#Iterative Functions

[math1089]

Exploring Collatz-Like Functions: The Power of 3n – 1

The mathematician, carried along on his flood of symbols, dealing apparently with purely formal truths, may still reach results of endless importance for our description of the physical universe. Karl Pearson Be careful! Do not attempt to solve this math problem – it’s very tempting, but it leads to never-ending cycles. Here’s how it works: Start with a positive integer. If it’s even, divide it…

[keii]

okay but what if... i added new characters in my tomodachi life and it's the love and deepspace guys

[loveydoveylex]

Isn't Tin Tin 15 years old?

short answer: no

long answer: no

if you see him as a minor I do not want you on my page because clearly neither of us will be comfortable with one another :p this is an age old discussion that no one can agree on a direct answer for (because it is up to interpretation...) but the most important part is I do not nor will I ever interpret him as a minor. if I did I wouldn't be selfshipping with him, that's weird and creepy. I only do so with the context of him being an adult.

I typically go with an age around 19 for him, as per an interview with hergé from 1970. although he's had one birthday since we first "met"... so 20, I suppose?

[likesummerrainn]

watch that poison blossom

Hangman Page Birthday Week 2024: ⤷ Day 6 - Favorite Feud: HangSwerve

[iteratorsex]

Also to be noted: The fact that gravity never turns off in LTTM's GSB/Neural Terminus, even though it fluctuates everywhere else, implies that the GSB has special properties possibly pertaining to gravity disruptors or collapse events, which wouldn't surprising considering how honestly important the puppet seems to functioning

[anarthursworld]

The Frondity Substack explores the connotations of a fractal universe. The link takes you to pages 8 To 15 containing The Journey Begins post of the Frondity publication.

[glamrockmike]

What character in fnaf do you wish got more attention/ characterization?

resisting the urge to say my usual suspects (gregory and vanessa) in favor of a character who’s always been kind of a sleeper favorite of mine, because i just recently realized the amount of fandom and canon attention he gets is really minimal and typically reduced to him being grouped together with the others of his line

funtime freddy (and bonbon) is my favorite funtime animatronic and one of my favorite freddies and it makes me so sad he’s barely developed in sister location, although the breaker room is so much fun. he’s so cool and mysterious in count the ways and in ucn too! in the rest of canon (except fnaf 6 which i haven’t played)…ehhh not so much. fourth closet i am talking to you. i just think he’s super silly and has a character that’s worth exploring, and in my opinion it should have been explored more in sister location. i kind of feel that way about a lot of the funtimes now that ive played through sl myself and found it to be pretty small and quick minus night 4, but it is a great game and installment in the series.

free my boy he’s done lots of things wrong but i don’t care. give him six seasons and a movie

[mirwx]

thumbnail submission for a map

[seyaryminamoto]

Scenes of a Peaceful World: Sokkla Saturdays 2024

Day Nine - Power

Rated: T

On FF.net//On AO3

Nighttime didn't always offer a spectacle as glorious as the one they would be privy to on that very special occasion: a meteor shower, witnessed from the heights of the Dragon Springs, a location unaffected by nocturnal lights that hid away the weakest stars, for the Dragon Springs stood at the peak of a grand mountain chain, distant from grand cities and settlements.

It was, thus, a place out of reach for most people, and only one peculiar human family was bound to visit it frequently.

"Alright! Snacks are here!" Sokka announced, proudly: he opened the first bag of sizzle-crisps only for the youngest children and their dragons to rush him, nearly tearing it to pieces. "Hey! Behave yourselves, you wild fiends! Azula! Azula, help!"

"You can hold them off, love! I believe in you!"

"B-but…! ACK!"

Unsurprisingly, Sokka wound up on the ground, overcome by their onslaught: Yuuna and Shun cheered as their dragons growled happily, everyone vying for the bag of snacks, as expected. Hotaru watched them with amusement, unwilling to involve herself, whether to help her father or join the younger children. Azula kept an eye on them as well, whereas Rei continued to work hard at their day's main attraction…

"I'd say he should be here helping you set up instead, but… watching him goof off that way never gets old," Azula told Rei, who laughed at her assessment.

"I've noticed. You seem a little smitten with him, I'd say," Rei teased. Azula gasped.

"Me? With that handsome, funny, strong man? Why… don't tell him that, of course. It'll go up to his head," Azula said, dramatically. Rei laughed, shaking her head as she continued working, tweaking the gears as she set every piece of her remarkable invention in place.

The telescope Rei had spent the past years crafting was finally complete: a beautiful work of engineering and science, with a polished metal finish, stylish and considerably large. By this point, she only had to calibrate the finishing touches, but by all effects, the telescope was as good as ready.

"I wonder how much we'll see tonight… the weather's clear," Rei said, excitedly. "I hope it will be amazing. I watched the meteor shower last year too, but the telescope wasn't ready…"

"You did a great job with it," Azula smiled, squeezing her daughter's shoulder. "And we're grateful that you wanted us to use it with you, too."

"Well, now… I think it's natural to want to share your biggest academic achievements with your family first," Rei grinned, peering through the scope and smiling. "Okay! It's ready now!"

"Is it?!" Sokka asked, sitting up again. Azula smiled, glancing at him.

"I thought you were moribund after being mauled to death by a little princess, a little prince, and two fearsome dragons…"

"Oh, uh, yeah. Of course I am. I'm dying…! Come save me, Azula…!" Sokka groaned dramatically, stretching his arms and legs out to further enhance his performance. The kids giggled, still devouring sizzle-crisps as though they weren't even slightly spicy, and sharing them with their dragons, too.

"I suppose I have time to spare to save him from this nefarious fate… it'll still be a few hours before the meteor shower, right?" Azula asked Rei. She nodded.

"Can I look already, though?" Hotaru asked, eagerly. Rei beamed.

"Of course! Come, come, this way… here's how you can calibrate the lenses," Rei explained, bringing her younger sibling to sit before the telescope.

The playful chaos between the kids and Sokka wouldn't dwindle easily: with Azula in such a cheerful mood, the children were perfectly content to disregard her requests that they gave their father a break and eased up on the food. Even so, Azula had a good enough card in her sleeve worth using against Shun, in particular.

"Ah, but what have they done to you, my handsome stud?" Azula said, kneeling beside Sokka. He stuck his tongue out.

"Murder. That's what they did. I'm all… murdered," he said, stiff. The kids giggled at his statement. Azula hummed.

"Well, that's a shame. Here I thought you'd get to witness the meteor shower properly with the telescope, but if that's impossible, then I must send you off the right way…!"

Shun cried out in disgust when his mother leaned in to kiss her husband, fully. Yuuna groaned once Azula's body obstructed her access to the sizzle-crisps: the mother slowly but stealthily clasped the bag and snuck it out of their reach before breaking the kiss. Her amused husband couldn't seem to stop smiling.

"Damn. I'll have to play dead more often, that was fun…"

"Oh, my! I'm so powerful I brought you back to life! That entitles me to the rest of the sizzle-crisps, then…"

"No! Mom!" Yuuna gasped, mortified while Shun gagged, still annoyed over witnessing the very brazen display of affection between his parents. Sokka, of course, was delighted and dazed, unable to stop laughing.

Their evening continued to be joyful and boisterous, as they enjoyed their picnic dinner while they waited for the right hour to arrive for the meteor shower. After the meal, Rei ensured to teach all the children how to look through the telescope, which Yuuna naturally took to, her curiosity ever triggered by anything related to investigation and science.

"What a loud, messy, fun family," Sokka smiled, wrapping his arms around Azula, who sat on his lap. She smiled too, closing her eyes and relaxing against him. "I think we did a decent job, didn't we?"

"Hmm. Decent. I suppose that's one word to describe it," Azula said. Sokka chuckled. "Think we could've done better?"

"More like I don't want to boost our ego that much. You think I shouldn't know how handsome, smart and funny I am for that reason, after all…"

"You… how dare you listen in to conversations I was holding publicly? Shame on you, Sokka," Azula huffed, playfully. Sokka chuckled, kissing her cheek.

"I love you so much," he said, earnest. Azula's smile grew gentler upon hearing those words. "I refuse to fathom any world where I wouldn't."

"Hmm… do you, now?" Azula smirked. Sokka huffed.

"I said I did. You don't believe me?"

"I mean, I constantly marvel over the fact that, despite everything, we made it this far," Azula said, with a soft chuckle. "It didn't seem likely, at multiple instances in time. Our troubled beginnings… neither of us ever imagined we'd wind up like this."

"Well… no. But all relationships do start by being strangers," Sokka pointed out. Azula snorted.

"Strangers and enemies are entirely different concepts," she said. Sokka smiled guiltily. "I'm just saying… the world where you somehow decided not to love me might actually exist."

"Pfft. Any Sokka who meets you and chooses not to love you, or to love someone else, is an idiot. So… not me, not whatsoever. He is now deemed unworthy of being called 'Sokka', and that's that," Sokka declared, proudly. Azula laughed, shaking her head.

"Very well, then any Azula who doesn't fall for you is no better. Our alternate selves are idiots, we've made that official now," she said. Sokka snickered.

"You know… there are so many stars up there," he said. "And there's stuff like… theories of the universe, you know? Rei's told me about those before… multiple worlds like ours, where matters play out differently?"

"She's mentioned those theories before but… I can't say I follow. It feels rather arbitrary for countless possible branches of choices to create parallel worlds every time. It's like… say your sister chose between eating papaya or mango during breakfast one day, and whatever choice came from it, it results in one world where she married Aang and one world where she married… uh, I don't know, Jet, maybe."

"Jet?" Sokka repeated, with a disbelieving snort. "I'm not sure Jet's the marriage type, but fine. Let's pretend she reformed him that much, huh? All because she ate… papaya. Or mango."

"See? Doesn't that seem strange?" Azula asked, amused. "It would imply that at some point or another, I could've made an entirely stupid choice much like it, like… eating something that sat wrong with my stomach."

"Azula: nothing sits wrong with your stomach. It's made of solid steel or something. All the spices you eat prove it."

"Not true, you said that once, Toph tried to bend it to prove you wrong and she couldn't do it, which means…"

"It means it's made of a stronger metal than anything she can bend," Sokka laughed. Azula cackled, shaking her head.

"Well, then…! Say that I never became such a big fan of spices. That, as a child, my parents refused to feed me any. Which means my resistance to spices was insignificant, and then because of that, on the day we were supposed to meet for the first time, I ate sizzle-crisps and… I got diarrhea."

Sokka burst out laughing, dropping on the ground as his shoulders shook: all four of their children glanced in his direction, astounded by his reaction. Azula smiled and waved a hand dismissively at them, even if their attention flustered her slightly.

"Is Dad okay?" Hotaru asked.

"I may have broken him, but… we're just theorizing on things. Nothing more to it," Azula said, with a carefree smile.

"He's so goofy," Shun smiled, shaking his head before focusing on the telescope again.

"What's so funny?" Yuuna asked, curious.

"Diarrhea," Azula said, with a wicked grin. Yuuna smirked.

"Oh. Good."

It didn't surprise Azula that their youngest would react as she did: if someone was entirely above being disgusted by gross subjects in their family, it was her. Yuuna giggled to herself, unaware of what the actual joke was, but delighted by whatever thoughts of diarrhea that she, somehow, found amusing.

"Okay… that was a good one," Sokka chuckled, shaking his head and sitting upright to hug Azula again. "Alright, well… maybe in the diarrhea world, we got together faster because we met later, in wholly different circumstances, and… we weren't enemies at all at first!"

"Huh. Damn. Now you actually make me wish I did have it," Azula said. Sokka laughed against her neck. "Oh, well. We'll never know. But… hey. We were discussing the notion that maybe there was a world where…"

"Nope. I won't allow it," Sokka smirked. Azula rolled her eyes.

"I'll give it another shot…"

"You will fail every time, love. I'm not going to lose against you on this one…"

"How about… a world where we were arranged to marry?"

"Say what?"

"Indeed. And because of how stubborn we are, we would have fought against the marriage, come hell or high water…"

"Uh. I see…" Sokka hummed, biting his lip. "And… say I ran away."

"Exactly!"

"And you did too."

"I… did?"

"Because you didn't know I'd run away as well, which means we bump into each other on our respective escapes. So… in this setting we don't even know what the other looked like. Which means that we ended up running from each other, but together!"

"Say what?"

"Hear me out! It'd be hilarious, because then we wouldn't realize that we were with the person we were supposed to marry, and we'd fall in love on our own terms, running from our families…! Only to end up discovering, in the end, that they'd arranged our marriage to each other and that the whole thing was a lot more agreeable than we thought at first."

"Y-you…" Azula scowled, glaring at him from the corner of her eyes. Sokka smirked giddily. "Okay, well…! How about a world where… where I got banished instead of Zuko?"

"What? You? That makes no sense…!"

"Makes enough sense if, say, my mother wasn't the way she is but… if she was much more cutthroat, you know? Maybe she… she killed my father too, and not just my grandfather. Maybe she went for both… and she was actually the big hazard to defeat. And because I knew what she did to my father, or I had strong suspicions about it, she banishes me…!"

"Well… that means you'd travel by the Water Tribe eventually," Sokka reasoned. Azula raised an eyebrow. "And you're smart, so… you wouldn't be traveling aimlessly. You'd look for allies. You'd go to the Water Tribe to find them and then we'd strike a deal to work together and overthrow your mom! There you go! We fall in love in the process, and…!"

"Goodness," Azula groaned: she couldn't stop smiling, despite herself, as Sokka beamed brightly.

"And you become Fire Lord Azula, and the world is bright and perfect after you take the throne!" he declared.

"Isn't that so smooth and easy?" Azula smiled at him. He snickered. "And you're the Fire Lady, of course."

"Of course, of course I… hey!"

"There's no reasoning with you," Azula smiled, shaking her head. "How about a world where I married someone else?"

"Pfft. Big mistake. You'd meet me and regret it in a heartbeat," Sokka smirked.

"And what if you married someone else?" Azula asked, amused.

"Same is also true, wouldn't be long before I filed for divorce and ran into the sunset with you. Easy as that," Sokka declared, smugly. Azula laughed, shaking her head.

"Alright, then… what about the most miserable possible option, then? A world… where you and I never met."

He raised his eyebrows. Azula waited eagerly for his reaction… and it didn't take long to arrive, in the form of a dismissive blown raspberry.

"Boo! That's a shitty world, is what it is. I don't want it. Bad idea, Azula. You should feel bad," he said. Azula chuckled. "Can you imagine how boring that would be? A world where we'd spend our lives knowing something's missing, but not knowing what it is, exactly?"

"A world where we'd always envy this version of ourselves, I suppose," Azula said, closing her eyes.

"Yikes. Nope. Awful. Stop giving me terrible nightmares. If I wake up in the middle of the night after a nightmare about this specific scenario, it's on you."

"Fine, fine. I'll bear the consequences," Azula chuckled. "Not that they'd be that bad, knowing you. You'd likely just… huh. Hmmm… well damn, I kind of want you to have that nightmare now, come to think of it."

"I can still wake you up for a random fuck in the middle of the night without nightmares involved, you know?" he whispered by her ear. Azula laughed and nodded, pressing her face to his neck.

"I'll appreciate it if you do. Sorry if that was a really awful scenario, though…"

"If? No 'ifs' about it, girl, that's the worst possible timeline," Sokka shook his head, certain. Azula smiled, leaning close to kiss his lips softly.

"Well, we have no idea if it ever happened… if any of those worlds we discussed are possible," she said. "So we can just… use the powers of our imagination to dismiss any such notions and cling to yours, alright? In any world, in any event…"

"Any version of us who chooses anything but this is a loser. That's my conviction," Sokka grinned. Azula chuckled, shaking her head.

"You're adorable. But… convincing, anyway," she said, glancing towards the kids. "We really did a good job. Took a broken world and set it on a new course… pretty much picked up the pieces of this mess to build our own. And because we did, we have our chaotic progeny… and a love people now write ridiculous tales about, elaborating on every little element of our relationship."

"We're just that much fun," Sokka smirked. Azula smiled and nodded.

"You know… I don't really care much, if those other worlds are any different. If those versions of you and me are smarter or dumber than we are," she said, turning in his arms. "I think the fact that every choice we made brought us here… it's something I can't help but treasure with everything I am. The lives we've built… I'm proud of everything that has gone into bringing us this far."

"And I know what it means for you to say that," Sokka smiled sadly, stroking her hair affectionately before kissing her lips softly. "It hasn't been the smoothest ride, but we did make it. We get to witness so many wonderful things now…"

"Indeed," Azula smiled, huddling against him. "Every day we spend together is another day where we can witness… well, I suppose I could call them the scenes of the peaceful world we built. And it's all because… we changed everything."

"We found the power to do so," Sokka nodded, hugging her tightly. "And who knows? Maybe we can transform more worlds besides our own… could be we can get Rei to put in some kind of magical power into her telescope, you know? And then we can reach into that world where we never met, and tell each other where to go and who to find…!"

"Okay, now you're talking nonsense…"

"We could, though! It'd be like reaching through the Spirit World, you know? C'mon, it's not that crazy…!"

Azula laughed, shaking her head as Sokka continued trying to convince her. His fingers nudged her, teasing her flanks, his lips peppering sneaky kisses over her cheek and neck…

She loved him so much, and that feeling only ever seemed to increase further as she processed just how much he loved her, right back. There was no denying that their love had changed their world… and as much as she had teased him, she wanted to believe that it would do so in any world, any universe where their paths crossed anew. They had endless potential, she remained certain of that… and it seemed to her that there was no better way to explore it than to do so by each other's side.

"I saw one! Rei, Rei, Hotaru, I saw one!"

Yuuna's voice startled her parents: the youngest girl was currently looking through the telescope when the first flashing meteor crossed the skies above.

"I wanna see! Me next, me next! Come on, Yuuna!" Shun exclaimed, eyes widening eagerly at the sight of the shooting stars.

"Well, I'll go after, then," Hotaru smiled, looking at Rei. "I can…?"

"Sure you can," Rei smiled. "All of you have one round each… then, the telescope's all mine!"

"Awww…"

"I have research to do, kids! It's my job…"

Azula chuckled upon hearing the siblings protest but submit to Rei's straightforward terms. Sokka nudged her gently, kissing her cheek softly anew.

"Think we're part of that group? Do we get a chance at the telescope too?"

"We'd better get over there if we want one, I fear," Azula smiled.

"We can always sneak a glance when she's taking notes, though…" Sokka snickered. Azula rolled her eyes and smiled, clasping his hand firmly.

"Come on. Let's wait for our turn," she said, pulling him to his feet.

Sokka clasped her wrist before she dragged him towards the telescope. He pulled her back towards himself, catching her in his arms. Azula raised her eyebrows… then, she smiled into the eager kiss he pressed against her lips. She didn't hesitate to return his affection, not even when she heard Hotaru's gasp, let alone Shun's groans of disgust: her hands cupped his cheeks as she pressed her brow to his.

"I'd choose you in every world, too. Any Azula who wouldn't… is certainly an Azula I'd pity," she said. Sokka smiled. "Her loss, really. There's no better husband…"

"No better wife, either," he said, kissing her softly again. "Not in this world, or any other…"

"True for you as well," Azula whispered against his lips. "We… we ought to make the most of those shooting stars. Don't people usually make wishes with those?"

"Some do," Sokka acknowledged.

"Might be the way to do it. That's how we'll fix the worlds where we never met," Azula smiled. Sokka smirked.

"Is that so? We're gonna use all the stars to wish to be together in every world possible?" he asked, snickering. "Okay, then… I really need a round at that telescope now."

Azula laughed, kissing him one last time before leading him the rest of the way to the telescope: Shun's disgusted faces faded quickly once his mother messed his hair, pulling him into a quick hug. Hotaru grinned at them, and a rather enthusiastic Sokka hoisted her with an embrace, startling her with his powerful grip. Yuuna giggled, pointing at the skies, and Rei sat behind her, stroking her messy hair affectionately, failing to tame it – for no one could ever succeed at doing so. A blanket of placid darkness spread across that blissful night, dotted with sparkles of infinite possibilities, all spread out before them… but out of so many lights, the peaceful world they'd built seemed to be the brightest one out of them all.

[isa-ah]

for people who have anxiety but live alone anyway: how do u deal with the panic? I live with 2 other people and still have bubble burst moments of random fear that only gets soothed by putting myself in someone else's eyeline. what do you do when the catastrophising starts???

[rotten-machinery]

"there will be debates at the function" they said. "you'll have such a great time at the function" they said. __ i hc that councils would definitely drag their iterator along to a fancy ceremony or function!! would the iterator like it? depends on the iterator really! RB sure as hell hates this :( i wonder that the ancients did at such an important ceremony that they needed to get all dressed up in fancy attire and so did their iterators. maybe they had very important governmental gatherings too? maybe it was some kind of debate? i hc that ancients value debates a lot, especially during court cases; where the dude who wins the debate will win the court case as well. and after the initial debate there'd be a whole ceremony for the winning team or individual! it'd be one of the only times iterators aren't doing any work so so much things to think about!!! but alas i need to actually write the lore, after all the lore won't write itself!

[toxictoxicities]

[detective-piplup]

fireknight, in almost all it’s iterations, is inherently doomed if not by their own actions then by knight’s mortality, in this essay I w-

[nrd-answers]

Lungs do all the fleshy bits mean you have to eat food now?

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[shuvva]

tfw you keep accidentally making your characters plural-coded through different forms of transhumanism, multiple timeline, and supernatural/possession shit

[awzominator]

"Uh Mikey- my Mikey- told m-me to give these to you, so uh, here... if you want..."

(Mikey is forcing him to do this as "exposure therapy")

Sending in a fellow spotted turtle! The fam didn’t wanna over whelm Leo w too many ppl at one. Mikey loves the colors they look super tasty!

go Leo!! He’s doin a great job!

@tmnt-iteration-compeition