/sci/ - Science & Math » Thread #12971230

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Anonymous Tue 13 Apr 22:22:03 2021 No.12971230 View Reply Original Report

Quoted By: >>12971261 >>12971968 >>12972754 >>12972777 >>12975538 >>12975965 >>12978349 >>12978807 >>12980243 >>12980545 >>12980558 >>12981345 >>12981493 >>12982340 >>12982983 >>12982995 >>12983024

What is the simplest rule that generates complexity?

Anonymous

Anonymous Tue 13 Apr 2021 22:22:53 No.12971233 Report

Quoted By:

various cellular automata

Anonymous

Anonymous Tue 13 Apr 2021 22:28:41 No.12971256 Report

Quoted By: >>12983018

The inability to convert all nonlinear differential equations into deterministic equations.
I don't know if the Three Body Problem is the first of these, but certainly by the time Lorenz found that 3D butterfly graph, it was clear that chaos is a thing.

Anonymous

Anonymous Tue 13 Apr 2021 22:29:38 No.12971261 Report

Quoted By:

>>12971230
The simplest I'm aware of is the ruleset for Conways game of life

Anonymous

Anonymous Tue 13 Apr 2021 22:29:57 No.12971263 Report

Quoted By:

Many of the intractable problems come from simple rules.

Anonymous

Anonymous Wed 14 Apr 2021 01:12:59 No.12971968 Report

Quoted By:

>>12971230
The negative implication, or inhibit, inference rule.

Anonymous

Anonymous Wed 14 Apr 2021 06:26:14 No.12972754 Report

Quoted By:

>>12971230
stephen wolfram liked this post

El Arcón

El Arcón Wed 14 Apr 2021 06:28:12 No.12972761 Report

Quoted By: >>12972770 >>12972805 >>12975317

Mandelbrot map

Anonymous

Anonymous Wed 14 Apr 2021 06:33:03 No.12972770 Report

Quoted By:

>>12972761
Julia is simpler since C remains a constant in each plot.

Anonymous

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Anonymous Wed 14 Apr 2021 06:36:49 No.12972777 Report

Quoted By: >>12978349 >>12980592 >>12982100

>>12971230
the logistic map is very simple yet has bifurctions and chaotic behaviour

Anonymous

Anonymous Wed 14 Apr 2021 06:39:05 No.12972785 Report

Quoted By:

The totality property for magmas

Anonymous

Anonymous Wed 14 Apr 2021 06:48:13 No.12972805 Report

Quoted By:

>>12972761
Surely multiplication over N is simpler? It generates the primes.

Anonymous

Anonymous Wed 14 Apr 2021 19:15:55 No.12975317 Report

Quoted By:

>>12972761
>Mandelbrot map
its like watching reruns of "I love Lucy".

Anonymous

Anonymous Wed 14 Apr 2021 20:20:01 No.12975538 Report

Quoted By: >>12976044

>>12971230
The Collatz Conjecture

Anonymous

Anonymous Wed 14 Apr 2021 22:00:38 No.12975943 Report

Quoted By: >>12976044

Creative recursion / observation

Anonymous

Anonymous Wed 14 Apr 2021 22:07:30 No.12975965 Report

Quoted By: >>12976044

>>12971230
pendulums attached to pendulums

Anonymous

Anonymous Wed 14 Apr 2021 22:24:02 No.12976044 Report

Quoted By: >>12976152 >>12977442

>>12975965
>>12975538
>>12975943
stop helping him you numbnuts, your naivity is going to doom us all should one of these CS pajeets figure out how to build god

Anonymous

Anonymous Wed 14 Apr 2021 22:46:14 No.12976152 Report

Quoted By:

>>12976044
still better than NORMAL

NEARAutomata

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NEARAutomata Thu 15 Apr 2021 05:42:15 No.12977442 Report

Quoted By:

>>12976044

Anonymous

Anonymous Thu 15 Apr 2021 12:12:04 No.12978349 Report

Quoted By:

>>12971230
See >>12972777
Iterate f(x) = 4x(1-x) with a random starting point between 0 and 1, and chaos appears.

Anonymous

Anonymous Thu 15 Apr 2021 12:14:03 No.12978357 Report

Quoted By:

a = a

Anonymous

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Anonymous Thu 15 Apr 2021 14:33:24 No.12978807 Report

Quoted By:

>>12971230
The second law of thermodynamics. Ensuring all systems seek their most stable state, if any of them can create a feedback loop with themselves and their environment well... It will attempt to fight entropy till the end of time itself

Anonymous

Anonymous Thu 15 Apr 2021 19:52:35 No.12980232 Report

Quoted By:

$ae=ea=a$
$a^{-1}a=aa^{-1}=e$
$a(bc)=(ab)c$

Anonymous

Anonymous Thu 15 Apr 2021 19:54:58 No.12980243 Report

Quoted By:

>>12971230
divide the circumference of a circle/cylinder by its diameter

Anonymous

Anonymous Thu 15 Apr 2021 20:55:30 No.12980545 Report

Quoted By:

>>12971230
matter attracts itself

Anonymous

Anonymous Thu 15 Apr 2021 20:57:36 No.12980558 Report

Quoted By:

>>12971230
1 + 1 = 3

Anonymous

Anonymous Thu 15 Apr 2021 21:06:19 No.12980592 Report

Quoted By: >>12982100

Can somebody clear this up for me. I thought at least dimension three was required for chaos, so what is the explanation for maps like in >>12972777

I feel like I'm getting thr notion of "dimension" misconstrued a bit

Anonymous

Anonymous Fri 16 Apr 2021 00:17:51 No.12981345 Report

Quoted By:

>>12971230
nothing->something

Anonymous

Anonymous Fri 16 Apr 2021 00:52:00 No.12981493 Report

Quoted By:

>>12971230
Class warfare in union with material dialecticism. You can derive everything of human value from that

Anonymous

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Anonymous Fri 16 Apr 2021 04:04:28 No.12982100 Report

Quoted By:

>>12972777
>>12980592

It's not really chaotic : For any initial starting point, you'd have the same pseudo chaotic behaviour.
A double pendulum is true chaotic.

Anonymous

Anonymous Fri 16 Apr 2021 06:11:21 No.12982340 Report

Quoted By:

>>12971230
True random generator.

Anonymous

Anonymous Fri 16 Apr 2021 11:04:54 No.12982983 Report

Quoted By: >>12983006

>>12971230
>What is the simplest rule that generates complexity?
Wolfram 2d automata rule 110 is a full computer. With enough memory and time, it could simulate anything in the universe including your laptop and your brain.

Anonymous

Anonymous Fri 16 Apr 2021 11:07:15 No.12982995 Report

Quoted By: >>12982996

>>12971230
Any rule(set) that can be said to be turing complete, idk which is the siplest.

Anonymous

Anonymous Fri 16 Apr 2021 11:09:08 No.12982996 Report

Quoted By:

>>12982995
Magmas aren't generally turing complete but the magma axioms generate complexity

Anonymous

Anonymous Fri 16 Apr 2021 11:16:34 No.12983006 Report

Quoted By:

>>12982983
can it simulate itself?

Anonymous

Anonymous Fri 16 Apr 2021 11:21:59 No.12983018 Report

Quoted By:

>>12971256
>Three Body Problem
This are three independent agents interacting where each of them follow simple rules but the interaction is chaotic.

Can it be stated as a general rule that complexity from simple rules applies to multi-agent systems?

Anonymous

Anonymous Fri 16 Apr 2021 11:24:05 No.12983024 Report

Quoted By:

>>12971230
Every possible quantum mechanical evolution of a system, think of this like the lorentz attractor ^ 1000

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