this text without first working through an ODE's book?

Anonymous

Anonymous Thu 04 Jun 2020 06:06:37 No.11760398 Report

Quoted By:

>>11760355
no, of course not

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