chaotic systems

A visualization of chaos: 41 triple pendulums with very slightly different initial conditions 

It is a good example of a chaotic system. In a chaotic system, small deviations such as a rounding error can cause such large changes that it seems impossible to predict the behavior of the chaotic system

There are actually 41 pendulums from the very beginning, although it looks like there is only one. Did you expect that? 

oh, shit, people actually asked me to follow up on Preaching The Good Word of A Functional Alignment System, okay

i hope you people know what you’re unleashing here

(whole thing prompted by this right here, notably including the tag #unpopular opinion: the definition of lawful and chaotic has been thoroughly twisted over the years since od&d)

So some of you (the ones who didn’t request this) might be wondering: “Alterz, why would you want to go back to the old alignment method? If people generally agree on the new alignment definitions then why confuse things by trying to change them? Is this just some old system nostalgia?”

Well 1) I’m too young by far for old system nostalgia but more importantly 2) people don’t? agree????? on the alignments???????

And that’s a problem, because the whole point of the alignments is to give some rough guidelines on how any given character is likely to act. It should be inarguable. The very fact that people can have arguments over what an alignment is means that the system has failed.

If you look in the alignment section on the more recent D&D editions, they literally have to go into detail on each alignment to explain what each one means. Worse still, for a system theoretically set up as a gradient, the different alignments are basically buckets and it gets really confusing if a character doesn’t neatly fit into one of those buckets.

Some examples from characters I have actually played: a mercenary who I labeled as neutral because I could make equally compelling arguments for why he should be lawful neutral, chaotic neutral, neutral good, and neutral evil. A hermit who at any given time was chaotic neutral or neutral good, but could never reliably be described as chaotic good.

Under the system I’m about to provide you, the mercenary is inarguably chaotic neutral and the hermit is unambiguously lawful good. End of sentence, all cleared up.

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An example of a Lorenz attractor as described by a color computer model.


Cristoforo Sergio Bertuglia and Franco Vaio, What is complexity?, in Nonlinearity, Chaos, and Complexity. The Dynamics of Natural and Social Systems, Chapter 28, Oxford University Press, Oxford, 2005, pp. 275-290  

Slytherins are NOT Lawful.

Classifying Hogwarts Houses under the Alignment system is incredibly difficult but I absolutely disagree with the notion that Slytherins are lawful. 80% of Hogwarts Houses + Alignment system posts I see classify Slytherin as lawful, the reason being that Slytherins use a moral compass and stick to this rule-system of morality even when it is not convenient. However, I believe, in contrast, that Slytherin exemplifies the paradox in believing that the only rule is that there are no rules; the only rule is that rules are meant to be broken.

“Those cunning folk use any means to achieve their ends”, the Sorting Hat says, and I stress ‘any means’. Yes, those means may include the law and it is not outside a Slytherin’s realm of possibility to manipulate or call on the rules in order to further their personal interests. However, the moment that the law becomes a hindrance to the Slytherin’s goals or well-being, it must be (and will be) discarded in favour of a more effective means to an end. In this regard, it is impossible to understand Slytherin house as absolutely lawful. 

If anything, a Slytherin is either chaotic or neutral. The former exemplified when Albus Potter rejects Rose Granger-Weasley’s friendship in fourth year because it comes from a disingenuous place (thus, he favours free will and agency over morality or even kindness), the latter shown when Andromeda Tonks marries a muggle born at the expense of her family’s traditions (in this way, her priorities are to her own personal happiness rather than a rule system). Whether a Slytherin is chaotic or neutral depends on their respective interests and this is the reason that classifying Hogwarts houses under the Alignment system is so difficult; likewise, how are we to understand Gryffindor when Harry Potter contrasts so strikingly with Peter Pettigrew? 

Regardless, I do not think Slytherins are lawful and I do not think classifying a house under one Alignment system category is helpful. 

Alignments and Purpose

Lawful Good: I must protect the innocent.

Lawful Neutral: It is my duty to enforce the law and follow orders.

Lawful Evil: I give lesser people a better purpose: mine.

Neutral Good: I strive to do good and encourage others to do the same.

Neutral: I guess I never really thought about it.

Neutral Evil: Making people suffer makes my life better.

Chaotic Good: I want to right the wrongs inflicted against the downtrodden by the system.

Chaotic Neutral: I do whatever I want.

Chaotic Evil: It brings me joy to kill as many people as possible.

new moon banishing ritual

a ritual to banish negative people and influences from your life, using the energy of your favorite/dominant planet

Originally posted by blackdove1010

During a new moon, the Earth and the Sun are separated by our dusty little satellite. The Moon rises and sets with the Sun, bright face turned away from us, giving us time to reflect and rid ourselves of baggage before setting out on our new endeavors come the first sliver of the waxing crescent.

The new moon is a time of darkness and an excellent occasion for ridding yourself of those darker influences in your life. Using the energy of your dominant/favorite planet, this new moon ritual can help liberate you from the shackles of your fears, bad habits, or negative people in your life.

What You’ll Need:

  • A black candle for banishing
  • A candle, crystal, or some other token to represent your planet of choice
  • Time for visualization
  • Optional: planetary tea blend


  1. Beneath the night sky or in a dark room, light your black candle.
  2. If you’ve chosen a candle to represent your planet, light it. If you’ve chosen a crystal or something else, hold it in your hands. Say these words:

    Oh [planet], give me the power
    to clear my life of these troubles.
    Like you, I want to clear my orbital path
    And turn each obstacle to rubble.

  3. Close your eyes and visualize yourself as your planet of choice. It’s early in the solar system’s formation. Asteroids, planetoids, and other chunks of rock soar chaotically throughout the solar system. Some are orbiting in your path.
  4. Examine the obstacles in front of you. How many are there? How big are they? Most importantly, what do they represent? Picture each negative influence in your life as a chunk of rock floating along the orbital path of your planet.
  5. Feel your planetary body hurtling through space. You’re so much larger and stronger than these obstacles in front of you. As you approach each one, notice how you bring about its destruction. Does it collide with you and crumble into dust? Maybe your gravity flings it out of your path and out of the solar system, never to be seen again. Is it small enough to capture and become one of your satellites, benefitting you rather than harming you?  Does it surpass your Roche limit (the closest a satellite can approach without being pulled apart by the planet’s gravitational field) and explode? If you’re a ringed planet, maybe the little bits of dust begin to orbit you and create your ring.
  6. When all of your obstacles have been destroyed, take a journey around the Sun. Nothing stands in the way of your orbital path. Perhaps now you know how to banish your real-life obstacles, or at least you have the strength to face them head on.
  7. Blow out your candle(s). Drink a planetary tea blend or perform any other ritual that will help fill up the spaces where the banished negativity used to reside. The next time you’re forced to face those fears, remember those moments you spent as a giant of the sky, and that you have the power to conquer any negative obstacle in your life.

happy-amateur  asked:

Funny how every one of those senators complaining about how federal power can jeopardize education all voted in favor of Devos. They can't even keep their rice-paper-thin excuses consistent.

I suspect a lot of them are anti-public schools and pro-private Christian charter schools, both of which are in line with DeVos’s own attitudes toward education. 

Mother Jones has a very good article here on the kinds of things that DeVos values and pays for–and the probable results of her policies:

Michigan now serves as one of the most prominent examples of what aggressive, DeVos-style school choice policies look like on the ground, especially when it comes to expanding charters. About 80 percent of the state’s charter schools are run by for-profit companies—a much higher share than anywhere else in the country—with little oversight from the state. In 2011, DeVos fought against legislation to stop low-performing charter schools from expanding, and later she and her husband funded legislators who opposed a proposal to add new oversight for Detroit’s charters.

Detroit, in particular, provides a cautionary tale of what happens when the ideology of market-driven “school choice” trumps the focus on student outcomes. The city’s schools—where 83 percent of students are black and 74 percent are poor—have been in steady decline since charter schools started proliferating: Public school test scores in math and reading on the National Assessment of Educational Progress have remained the worst among large cities since 2009. In June, the New York Times published a scathing investigation of the city’s school district, which has the second-biggest share of students in charters in America. (New Orleans is No. 1.) Reporter Kate Zernike concluded that lax oversight by the state and insufficiently regulated growth—including too many agencies that are allowed to open new charter schools—contributed to a chaotic system marked by “lots of choice, with no good choice.”

A 2015 study from Michigan State University’s Education Policy Center found that a high percentage of charter schools also had a devastating impact on the finances of poor Michigan school districts like Detroit. Researchers reported that, under the state’s school choice and finance laws, it was hard for districts to keep traditional public schools afloat when charters reached 20 percent or more of enrollment. While per-student public funding follows kids to charters or other districts, traditional public schools still have fixed costs to cover, like building expenses and faculty salaries. Charter growth also increased the share of special-needs students left behind in traditional public schools, and the extra costs for educating such students weren’t adequately reimbursed by the state.

anonymous asked:

I've always wanted to be mutuals with you, how does one do that so we could be friend?


Well I mean, the first criteria is that you have to be a Voltron blog (I prefer Voltron only, but having mostly Voltron and then some other appropriately tagged stuff is fine). I am a Voltron blog. I’m only going to follow blogs that will give me the content I need for my own blog. There are some exceptions to this rule; some of my mutuals are just my friends, or people I met in servers. I’d feel bad if I weren’t following my friends, even if they’re in different fandoms.

I also prefer people who tend to make original content!! Mainly because i don’t like seeing the same posts circulate on my dash. Especially if you’re just reblogging things from me, I don’t need to constantly see posts I just reblogged on my dash again two minutes later.

This is a kind of shallow thing, but I also follow blogs based on urls! Especially urls that are Clearly Voltron Related, so I know what I’m getting from the get go.

Finally, a lot of things just depend on what your blog is like. I’m not constantly looking at new blogs, but I do occasionally look at mutuals of my mutuals. I guess some things I judge for is… theme color, kinds of posts, your attitude (I like funny blogs lmao), your tagging system, and your icon. Little things like that.

Also, I totally admit that sometimes I search for my URL on people’s blogs, because 1. I like to see what they tag my stuff as, and 2. I’m nosy like that.

Perverted Bunny Mask: Jeon Jungkook x Killer AU ft. Min Yoongi Part 9

| Part 1| Part 2 | Part 3  | Part 4 | Part 5 | Part 6 | Part 7 | Part 8 | Part 9 |

Perverted Bunny Mask: Jeon Jungkook x Killer AU ft. Min Yoongi Part 9

Author: Taettybear

Words: 4.1 k

Genre: Smut/Gore/Assassins/Killer JK/ Drugs/ Gangs

Rating: M



Originally posted by jimiyoong


Even when growing up, you’ve never acted bratty or whiny because you didn’t have the luxury of being able to do so. You sucked it up and walked on, not looking back as you moved forward.

However, it now seemed like the appropriate time to actually throw a tantrum as you sat in your living room, surrounded by seven males who awkwardly huddled together.

You sat beside Yoongi, nearly sitting on your brother to be as far away as possible to the man who sat on your other side.

Yoongi obviously noticed, however, decided not to comment, his dark eyes staring at Namjoon, your leader who looked deep in thought.

You, on the other hand, couldn’t keep your attention on your leader and Taehyung’s conversation, hating how close Jungkook was to you. You could partially feel his heat on your leg through his black skinny jeans. Even his stare on your face was so heated, you felt like he could burn holes in you any moment. It sent unpleasant shivers through your body and you absolutely despised it.

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In dynamical systems, a bifurcation occurs when a small change made to the parameter values of a system causes a sudden qualitative or topological change in its behaviour. The name “bifurcation” was first introduced by Henri Poincaré in 1885 in the first paper in mathematics showing such a behavior.

Even in simple systems such as the logistic map, bifurcations can arise and introduce chaos. A rough description of chaos is that chaotic systems exhibit a great sensitivity to initial conditions. The animation depicts a cobweb diagram of the logistic map and shows its chaotic behavior.

Waking Days Ch. 2 - Rift

A/N: Finally, after a two month hiatus! To be honest, this chapter was a lot more difficult to write, mostly because there’s been, ahem, other fandoms that’ve grabbed my attention as of late. Also the content. As you may have noticed, I’m a lot more into character interaction than any real plot. Plot just helps give more character interaction, in my opinion, so writing a chapter that’s mostly plot and little character development is hard. That’s it. That’s my excuse. 

hopefully though, this chapter would be worth the wait. As usual, I take any questions you guys wanna ask about the state of the fic, if anybody’s worried or confused or just wants to gush with me about fandom. 

AU by my pal @doodledrawsthings. Based on Flat Dreams by @pengychan.

Thirty years took a great toll on his memories, but Ford still remembered this place. Dimension 52 rested in the back of his mind, even as he fled from one universe to another, meeting hundreds of people, places, and searching frantically for a concrete way of stopping Bill. It was one of the few worlds he knew that truly meant him no harm, where his stay wasn’t stained with loss and terror and Bill’s chaos. Years of voyaging had left his memory of this place faded and washed out like a watercolor painting, and remembering little details grew harder and harder, but as Stanford set foot into the temple, it was like he hadn’t even left.

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Right-Libertarian: why care about the lower classes when we’re the ones raining down social and economic wealth in the country?

Communist: mainly because the lower classes can never afford the same quality and quantity of luxuries “created” by you.

Right-libertarian: that’s because the state intervenes in our businesses and taxes the people and bleeds us all dry!

Communist: no, the state intervenes in the capitalist system because dozens of historical social movements led by the people demanded it–if the state never intervened and never gave concessions to the people, the state risks constant revolt.

Communist: also if it weren’t for these movements in the first place, individual capitalists would shift worker wages around, forcing laborers to work either long hours or short hours for variable pay; enforced workplace condition standards would disappear, child labor would still exist, mandatory breaks wouldn’t exist, legal business practices wouldn’t exist, monopolies would be everywhere and on everything, recurring great depressions would happen, unethical business practices would largely go unpunished, etc.

Communist: honestly without a state apparatus, capitalism would be a truly chaotic system.

Right-libertarian: okay but why would Murray Rothbard and Ron Paul lie to me :/

Communist: because you wanna be edgy but not lose daddy’s credit card privileges.


Fandom: Bungou Stray Dogs
Pairing: Dazai Osamu & Nakahara Chuuya
Rating: Gen. 
Warnings: None

Summary:  Dazai’s always there to bring him back, and there in the days after, too, when Chuuya needs him just a little more.

Read on AO3

Entry for @soukokuweek 2017, Day Two - “That’s what being a partner means, right?” 

The apartment is still, almost too quiet for the middle of a weekday. Dazai has kicked everyone out – all the visitors and well-wishers, every person with curious, prying eyes and pressing questions, too. The only person he hasn’t is Kouyou, but there’s no kicking Kouyou out of anywhere and she’s left on her own already; she simply knows when space is needed.

And Dazai needs it, badly.

He leaves the living room, littered with cards and slowly browning flowers, bags of get well soon gifts and other bullshit that’ll probably end up in the trash, to head tiredly to the kitchen. There’s scotch in the cabinet with his name on it, fresh ice in the freezer and he pulls out a glass and fills it full with both. He sighs as he does, long, drawn out, too weary for someone that hasn’t cleared seventeen yet and while he’s got his mind on Kouyou and how maybe, perhaps, he could have done with her in his space after all right now, she likely wouldn’t approve of his methods of coping.

Regardless of his ill-timed regrets, he’s got his scotch, anyway, and the burn of it down his throat when he tosses it back is welcome. Dazai hasn’t been able to feel much of anything but a general, encompassing numbness since that night, and as feeling slowly ebbs on in, he can’t help the desire to chase it all away again with more burning alcohol, and feel a little less human than his mind and body are trying to make him.  

It’s not the first time that they’ve done this, but each time he has hopes it’s the last time, as unlikely as that is. They still don’t have a decent handle on Corruption – no clue how long Chuuya can actually last while in it, no real idea what it even is, though Dazai has some guesses and none of them are particularly pleasant. It doesn’t really matter they’re inexperienced with the whole thing, and the fact that they can’t safely toy around with it is part of the reason Chuuya’s knocked out in his bedroom, pumped full of painkillers, practically dead to the world.

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Original Imagine Imagine being in class while Kol fingers you under the lab table (Part 2)
Imagine Kol having you pick a number between one and ten, not telling you the number would be the number of orgasms he would give you that night

Author: daenerystormboern

Reader Gender: Female

Word Count:  2, 214

Warnings: Smut

“Kol Mikaelson!” I yelled harshly when I finally spotted him after school had left out. He was surprisingly alone, and looked as if he was heading home, no longer interested in Elena Gilbert after school hours. The halls were completely empty.

“You,” I jabbed my pointer finger into his chest, “what in the hell,” I gave him an additional shove, “is wrong with you?” I smacked his arm for emphasis, although I would’ve much rather aimed for his head instead. However, there was a small part of me that had a shred of self-preservation not to piss off an Original vampire.

“Nice to see you, too, Y/N. You’re hurting my feelings, you know.” Kol said, smiling like the cat who caught the canary. He stepped forward, moving closer as I matched his steps backward.

He continued to move in closer, until I was backed up against the lockers.

“Don’t touch me,” I warned.

“That’s funny coming from you, darling. I seem to remember you guiding my hand up your skirt only a couple of hours ago.” He taunted with a smile.

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anonymous asked:

do you think of chaos as only pure disorder, or do you believe in chaos as more of a balanced connection between order and disorder?

Neither. I don’t personally find the colloquial definition of “disorder” particularly useful and order/disorder are functions of chaotic systems rather than chaos itself. When describing chaos as it relates to magick, I tend towards the mathematical definition: a complex system which is highly sensitive to initial conditions [1] . This is commonly illustrated by the butterfly effect - a butterfly flaps it’s wings in Texas setting off a series of atmospheric changes which culminates in a storm in Hong Kong. This has two important implications for magickal workings:

  1. Seemingly random systems have an underlying pattern which can be manipulated
  2. We can greatly effect a system by introducing minute changes

Magick at it’s core is the manipulation of the probability of a given outcome by changing the initial conditions in a chaotic system. Peter Caroll describes this by the illustrative but computationally useless equation Pm = P + (1-P)M1/p 


  • Pm : Probability of desired outcome
  • P : Probability event will occur without any outside manipulation
  • M : Magickal factor (M = GL [1- A] [1-R])
  • G : Gnosis
  • A : Conscious awareness
  • R : Subconscious resistance
  • L : Magickal link/taglock  

So to increase the probability of an event occurring ( Pm = 1), we need to choose an event already somewhat likely to occur (has a value of P close to 1) and decrease conscious awareness and subconscious resistance (values of R and A closer to 0). Simply stated, this means that a properly executed magickal working introduces turbulence into the system the magician is attempting to manipulate thus changing the final outcome (ie alters the value of  Pm).  Ideally this produces the desired outcome however since the system is highly sensitive to initial conditions, this can produce unpredictable and seemingly random results (typically referred to as “backfire”). Thus the more tightly we control the initial condition, the more likely we are to produce the intended result. 

[1] Please note that the mathematical definition of chaos is much more complex than this however the butterfly effect is the aspect most relevant to magickal practice

What do schools of fish and clusters of neurons have in common?

The answer lies in a concept called ‘emergence’, or the spontaneous creation of sophisticated behaviors and functions from large groups of simple elements.

Like many animals, fish stick together in groups, but that’s not just because they enjoy each other’s company. It’s a matter of survival. Schools of fish exhibit complex swarming behaviors that help them evade hungry predators, while a lone fish is quickly singled out as easy prey. So which brilliant fish leader is the one in charge? Actually, no one is, and everyone is. So what does that mean? While the school of fish is elegantly twisting, turning, and dodging sharks in what looks like deliberate coordination, each individual fish is actually just following two basic rules that have nothing to do with the shark: one, stay close, but not too close to your neighbor, and two, keep swimming. 

As individuals, the fish are focused on the minutiae of these local interactions, but if enough fish join the group, something remarkable happens. The movement of individual fish is eclipsed by an entirely new entity: the school, which has its own unique set of behaviors. The school isn’t controlled by any single fish. It simply emerges if you have enough fish following the right set of local rules. It’s like an accident that happens over and over again, allowing fish all across the ocean to reliably avoid predation.

What makes emergence so complex is that you can’t understand it by simply taking it apart, like the engine of a car. Taking things apart is a good first step to understanding a complex system. But if you reduce a school of fish to individuals, it loses the ability to evade predators, and there’s nothing left to study. And if you reduce the brain to individual neurons, you’re left with something that is notoriously unreliable, and nothing like how we think and behave, at least most of the time.

Regardless, whatever you’re thinking about right now isn’t reliant on a single neuron lodged in the corner of your brain. Rather, the mind emerges from the collective activities of many, many neurons. There are billions of neurons in the human brain, and trillions of connections between all those neurons.3:28When you turn such a complicated system like that on, it could behave in all sorts of weird ways, but it doesn’t. The neurons in our brain follow simple rules, just like the fish, so that as a group, their activity self-organizes into reliable patterns that let you do things like recognize faces, successfully repeat the same task over and over again, and keep all those silly little habits that everyone likes about you.

As more and more neurons are connected, increasingly complex patterns of activity emerge from the network. Soon, so many neurons are interacting in so many different ways at once that the system becomes chaotic. The trajectory of the network’s activity cannot be easily explained by the simple local circuits described earlier. And yet, from this chaos, patterns can emerge, and then emerge again and again in a reproducible manner. At some point, these emergent patterns of activity become sufficiently complex, and curious to begin studying their own biological origins…not to mention the concept of emergence itself!

And what we found in emergent phenomena at vastly different scales is that same remarkable characteristic as the fish displayed: That emergence doesn’t require someone or something to be in charge. If the right rules are in place, and some basic conditions are met, a complex system will fall into the same habits over and over again, turning chaos into order. That’s true in the molecular pandemonium that lets your cells function, the tangled thicket of neurons that produces your thoughts and identity, your network of friends and family, all the way up to the structures and economies of our cities across the planet.

From the TED-Ed Lesson How do schools of fish swim in harmony? - Nathan S. Jacobs

Animation by TED-Ed