#lorenz attractor

[art-of-mathematics]

(Lorenz) attractors and probability intensity

... I do not know what I did here...

It was inspired by another note I scribbled down some months ago...

(I did (and still do) not really know what I did here either... )

#chaos theory #chaos #attractors #chaos attractor #lorenz attractor #probability #probability intensity #nonsense math #math #mathematics #math stuff #mathposting #mathpost #statistics #dynamical systems #chaotic processes #emergence #self-organization #math notes #my math notes #visulaizing my thoughts

[prententiousjackal]

Why aren't there more lorenz attractors in this color scheme. (I just hue-shifted wikipedia's lorenz image) This world needs neon bisexual neurodivergent chaos butterflies.

I wanna use my butterfly accelerator to smash particles and anti-particles together to discover the yin-yang of the universe, origin of all order and chaos, the mobius strip ouroboros snake that somehow got out of balance leading to the big bang and the accelerating expansion of the universe. The disturbance so small, yet it created everything.

#lorenz attractor #bisexual colors #neoncore #mypost #butterfly effect #nonsensical symbolism #max derrat messed up my brain #arcadecore

[blacklinesw9]

Check out this awesome 'Chaos theory: Lorenz equation' design on @TeePublic

#blacklinesw9 #lorenz #Lorenz attractor #Lorenz equation #chaos theory

[tea-and-panthers-art]

These where some renders of attractors I did while playing around with scripting in blender.

The first image is of a Thomas Attractor which has to be my favorite attractor our of all of them, I like how it resembles and alien ship or mega structure of some kind.

The second is of a Lorenz Attractor, which is commonly used as an example of the butterfly effect.

#art #attractors #blender #lorenz attractor #thomas attractor #python #3d art

[positivelyapunovexponent-good]

I to an undergrad math conference which means I am wearing my mathiest apparel for luck!

I get the to present on research regarding fractals and fractional Brownian motion specifically, two subjects I am VERY fond of

#personal #Not pictured: my Mandelbrot set pin which is packed #Golden ratio and Lorenz attractor my beloveds

[lightdrew]

Sooo I made a Lorenz system in p5js Here it is for anyone who wants to see it  (ik my code is probably crap but hey it works ok)

#p5js #chaos theory #strange attractor #lorenz system #webgl #javascript

[a-lesson-you-never-asked-for]

Dynamical Systems

When we talk about dynamical systems, we broadly refer to the way a particular system evolves under certain conditions. For example, if you have a particle and you give it some terrain to roll around on, what path will it follow? If you have an electron and subject it to a magnetic field, what trajectory would it follow? Or if you impart forces on a block of water, how would the shape of the boundary change?

These are all types of questions that can be answered by dynamical systems, and involve a significant depth of analysis to truly understand their mechanics. (But truthfully, I've only ever been in it for the pictures).

The Tinkerbell map The Lorenz Attractor

As usual, if anyone has any feedback or errata to point out, please do shoot me a message :). I'm still getting back into the groove of things with this so I might be missing out on stuff.

Some basic definitions

We have 2 different types of trajectories, discrete and continuous.

discrete time dynamics - this means that you have observations at discrete points in time. You take a snapshot at t=1, t=2, etc. Take the Tinkerbell map above for example. You start with a point, then apply some sort of rule, and you end up at the next point. Things happen in steps.

continuous time dynamics - this means that at each point, you prescribe a velocity (a speed and direction) in which a particle should move. So if a particle is located at (0,0) for example, in an arbitrarily short period of time, it would move in a particular direction. A good example of this is the Lorenz map, as shown in the right hand image.

The Tinkerbell Map - equations of motion

The Lorenz Map - equations of motion

NOTE: In the first case, we talk about where the next point explicitly, whereas in the second case, we talk about in how fast in a particular direction we will end up moving.

A brief discussion on derivatives

Here's a visual to explain - suppose that the blue line represents how far away you are from some particular location. The average velocity would be the slope of the green line. But the instantaneous velocity would be equal to the the slope of the yellow line.

The way we denote this derivative is as follows

The numerator describes the change in the y-values, the denominator describes the change in the x-values, and the ratio of this is the gradient (or the slope).

So in a nutshell, the average velocity represents a change in distance over a period of time, and instantaneous velocity represents a change in distance of an arbitrarily short period of time.

Where to from here?

From here, we'll introduce some broad notation around maps, orbits, and some terminology that underpin dynamical systems. If there's enough time, I'll also describe some other concepts regarding different types of orbits, and thereafter we'll get into some really cool stuff.

Anyway, that's it for now! Adios :)

#a lesson you never asked for #dynamical systems

[keishiro-ueki]

3D printed Lorenz attractor

#math art #3d printing

[slack-wise]

Lorenz Attractor

#Edward Norton Lorenz #Edward Lorenz #Lorenz #Lorenz Attrator #Lorenz System #maths #mathematics #lines #splines #videos #gifs

[84k3r56023n]

Niraja Lorenz - Strange Attractor #14, 2015, Quilted textile, 80" x 81"

#art #quilt #niraja lorenz

[vermillioncrown]

🤡 for anything you’ve written!

🤡 What's a line, scene, or exchange you've written that made you laugh?

here's a few:

the taiga&kuroko badminton heart-to-heart (ball is life ch 3)

yuuri smashing fruit in retaliation to viktor tossing his old suit (pacing ourselves ch 6)

lan qiren demanding that lan wangji and lan xichen explain what happened at the conference, and the implication that lan wenhui got into a slapfight with her twin and had to be separated into different courtyards (lorenz attractors ch 2)

whenever jin zixuan demands zhu yunxun to stop making Faces at him and they instead make it harder for him to see their face of judgment (dream before daybreak ch 9)

#inquiry #minjad #fanfic #verm ask game

[visual-calc]

Thoughts on the Lorenz attractor go

Sexy.

#skillsposting #ooc: two fractalposts back to back? damn

[blacklinesw9]

(via Chaos theory: Lorenz equation Tote Bag by Blacklinesw9)

#findyourthing #redbubble #Lorenz attractor #Lorenz equation #chaos theory #butterfly effect #blacklinesw9

[megraen]

Two Quiz Game

Tagged by the lovely @socially-awkward-skeleton

uquiz 1 - What does your OC’s heart look like?

A guiding, golden light - Just because you cannot see your own heart doesn’t mean that others can’t. Your heart is blinding, captivating, a fire so bright that others can’t bring themselves to look away. It illuminates the path they follow and cements you as a guiding star for their own wayward hearts. Every experience you’ve lived through has built your lighthouse heart up just a little higher. You are inspirational, a light that doesn’t go out.

uquiz 2 - What does your OC’s path lead to?

The Wisp - A glow dancing along the moors, that what you left behind to free yourself. A twin or a shadow? A mirror? Do you know, do you care? (A moonless night, cold stars gazing down.) Do you remember, you had prayed for so long (someone, please someone help, please-)? Is it murder if you cleave yourself apart until you can’t even remember what you lost? You have left the forest, left the parts you couldn’t shoulder, behind. Sometimes, you have to break yourself apart, sometimes there is no other way

uquiz 1 - What does your OC’s heart look like?

Broken, missing pieces that once were there - Your heart has been torn before, chipped and maybe even shattered. Some pieces will never be recovered, and you are shaped by the loss. But it can still be shaped into something tangible, something good, even with its flaws and imperfections. You don’t have to do all the work of rebuilding by yourself. Allow other hands to leave their fingerprints on the new heart you create from the remnants.

uquiz 2 - What does your OC’s path lead to?

The Messenger - A creature of flesh and bones but wrong, wires wrapped around limbs and a steady ticking accompanying each step. His home is in the forest, pale trees with dark eyes, and he clutters on, his bones creaking with every step. The clock keeps on ticking, every moment a blink in the eye of the universe as the years fly by. His steps continue forevermore, an ouroboros lumbering on and on, a mechanical being made from the dead. On and on he clatters, a void that can never be filled, with bloody feet and a chittering voice.

uquiz 1 - What does your OC’s heart look like?

A compass that doesn’t waver - You are someone who is certain of what you want. Maybe you always have been, or maybe you made a discovery that you haven’t been able to tear your eyes away from. Your heart is set and certain. You fight endlessly for your goals. Above all else, you know who you are and what you are trying to achieve. Just be careful not to tear yourself or others apart in pursuit of your ideals.

uquiz 2 - What does your OC’s path lead to?

The Luminosity - You opened a door. There is light. (There is a door. You open the door.) The light is blinding. (There is a door. Will you open the door?) It feels like you're the only real thing left, the only tangible thing. Time is rushing past in dizzy streams, parting around you and leaving you untouched. You wander, there is no way back and no way forward and you wouldn't be able to tell if you had moved at all. Time moves around you but it doesn't affect you. You are there for a second, you are there for a life-time, for thousands, for the end of everything, and the beginning of the universe. It is beautiful in a terrifying way, an unshakable knowledge that there is no way out, that this is it, the point of no return. So you wait, you don't know for what or for whom but you wait. And when it arrives in a choir of equations with the lorenz attractor for wings you find yourself weeping crystalline numbers.

uquiz 1 - What does your OC’s heart look like?

A cage with iron locks - You are an enigma. You take care to remain that way. You aim to keep people guessing; your motives are uncertain even to yourself. What is it you truly want? You’ll never know if you keep your heart locked away like that. You deserve to be known, truly and fully. Stop being afraid of what you might find if you open your heart up to self-reflection. Stop thinking that no one will love you the moment they understand you. You are more than the facade you put on.

uquiz 2 - What does your OC’s path lead to?

The Corruption - Error. Data not found, try again? yes [ ] no [ ] who am I? [x] You have been here before and you will be here again, the cursor is blinking at you but the words are swimming before your eyes, blurry and searing at once. The room is dark, the only light your screen. You don't remember where you are, you don't even remember who you are. The cursor keeps blinking, a rhythmic pulse, and you feel numbness creeping into your thoughts. The words on the screen sharpen, form a short message, a cry for help, before being wiped away again. Darling, what are you nervous about? Darling, why are you crying? Darling, do I have to take you apart again?

Tagging: @ladykatie512 @miss-jennifer-cormier @glitchinginthegarden

#tag game #oc: sara briggs #oc: jeanne gardner #oc: abigail fehn #oc: johanna lynn

[tomorrowillbeyou]

scrolled to a random page in my meteorology textbook and saw the lorenz attractor and yelped in excitement

[arbieroo-art]

Has Red Dot gone on strike? Is it injured? What's going on?! Actually, Red Dot starts at x=y=z=0 and the equations of the Lorenz system are such that, starting there means staying there. This behaviour is called a "fixed point," - a remarkably apposite name. The entire line x=y=0, z=any real number, behaves strangely, in fact. For any value of z, with z not equal to zero, and x=y=0, the motion will be directly towards x=y=z=0 but it slows down as it approaches and in fact will never actually arrive in any finite time interval. Meanwhile, starting arbitrarily close to x=y=z=0 but with x or y not actually zero, it's off to the Lorenz attractor you go, as the rest of the Rainbow Dots demonstrate.

#art #code art #algoart #algorithmic art #generative art #chaos #chaos theory #Lorenz #Youtube