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art-of-mathematics · 1 year

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Thoughts about the rectangles with side lengths a la Fibonacci seuqence - and this pattern I came up with earlier today...

I imagine it as a kind of "re-distribution of information".... much like depicted in the video of this neuron:

[Source: YT]

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Also:

#fractals #fractal #fractal geometry #geometry #rectangles #fibonacci #neuron #gif #math #mathematics #math art #dynamical systems

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a-lesson-you-never-asked-for · 9 months

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4 Tinkerbell maps overlayed on top of one another. Plots and trajectory calculations done in GNU Octave.

The Tinkerbell Map equations of motion

#maths #mathsblr #dynamical systems #chaotic trajectories #tinkerbell maps

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missbrunettebarbie · 6 months

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I am desperate enough to ask this on f-ing tumblr, but nothing else has helped so far:

Does anyone know if the 2 equilibrium points (that are not (0,0,0)) of the Lorenz system are stable or not? And what is their classification (eg saddle point etc)?

I am going insane trying to figure it out but I just can't.

#lorenz system #lorenz butterfly #marhematical modelling #dynamical systems #mathematics #computational mathematics

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bubbloquacious · 2 years

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Very sorry to report that the math I'm learning this semester may have some Applications

#math #dynamical systems #algebraic curves #lie groups

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gardenfractals · 9 months

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Liquid computers for constrained computation using fluid dynamics

Read more: https://royalsocietypublishing.org/doi/10.1098/rstb.2018.0372

#moniac #fluids #dynamics #dynamical systems #mechanism #physics #computer #computerscience #complex systems

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tomorrowalready · 3 months

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youtube

#Discrete Time #Continuous Time #Dynamical Systems #Youtube

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unipacas · 11 months

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miguel having beef with a teenager: a case study

#across the spiderverse #miles morales #miguel o'hara #spider-man #spider-man 2099 #across the spiderverse spoilers #fanart #my draws #i have to get some memes out of my system before anything else pls bear with me #im ok with this dynamic actually. i kind of love it

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vebokki · 4 months

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go go demon gang

#also i love thinking art the dynamic between these three kjfnhkd #i think she hauling and binghe have the potential to be the most annoying and loud and bicker-y sibling pair to exist #and mobei jun has just grown accustomed to their shit so he stands mostly ignoring everything they say #but making sure they dont kill each other or accidentally die a gruesome death when theyre being competitive #they all like each other ok. they love each other ok. ok. ok.#scum villains self saving system #svsss #luo binghe #svsss fanart #sha hualing #mobei jun #人渣反派自救系统 #mxtx

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nibbelraz · 4 months

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A writer and His number one fan hater

#svsss #shen qingqiu #shang qinghua #platonic cumplane???#Shen Yuan #scum villian self saving system #scum villains self saving system #scum villain's self saving system #scum villain #I actually have a lot of thoughts about them that i wasnt able to articulate right with words or drawings #i just think #That Shen Yuan really did like the story #like he was upset on behalf of a good character #he was upset about its potential #he absolutely wanted more for him and was upset that it was thrown away to please the masses #he had no idea what Shang Qinghua was going through #absolutely just ranked on him and YEAH IT WASNT THE BEST WORK BUT clearly it still was good enough to make Shen Yuan care #like ah #I would love to read more dynamics about them about a struggling writer and his most trusted hater to yell at him to write his heart out #also Shen Qingqiu going through svsss and seeing how much thought Shang Qinghua actually put into the story #and how much effort he actually had in it before he had to settle and scrap #like AAAAHH Im not the analysis type and my thoughts about them really are all other the place but really I think nothing is stronger then #an author and a reader #cause my man read to the very end the ABSOLUTE END #hE CARED HE CARED HE REALLY CARED NO MATTER HOWWWW MUCH HE CRIED ABOUT IT #alright dont look at me they make me go crazy #my art #nibbelraz

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eggsploded · 5 months

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cant keep their quadrants straight

#the solkat was in fact not out of my system #really funny kismesis dynamic because its not actual real hate rather than a synced temper tantrum between the two #their pitch flirting was pretty weak anyway #i hate myself more than you hate yourself NUH UH and im better at you in smash bros #then karkat meekly asks if theyre still friends and sollux tells him to shut up and boots up a show on discord to watch together #pitch hatred based on the other guy knowing too much about you and caring really hard about your wellbeing and its embarassing #love. its love #homestuck #egg art #solkat #sollux captor #karkat vantas

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art-of-mathematics · 1 year

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(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... )

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a-lesson-you-never-asked-for · 2 months

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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

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hussyknee · 1 year

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DARVO: Deny, Attack, Reverse Victim and Offender.

An abuser denies the abuse ever took place, attacks the person that was abused (often the victim) for attempting to hold the abuser accountable for their actions, and claims that they are actually the victim in the situation, thus reversing what may be a reality of victim and offender. It often involves not just "playing the victim" but also victim blaming.

TL;Dr: Stop pathologizing neurodivergent people and individualizing abuse, and start treating abusers and bullies as a social failing that are products of privilege.

Unless you want to insist that every bitchass who's ever plagued marginalized people has NPD.

#ableism #npd #bpd #aspd #cluster b #abuse #abuse dynamics #bullying #anti bullying #interpersonal relationships #systemic issues #social justice #capitalism #pop psychology #white people #capitalist individualism is a disease #twitter #elongated muskrat #knee of huss

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junesfool · 4 months

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damn I love this brush

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hiyogdh · 8 days

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the only thing on my mind right now is liu qingge...

#ren zha fanpai zijiu xitong #scumbag self saving system #scum villain #mxtx svsss #svsss #svsss art #svsss fanart #liu qingge #action poses sure are actioning #he deserves all the dynamic fighting poses

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jade-len · 11 days

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well what if the only person sqh doesn't know ANYTHING about is lqg because he was just there to be killed off and so he has to actually try to get to know him and can't use his author knowledge and so they bond and he sees lqg as so much more than just a character whose life was meant to end for a cheap shock and lqg also gets to know him as well and sees sqh in a new light because that coward he grew up distantly with is weirdly able to understand him and actually see him as a person and not just a dumb brute and a new friendship blossoms and

anyways i created the perfect ship/platonic ship name for them it's attack helicopter thank you for coming to my ted talk

#plspls hear me out #PLEASE THE DYNAMIC WOULD BE SO GOOD AND INTERESTING I LOVE IT #theyre both weird in their own way #shang qinghua understands him bc liu qingge shows signs of autism forreal #he comes from a modern world he knows it when he sees it!!! hes very gentle abt it too compared to others in ancient china bc #obv they dont know what that is #i need to. create a fanfic with this holy shit #svsss #mxtx svsss #the scum villain's self saving system #shang qinghua #liu qingge

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