#Yeah - I know that's a koch snowflake
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The coastline paradox is the counterintuitive observation that the coastline of a landmass does not have a well-defined length. This results from the fractal curve–like properties of coastlines; i.e., the fact that a coastline typically has a fractal dimension. Although the "paradox of length" was previously noted by Hugo Steinhaus,[1] the first systematic study of this phenomenon was by Lewis Fry Richardson,[2][3] and it was expanded upon by Benoit Mandelbrot.[4][5]
Yeah, that Mandlebrot
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Snow Day
Kelsa looked out her window as she groggily became aware of the world. The..strangely very...white world. Her eyes widened as she realized that the small shrieks that had wormed their way into her dreams were from children throwing snowballs at each other.
“It’s snowing!” she yells, pressing her face against the glass.
She huffs out a breath to fog it up and draws a smiley face, her own face lighting up.
“Are you going out in it?” a groggy voice asks from behind her.
Kelsa turns to see Derwyn squinting up at her, the hand that isn’t propping him up fumbling for his glasses. She smiles at how wild his hair has gotten in the past night and hands him the glasses he was still searching for.
“Ah, thanks. Can never find these things,” Derwyn mutters
“You could always summon them to you, yeah?” Kelsa replies, smirking
“But I have to be able to see them to do that, smarty,” he returns
Kelsa opens her mouth to retort back, but is interrupted by Molly calling everyone downstairs for breakfast.
“This conversation isn’t over”
“Yeah, yeah. Let’s hurry, I’m hungry”
*
Downstairs is chaos, just the way Kelsa likes it. After the war separating the Southern and Northern sides of Koche ended, the Juniper family decided they would never be separated again. So with the stipend the government gave them after their family farm was destroyed in battle, they built a new home out in the countryside. Which would be calm and domestic if Kelsa didn’t have so many siblings. Not to mention their significant others and the family members they bring with them. Breakfast is a big spread as usual and while she would love to dig into that heaping pile of bacon her mum made, Kelsa knows that there’s a girl who needs some cheering up right about now. She starts to grab a piece of toast before a hand comes into her field of view stopping her.
“I figured you’d be rushing out of the house as soon as you woke up so I already made you some wraps to take along. There’s enough for Peregrine too.” Priyanka says, handing Kelsa a bag emitting a delicious smell.
“Thanks, Pri.” Kelsa says with a large grin, taking the bag and heading out of The Burrow.
The weather is as cold as it looked from the window, but the wraps Priyanka made are warm and full of savory bacon and eggs, warming Kelsa on her hilly trek to Peregrine’s house. She takes a few moments to look at the snow around her, reveling in the way the soft white substance coats the trees and ground, sparkling in the morning sun. To her surprise, her boot hits something solid in the snow, causing her to jolt back.
“Peregrine, what are you doing in the snow you goose?” Kelsa says, a bit louder than she meant to due to her shock.
Half buried in a snowdrift lies Peregrine Olivewood, her pale eyelashes and hair covered in equally delicate looking snowflakes. Kelsa doesn’t fail to notice the tears that have frozen to her cheeks as well.
“Father and I had another disagreement. I just couldn��t stand to be in that house anymore,” Peregrine says, voice cracking slightly, “I wonder why they call snow a ‘blanket’, it isn’t very comfortable.”
“It’s a blanket for the ground, Peregrine, not a girl.” Kelsa says, offering a hand.
Peregrine takes it and pulls herself up to a sitting position. Her and Kelsa spend a few moments brushing off the snow that’s piled up on top of her legs and torso. Kelsa doesn’t know what to say about Mr. Olivewood that would be helpful so she settles for handing Peregrine one of Priyanka’s breakfast wraps. Peregrine gently takes it with a small smile and eats it quickly, making Kelsa wonder just how long she’s been out here. Looking around so she doesn’t watch Peregrine eat, Kelsa’s eyes fall on the pile of snow left over from cleaning up Peregrine’s clothes and an idea strikes. She slowly moves her hand to her side so as not to cause suspicion and begins to pack some snow in the palms of her hands.
“Hey Peregrine, what does a Snowman play sports with?” Kelsa asks.
“Hmmm. Oh I know! A sn-” Peregrine is cut off with a splat of snow hitting her shoulder.
Kelsa laughs raucously at Peregrine’s face that’s frozen in a mix of shock and a smile.
“Kelsa Juniper, you know I take riddles very seriously! The gall of using it against me!” Peregrine laughs while proceeding to make her own snowball arsenal.
“Sorry Perry, you make it so easy!” Kelsa shouts back, rearing up to take another shot.
The two engage in a spirited battle, full of shrieks and squeals, as they pelt each other with their snowy projectiles. After a mighty fight, Kelsa cedes, having done her job in making Peregrine feel better (and certainly not because she was losing, thank you very much). Kelsa flops down onto the snowy ground and pats the space beside her to invite Peregrine over. After peeking from behind her tree shield to ensure this wasn’t a trap, Peregrine skips over to sit down beside her, smiling wide. Kelsa starts drawing in the snow so she doesn’t have to look at Peregrine when she reveals the real reason she came over.
“Hey Grine?” Kelsa starts
“Yes?” Peregrine says, looking over at the scribbles in the snow Kelsa’s made.
“I know you and your dad don’t get along well after...everything that went down,” Kelsa says, pausing to glance up at Peregrine’s face, “Well, I just want you to know our house always has room for one more. And- and if you wanted to room with me and Derwyn, you’d be welcome to it.”
“I- what is it you’re suggesting, Kelsa?” Peregrine asks.
Kelsa looks up at her face, which is a bit red. Kelsa doesn’t dare assume it’s because of her and chalks it up to the exertion of the snowball fight.
“I’m sayin’, I-” Kelsa stutters, gulps and starts again, “I’m saying, I love you, Per. And everyone else back home cares for you and wants you to be safe and happy. After that last time you came over crying, I realized that I never wanted you to be that alone feeling again. So I want you to come live with me where I know from experience you won’t be alone.”
Kelsa doesn’t have the courage to look up and keeps herself as still as possible, wishing she could disappear into thin air. Peregrine puts her hand against Kelsa’s cheek softly, turning her head so she can look into Kelsa’s slightly watery eyes.
“I think I’d love nothing more than to live with you,” Peregrine says softly, brushing her thumb against Kelsa’s cheek, “Nothing more, except a kiss? If that’s alright.”
“It’s more than alright” Kelsa whispers.
Peregrine’s lips taste like a breakfast wrap, but Kelsa couldn’t care less. She hopes that Peregrine feels the same.
The two have trouble knocking on the door with their arms full of stuff, but they eventually get an answer by kicking at it. As they walk into the warm home, Kelsa starts hauling everything upstairs to her room, hearing her family below welcome Peregrine and sit her down to the rest of her breakfast. Peeking around the corner as she comes back down, Kelsa sees the large smile that’s plastered on Peregrine’s face. She warms up inside realizing that it’s a smile she’ll now be able to see everyday.
#[Holy shit I actually wrote something! I'm so excited I haven't written in such a long time and this was like coming home after years away.]#excite!!!!
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The Partisan Generation
This generation
It was the morning that his daughter airily declared the moon landing a fake news Jewish plot to let liberal scientists run the government that Lenton Ayre realised things had gone a bit far with this generation.
“and, you know its because gun control libtards in the Hollywood elite that we lost the Iraq war” she added, gazing into her eglasses at the endless stream of retweets, status updates and weather pattern like emojis swept over her “because, you know. There were WMD’s - that’s the truth. Only the cultural Marxists wanna cover it up. There’s like a whole thread on ReddChan about it and all the instagram influencers are saying…”
“honey, I just asked what you were gonna be studying in school today” he replied, cutting her off before she could do the whole ten minute screed on the snowflake liberals that then could segway into a whole monolog that took in every conspiracy theory from JFK to flat earth. Instead he would rather talk about their real education. As someone who was assiduous in his working habits and concerned for his children’s future he had of course taken them out of the local state school and put them into the Musk-Bezos academy that had opened in a refurbished mall just out of town. This was less a matter really of intellectual choice, more that since his own employer was a subsidiary of a subsidiary of a subsidiary of Amazon he could either send his kids to the Inspire! Academy or he could find himself a new job.
That Lenton would not have minded quite so much, but all his rivals could only offer him the Netflix online-ed course for his two teenagers. That would hardly have been good fathering, he had figured. Although considering his two children’s current subjects of conversation he wondered if it might just have been better to join one of the local Trump Revival churches and get them home schooled. At least he wouldn’t have had to worry about exams, and they would have a willing audience to talk conspiracy theories with.
“Rani, dude. What is that libtard bullshit?” Ayre’s son retorted, his own smartglasses reflecting the latest news from the hardcore manosphere where he spent most of his time. Since he was wearing his ‘science is my superpower’ tshirt his sister was clearly in a trolling mood “you’ve been sucking down that stupid crap your latest gaywad lametoob boyband crush soyboy has been saying, right? Everyone knows that they’re just a front for Kremlin. Those pretty commie boys want to turn you Stacy’s into their harem so that honest patriots like me can’t get what we’re owed….”
“Kev, you can’t get a girl cause you’re a fucking misogynist incel loser” said his sister quickly “don’t start blaming other people for your problems”
“okay, kids please” said Lenton raising both his hands in what his NLP Yoga teacher had assured him was a calming pose that leant him an air of kindly authority “can we have some calm? You know something a little less partisan at the breakfast table?” lenton scrolled through his own smartglasses looking for non controversial content. It was surprisingly hard “now, can we all agree that congress are a bunch of assholes? Or that kittens are super cute?”
His son opened his mouth to argue
“okay, how about dogs in cars, with their heads out the window?”
Kevin shut his mouth and nodded.
“I mean, I don’t know where it comes from” moaned lenton later at the popup office where he spent his days in online content creation “my daughter spouts anything that comes from the Kremlin via whatever hot youtube boy she’s currently hard crushing on, and my son says anything that some rock hard libertarian science guy says. Neither of them give it a second thought. I don’t know why, cause whenever I say anything they’re on me with laser sight scepticism”
“eh, I blame the technology” complained his colleague as she thumbed through mentions in her livefeed, feeling the desperate need for validation more than the caffeine hit in the cup in her hand “these kids, they wanna be spoonfed everything. I remember when we was their age. We hadda actually google search stuff. If you wanted to throw shade you hadda go to the effort of writing a livejournal about it. Now these kids just get a bunch of recommendations straight into their eyeballs. No thought required”
“too right, Tina. Its about hard work” said Lenton, looking at the day’s workload “it’s the attitude that’s the problem. They’re just too lazy to challenge anything” he scanned the list of hot button to do items “so, what talking points are we monetising for cultural leaders today?”
“we got a contract in from Russia. They want to see the latest round of the Israel Iranian conflict spun as being caused by Jewish bankers. Was thinking we can feed that one in via the Foxosphere. They love a bit of Jew baiting so long as we call em progressive liberal internationalists”
“good call” said Lenton, paging through the various socially destructive ideas and fake news he was being paid a hefty commission to inject into public discourse “we’ve got our screaming mob on retainer. Can get them with placards and slogans anywhere we need them. Although the RNC still hasn’t paid them for that last job. Something about how they weren’t violent enough against those BLM people…”
“they’re actors” sighed Tina as she refilled her mug from the genuine organic roast machine. Her mug bore the cheery slogan ‘world’s greatest stripper’ always reminding her of her grandmother, whose gift it had been “if they want proper violence then they have to get the real white supremacists, but they’re all booked up defending the Canadian border from UN one world government liberal invasion, or whatever we told them was the problem”
“thought it was LGBTQ infiltrators?” replied Lenton. It was hard to keep up. They were after all paid to shape the news and the information that influenced people, the consequences were not really in his pay grade.
“whatever” sighed Tina as she took another high protein cookie from the stack. They were super moreish but were almost physically indigestible. The resulting diarrhoea was always good for the waist line “and we got another Koch brothers contract up. Top dollar to get the key 18-25 demographic thinking that renewable energy is a problem”
“simple. Thread through the manosphere as being that renewable energy is unmanly and feminising. We can to nostalgia stuff around the petrol engine. The far right will love a bit of Tesla bashing….”
“and Tesla will pay us double to spread the counter message” said Tina, finishing her coffee “cool” she paused “look, don’t worry about your kids. They go through phases. Shit, I was tumblrd out when I was their age, woulda cut my best friends head off if she’d said a word against my fandom. They grow out of it”
“yeah” said lenton, already downloading the days false news and astroturf memes ready to infect the information stream of the western world with “but, you know they just seem so extreme. I don’t get why” he added as he pumped a thread blaming vaccinations for causing sexual inadequacy into a mainstream news forum where it would have an active effect on roughly forty five percent of the readership “I just don’t see where they get those ideas from”
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Fractals
This is the first chapter of an original story I wrote, that I’m unfortunately never going to finish.
Chapter 1
“Hey! Aki, wait up,” I call as my best friend Akiva jogs ahead of me. We jog over cracked pavement that leads to our school, whose pristine cement walls look out of place among derelict shacks and cottages that people like my parents, lower class workers, inhabit. Luckily, I will avoid that fate. I guess that’s all it is though, a serendipitous turn of events that led me to be born with a Koch Snowflake fractal, the rarest one. Next year, when I’m 15, I’ll be out of this place, and into a boarding school, but away from everything I know. I don’t want to leave my parents and my friends, but I can’t deny that I’m excited to see what life is like for the upper classes.
“There isn’t time.” Aki responds, interrupting my thoughts. “You know Mr. Hall hates it when we’re late.”
“He’s not that bad,” I argue. I’ve never even heard him say a cross word. He’s pretty mild, even if he is the sort of suck up who gives me perfect scores when I know I’ve gotten something wrong. Technically, all the teachers are supposed to be the same across the neighborhoods, but everyone knows that the higher ranking neighborhoods get much better teachers.
“He treats you better because you’re a Snowflake. The rest of us mere ‘commoners’ have to deal with him hating us.”
“You’re a Mandelbrot, so technically of a higher rank than him. He’s just a Sierpinski who did superbly well on the test.”
“Yeah, but I’m not a higher class, that is unless I also do fantastic on the test.”
“I’m sure you will, you’re literally a genius. Plus, we still have plenty of time left to study, and our grades matter too.”
“Are you kidding me? There’s only eight months and seven days! You don’t have to worry about the test, there’s no other option but success. For me, it could change my entire future. Just because my best friend is a Snowflake doesn’t mean that I also get a free ride to the life of my dreams.”
“I’m sorry, Aki, that was unfair. You’re right; it’s not my place to say things about the test. But just know I’m sure you’ll be phenomenal. Now we should really hurry, I just heard the first bell ring.”
We rush inside the school and slide into our seats just as the second bell rings, announcing the end of our passing period. “All right class, it’s time for our daily report, then after that we’ll have our morning announcements.” Mr. Hall announces. We all watch as the projector in the middle of the room begins to glow with a bright blue light, before the hologram forms.
“Dear Aelia,” the Supreme Leader, Hunter, announces, “today is a gorgeous day to be in our country. We are blessed with our wonderful government, beautiful country, bountiful crops, and the fractals marking each of our wrists. Without the fractals, our system would be in disarray, and no one would know their proper place. We thrive with them as our base, our guide to the classes.” His face is plastered in an all too plastic smile while he recites the same lines he does every morning.
“Yeah, a blessing if you’re a Brot or Koch,” Freddi retorts. He’s always the one who talks out in class, but everyone acknowledges it’s because he’s bitter to have been born Apollonian. Hunter continues, oblivious to the small act of defiance, spoken from an unexceptional child in a small school in a poor neighborhood in a lower class district that he probably has never heard of.
Hunter says, “For all students turning 15 this year, we have moved the examination date to seven months earlier. All of your examinations will be moved up as well.” Indignant protests erupt from members of my class.
“That’s outrageous!” Carlia, a blond Sierpinski who is usually quiet, yells, “We’ll only have a month to prepare! We were supposed to have eight.”
“Now this may seem like a shock, but keep in mind, everyone has the same test date still, and the tests are on a curve, so everyone will still have the amount of time to prepare.” Hunter carries on. “I’m sure everyone will do great. Now let us recite the pledge.”
We all stand with him and recite, “We pledge to the land of Aelia that for the rest of our lives, we will be loyal, obedient citizens who understand that our government knows best. We will remember how blessed we are to live in this society, where fractals determine classes so everyone may know where they belong.” The hologram fizzles out and we all sit down.
“Very good, class. I would even say that was laudatory.” Mr. Hall praises. “Does anyone know what that word means? It could be on the test.” Six hands shoot up, Aki and mine among them. His eyes scan the room, before falling on me.“Yes, Kalia?”
“It means worthy of praise”
“Excellent as always. I’m sure you will do very well on the test, despite the change in date. But of course, you are a Koch Snowflake, so I suppose it doesn’t matter, does it?” he says with an awkward chuckle.
“Yes sir, but I intend to study hard so that I may do well anyway.” I respond, my words forced, but the meaning true. I do in fact intend to study and do well, but I have to be perfect, even when stating the truth.
“Very good. That sort of devotion is indeed laudatory, but we must continue. Class, there aren’t too many announcements today, but they are as follows.” He takes a deep breath, before quickly reading, “‘This pod will have a government class, computers and technology class, lunch, then a full grade assembly to learn how to study, due to the change in test date. Today is spaghetti day, but as there is a shortage in produce we will not have tomatoes or cheese. Please remember that today is national Keep Your Socks On day.’ Wow, that one breath rendition of your announcements must have knocked everyone’s socks off.” He laughs again, but no one joins him. No one likes teacher jokes, and everyone is too worried about the test date being moved up to care anyway.
The bell rings, and we all head to government class. This is Aki’s favorite, because they want to be a politician someday. It’s possible, because they’re a Mandelbrot Set, but it’s not very likely unless they do really well on the test. Even then, it’ll still be hard because practically all the Koch Snowflakes either go into politics or become CEOs. Everyone thinks that being a Snowflake means a life with no restrictions, where your every wish is handed to you on a silver platter. In reality, we are forced into a small set of jobs, with no room for anything else. My dream of being a poet can never and will never come to be. Despite the harsh truth, I haven’t lost hope. I desperately want to write poems, and I’ll never stop dreaming about it.
We enter the classroom, a bright, airy space with windows on every wall looking out on the world around us. In nicer neighborhoods, nicer cities, I am sure it is a beautiful sight, but here all you can see are drugged up homeless people leaning against the windows. “All right children!” Ms. Ashwood calls. “It’s time to start government class. Please be seated and read the lesson plan on the board.”
Aki and I grab seats in the front. When I read the lesson plan, I find that we are reviewing our government for the test. It seems like an odd choice, considering how many times we’ve gone over it, but I guess more review is always good. “Akiva, hand out this review sheet,” our teacher directs.
“Of course, Ms. Ashwood,” Aki responds. They get up and hand out the papers. I grab mine, and see it’s just a flow chart of our government. The supreme leader is at the top, with control over everything.
Then comes law formatum, conparantes, and illigo, our branches which form laws, interpret laws, and enforce laws. It’d be really boring to explain it now, but basically it’s a corrupt way to give all the power to Mandlebrots and Koch Snowflakes, so that they can continue to be in charge. I don’t think everything should be decided on what is on the inside of your wrist. Akiva doesn’t agree with me. Everyone seems so happy with the system; it’s sort of odd.
In class, all we end up doing is discussing the class systems. We’ve already done this a lot, so I zone out a bit. Aki is super engaged, though. They make a lot of amazing points, and it’s clear to everyone they'll probably become a politician when she grows up. I wish I was the same way; super involved. Because I don’t have a family company to inherit, so I don’t really have any options besides government. No Snowflake who comes from the lower classes can become a spy, which is the third option, because they are worried about loyalty.
My musings are unpatriotic, and I feel guilty about that, so I tune back in. “You will have a final project in your next school, necessary to graduate. It will be to do a presentation on a way to improve our government. It’s a very important project, and many Mandelbrots and Kochs end up going on to make the changes they proposed back in boarding school. You should start thinking about what you want to do now.”
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So I’m gonna list a couple ways to imagine these shapes here. My strategy is just throwing all the spaghetti at the wall, and if any sticks, we’re golden. So. Method #1: The Super Squiggle
This is how I imagine it.
Top line is baseline. We’ll just say it’s 2’’ long. I’m not gonna measure it.
Red line beneath it, if you carried it forward, is going to be more than 2 inches long. I don’t know by how much, but I can see that the extra distance is from distance wasted going up, then going down, then going up, then going down. Like switchbacks on a trail.
The third line is just showing that there’s no limit to how much you can scrunch the second line up. You can squish it up like an accordion and keep all the up-down waste, while also covering less horizontal distance. If you did that to the max, full on, infinite scrunch-horror, you’d get something like this.
Oh that looks fine, what makes this-
-oh sweet jesus
And then for the final bit of fuckery, you’d just that that infini-squiggle and bend it into a circle. It’d be kind of like a gear with infinite teeth. Ta-dah!
Method #2: The Paper Door
This is similar to the last approach, but running in reverse. I was actually halfway through writing it myself when I found the WikiHow article on it, and they do such a lovely job I’ll just leave it to them. The only addition I’d add is to imagine that you had infinite sharp scissors and infinitely strong paper - then, if you wanted, you could modify their design so as to turn a single sheet of paper (a very finite area) into a loop big enough to encompass the entire world. You’d just have to add more of the up-down sections. You'll see. They did great.
Method #3: Fractal Hell
I’m just gonna link you the wikipedia article on Koch snowflakes. Wikipedia's explanation of math areas tends to be pretty... abstract. But, again, they have a lovely image set, and I think that does 99% of the heavy lifting.
…Now in 3D?
Yeah. It seems like a big leap, but the easiest way to convert all just imagine these as like, blocks. Same 2D shape, but you just drag them forward a little. Like so, but with any shape and not just a star:
The Watership Down rabbits removed an additional 0.1 nanometers constructing their warren, although that was mostly soil. British rabbits have historically mined very little coal; the sole rabbit-run coal plant was shut down in the 1990s.
UK Coal [Explained]
Transcript
[The following formula is shown (with the divisor below a horizontal line in the comic, rather than inside parentheses):] UK total coal production (1853-present, UK DESNZ) / ((coal seam density) × (UK land area)) = 25 billion tonnes / (1.3kg/L × 240,000km²) ≈ 3 inches
[Cueball is standing to the right of the formula, upon a dotted line representing the prior ground level. Two arrows indicate that the dotted line is 3 inches above the solid line that is the current ground level.] [Caption below the panel:] The UK shut down their last coal power plant today, which means that over the course of the industrial revolution, they dug up and burned an average of 3 inches of their country.
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