Oops Lol - Tumblr Posts
I think the perfect episode for me now would be if felix had to step in as the black cat holder for whatever contrived reason and plagg’s like “since you’re so good at copying looks, you can just be this dude” and felix is like ok yeah. so he fights with ladybug and the whole time felix is thinking “what the actual fuck marinette you are all OVER this dude?? you are dating my brother/cousin???” and then is even more confused when she starts crying about how she misses chat
so after the fight felix tells adrien “idk I know you were a fan of ladybug but um it kinda seems like she sucks. she’s in love with chat and cat walker wtf” and adrien starts crying happy tears and felix is like these people are UNSTABLE and then returns home to play the most insane teenage hormone fueled game of chess with kagami
damn i just realized how freakin unhinged I am when sleep deprived
ok so important correction. apparently I've not been careful enough with my definitions. for example, square(n) := nn (to which I assigned a complexity of 1), if defined recursively (as it should be by the rules), is actually
square(n) := recₙ(0 -> 0, s(n)s(n))
with complexity 3 (two successors and a multiplication)
generally a function of type g(n) := f(n,n) should not have complexity c(f), but rather c(f)+2 (at least. depending on the base case)
there are two choices we can make:
1. reindex the recursion rule, so now it takes a base case (as before) and a definition of f(n) given n and f(p(n)), when n≠0. as an example, the square function would then be defined as (I've added an asterisk to denote that it's not the standard recursion):
square(n) := recₙ*(0 -> 0, nn)
which does have complexity 1. then my previous argument works, and the maximal complexity is even lower:
m+n := recₙ*(0 -> m, s(m+p(n))) -> 1 (succ)
mn := recₙ*(0 -> 0, mp(n)+m) -> 1 (addition)
m↑ⁱn := recᵢ*(0 -> nm, recₙ*(0 -> m, m↑ᵖ⁽ⁱ⁾(m↑ⁱp(n))) -> 1
(notice I changed the "0 -> s(0)" in the original definition into "0 -> m", which saves 1 complexity. this no longer describes the usual "m, then i arrows, then n", but that doesn't matter here)
↑↑n := recₙ*(0 -> 0, n↑ⁿn) -> 1
〈n,m〉 := recₙ*(0 -> m, ↑↑〈p(n),m〉) -> 1
〈n,ₐ m〉 := recₙ*(0 -> m, 〈〉,ₚ₍ₐ₎ 〈p(n),ₐ m〉) -> 1
〈〉,ₐ n := recₙ*(0 -> 0, 〈n,ₐ n〉) -> 1
and as 'a' grows, so does 〈〉,ₐ 2, which means the maximal complexity is c(〈〉,ₐ)+c(2) = 3
2. if we don't want to change the rules, we instead get that each 〈〉,ₐ has to be more complex than 〈〉,ₚ₍ₐ₎, because of a kind of inherent "friction" of our recursion - to make 〈〉,ₐ n = 〈n,ₐ n〉 we need to use "〈s(n),ₐ s(n)〉" in the definition (or at least "〈s(n),ₐ n〉" if we just want it to grow with a)
conclusion: the puzzle as I originally formulated it is still open X| - it might still be the case that arbitrarily large complexities arise.
anyone who's found my explanations at all coherent is welcome to share any ideas they have!
I finally caved and watched combo-class's new video, and now I'm obsessed with variations on the idea of integer complexity. my current puzzle is finding the "complexity" of natural numbers with these rules -
the allowed constructions are the following:
1. the constant 0
2. the successor operation (e.g 1 would be s(0))
3. recursion with natural variables, by specifying a base case f(a), and the value of f(n+1) given the values n and f(n). the notation I'll use is -
f(n) := recₙ(a → f(a), f(n+1))
where a and f(a) are previously constructed numbers, and "f(n+1)" is to be replaced by some term which may depend on n and f(n)
finally, the complexity of a number, c(n), is defined to be the least possible number of successor operations in its definition - including successors that appear as parts of recursive formulas. let's do a few examples.
c(0) = 0, since it's given as a constant, and thus doesn't require any use of the successor. every other number has complexity at least 1, since this is the only free constant.
1 = s(0), and so c(1) = 1
2 = s(1), and so c(2) = c(1)+1 = 2
we have c(3) = 3, which is boring, but then the fun begins. we can define a "square" function with a complexity of only 1, and then we'll have 4 = square(2), therefore c(4) = c(2)+1 = 3. we'll start by defining addition the usual way:
m+n := recₙ(0 → m, s(m+n))
[so to be clear, what the definition is saying is: "at n=0, m+n=m. and to compute m+s(n), take s(m+n), in which "m+n" is assumed to have already been computed by the recursive hypothesis]
the complexity of this definition is 1, because of the use of the successor in the second part of the definition. in short, we write c(m+n) = 1+c(m)+c(n), or simply c(m+n) = 1. the notation "m+n" should be thought of as just shorthand for the recursive formulation above - so (l+m)+n has complexity 2, because it uses addition twice.
now the usual definition of multiplication:
mn := recₙ(0 → 0, mn+m)
the definition uses addition, which has complexity 1, and so c(mn) = 1[+c(m)+c(n)].
now for my last trick:
square(n) := nn
and we get:
c(square(n)) = c(nn) = 1
c(4) = c(square(2)) = c(2)+1 = 3
as desired.
the usual definition of the predecessor function:
p(n) := recₙ(0 → 0, n)
[again, this should be read as "p(0)=0; p(s(n)) = n"]
has complexity 0, and so c(n) is order preserving - once we have a definition of n with complexity c(n), we automatically get a definition of p(n), p(p(n)),... all the way back, with the same complexity c(p(...p(n)...)) = c(n)
as I said, 0 is the largest (and only) number with complexity 0, 1 is largest with c = 1, then 2 with c = 2, and 4 with c = 3. I'm fairly confident that for c = 4 the largest number is 16 = square(4) [or raisetofour(2), which has the same complexity], then 256 = square(16) with c = 5. but after that a new strategy becomes viable, and the largest number of complexity 6 is at least 4↑↑↑↑4 (that's 4 arrows! absolutely gigantic number), using the function n(↑ⁿ)n which has complexity 3
Another Warriors OC!
Meet Fallenbranch, the original main character of my story, Distant Sun
She doesn't have much going for her aside from her wife and her family, so let’s look at all the art below the cut!
(Warning: old art)
Fallenbranch adores her wife, Greymoon. They grew up together and were besties before dating. They are actually also really close to Jadepaw’s mom as well!
Fallenbranch has A LOT of siblings. Like, a lot. Her mom just kept pumping them out
She has a littermate named Featherpaw (second cat), who was a medicine cat. Featherpaw was born with a missing leg, so she was forced into the role. She hated it and ran away. She now is called One-Foot and leads an aggressive rogue group who keeps testing the WillowClan border
Her next sibling is Amberfeather (third cat). Amber is aggressive and angry. She feels overlooked by her mom as the oldest of the litter of five and hates the fact that her mom got remarried. To another she-cat too! So Amber is going through it AND she's homophobic. Yay!
Next is Snakescratch (fourth cat). He's kind of a goof and just does what he wants. He gets along best with his brother as the only boys in a family of girls. He also is currently kind of sort of courting another cat called Lilyfur, but shhh.
Fluffypelt (fifth cat) is next. He's loud and goofy and loves to make trouble. He's also kind of a bully, but mostly playful. He likes to run around and hunt in the river with his brother and his GIRLFRIEND that he managed to pull, Gemspot.
Spotleaf (sixth cat) is the next oldest. She's considered the pretty one and a lot of cats have a crush on her. She doesn't pay attention to them, though, because her bestie is her younger sister. She likes to hang with her baby sister and make eyes at the toms on the other side of the border.
And finally there's Larkwing (seventh cat). Lark is quiet and keeps to herself. She doesn't make friends, aside from her sister, she isn't interested in romance and she's terrified of talking to the leader and deputy.
Fallenbranch also has three step-sisters thanks to her new step-mom, but they're nor pictured.
And now there's her kits!
Fallenbranch was the bio mom of she and her wife's first litter, Featherkit and Mistykit. But the kits were stillborn and it devastated her. (BTW, they asked a friend of theirs to be the donor dad)
About a moon later, Greymoon found some kits on patrol and they instantly adopted them. The kits are Bluekit (blue), Whitekit (white w/ cyan eyes), Flamekit (ginger w/ green eyes) and Knotkit (ginger w/ purple eyes)
And that's all for Fallenbranch! You can read her complete story on my Wattpad, Moonsong1234. Her story is Distant Sun: Thunderstorm
Abode of a modern vamp
abbyrchrds:
Abby snorted. “I think my grandma wishes I was annoying. You know how there are those kids that talk way too much about everything and just get into everything? I was the exact opposite of that. I think she thought I was mute from the time I was ten until I was twelve.” Of course, she might has well have been mute the first couple of years she spent without her father. There was no one else worth talking to. “Exactly. Its left open to interpretation. Unless an author specifically stated ‘this is what this means’ or ‘this is what I think the Green Light represents’ we really have no way of knowing. With history, the only things left up to chance are the things that weren’t written down. And even still, there’s always skewed interpretation depending on who wrote it. History was written by the winners, as they say.” She screwed her face up. “I understand that some people don’t want others to think that they feel the way that the characters and the writer do about certain themes, but that’s the whole point. Every novel that’s been banned is almost a cautionary tale about behavior and morality.”
Although Aiden didn’t know the circumstances in Abby’s life, he could definitely relate. “Yeah, I’ve always been a quiet child too. I honestly didn’t really have many friends either. At least you got out of your mute stage pretty early on. I was a mute until college. I realized that if I was going to become a teacher, I had to actually talk to other people and be able to have that extrovert persona even though I am definitely not an extrovert,” he continued on. “Yeah, that is true. I really want to get more into history. I might ask you to teach me a few things. I’m curious about how the other side of history was like, for those who didn’t get a chance to explain their point of view, but I also know it’s hard because obviously people didn’t have technology or things to record their day to day life.” He understood where she was coming from. “Yeah, I get you. I wish there was something I could do about it, but it’s either follow the rules or get fired and I don’t want to be without a house.”
Alright, I was going to wait to post this until tomorrow but honestly I’m just too excited I can’t wait. Finally, after working on and off this project for two years, my Madney video edit is done.
Here it is!
Hopefully everyone likes it as much as I do. I get the scene overlays could look confusing to some eyes, but personally it was one of the things I loved about making it.
I tried my best with the editing, then came to the point where I had to just say it was done, or else like any other work of art you’ll always find something to fix.
Anyways, hope anyone who sees this enjoys! I absolutely just had to do this for Maddie and Chimney, because look how happy and in love they are! 😭❤️
Credits
Song:
Better Place By Rachel Platten
Editing Overlays:
No Copyright Motion Graphics
Josh Relax
The Epic Slog
There once was a wee lad who thought virtual humans just didn’t look right without cat ears, so he learned to mod his game.
He grabbed a handful of cool things online, and haphazardly cast them into the shallow basin the tutorials told him was the answer to his pain.
Not first did he consider to organize. No. He rubbed his hands together anxiously and clicked on the game.
And he hoped, and he prayed.
And he clicked “New Game.”
And there she was. The first modded sim. He cloaked her in a wrap of hyperrealistic flesh and filled her skull’s sockets with the gelatinous orbs that actually sparkled in the warm light of a cheese-born stove fire.
And his heart soared at her existence.
But his heart was also dripping as it flew, slowly. And why does a heart drip slowly? That is because a heart penetrated by a blade will not fully rupture, but only bleed with each passing beat. Little at a time, leaking out when not clamped shut by the pressure of the muscles tensing as they propelled blood.
And penetrated his heart had been. Not by dagger or spear, but by the claws of a little writhing worm.
And he required more.
And he went out hunting for more.
Day and night, the ritual repeated. More, more. More modifications. More files. More customized content for this digital world.
Add to the pile. Add to the pile!
The shallow basin dug deeper, and deeper. And across years it became a churning sea of files. Packages like eels, slithering around in the dark. Folders like grand wales, with bellies full of secrets.
And finally, the lad had to look upon what he had made. A massive monument to his lack of caution. For what he had made he had no longer tamed. …because due to poor environmental management, everything was actually completely and utterly dead.
And THAT is why you organize your mod folder! Don’t let it accumulate into forbidden primordial soup over several years.
Because untangling the forbidden primordial soup is very long and very, very boring!
(On a very unrelated note, what is your favorite method of organizing your mod folder?)
