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.

anonymous asked:

Prompt: Regina does her best to erase Marilena from Robin's mind sexytimes.

Shaking off the cobwebs here guys - i’m not keen on this at all, but I hope you enjoy it all the same, Nonnie. Thank you for the prompt!

Regina’s nervous.

Insides twisting in tight knots, stomach fluttering as she sits at the foot of the bed and watches as Robin rolls her stockings down her leg.

Slow, sexy, he’s holding her gaze and skimming his hand over her bare skin, those dimples deepening just slightly, and she thinks he might well be nervous too.

She doesn’t want him to be. He shouldn’t be. Hell, neither should she, and yet her heart is hammering against her ribs and her palms are getting sweaty for all the wrong reasons.  

It’s their first time since…

“I’ve missed you,” he tells her, pressing gentle kisses to the inside of her thigh before planting his hands either side of her hips and catching her lips with his own.

She breathes out a laugh, nods, wants to tell him she’s missed him like this too. Missed his hands, his mouth, his body, but the words seem to be stuck in her throat.

The last woman he was with was…

But she can’t think about that. Won’t let herself wonder if he did this with her, if he gripped her thighs as she wrapped her legs around his waist. She can’t think about how his tongue has probably trailed every inch of her skin just like it has Regina’s.

Robin has kissed her, held her, made love to her and just the thought drives Regina crazy.    

So she kisses him. Hard, hurried, hungry. She kisses him as desperately as he did her, back when it was their first time, and how long ago that feels now. Like a lifetime.

“Regina,” he murmurs as she pulls him closer, flips them around so he is sitting and she is straddling, attempts to drive him (drive herself) to distraction by grinding against him and get the images out of her mind that she’s conjuring of Robin fucking Zelena - Marian, he thought it was Marian - “Regina,” he murmurs again.

She ignores him.

He relents after a second or two, finally meets the hunger in her kiss and weaves his hands through her hair, and yes… this is better. She rocks against his hips, moans into his mouth because she can feel him hardening beneath her, grips the edge of his tee to pull it over his head - drags her nails down his chest until her fingers hit his belt.

It’s a fumble after that. He manages to stop her hands from unbuckling his pants just long enough to rid her of her bra, tries to flip them back so he’s on top, but no, she can’t have that. Won’t have that because what if he does with Regina what he did with her sister?

She needs to lead this. She needs this not to mean as much as it does, wants one meaningless fuck if only to get rid of the butterflies that are still plaguing her mind and her heart.

“Regina,” he says again, as she drags her tongue down his throat and nips at his skin. his hands come up to where she holds his face, softly stroke her arms until his fingers find her wrists - and then he’s not so soft anymore.



They’re both breathless, chests heaving as she pulls back to find his eyes, and she’s pretty sure her face is wearing a scowl similar to the confused one he wears too.

“Talk to me, what’s the matter?”

“Why would there be anything the matter?” She scoffs. “I’m trying to have sex with you, I’m pretty sure there’s not anything wrong with that.”

Robin raises his brow, doesn’t hide the skepticism in his expression, and Regina scoffs again. Shakes her head and drops her hands into his lap, avoids his eyes because there’s suddenly a lump in the base of her throat.

If she looks into those baby blues, tears will start that will not stop.

They’re silent for a moment, he’s watching her, waiting for her, and she knows he’ll never push her to talk to him - thinks it’s one of the reasons she does so so easily. And it’s only when his hands find her neck, when his thumbs stroke the edge of her jaw so gently it almost tickles does she find the strength to swallow the pain in her throat and find his eyes.

“The last time you did this… you were with her.”

“I know,” he says gravely, quietly.

“It’s just… it’s messing with my head,” she admits. “I keep wondering if you’ve done this with her, if you’ve said things to her like you’ve said them to me, and you’ve…”

“I’ve what?”

“You’ve… been with her… more.”

“Regina,” he breathes out softly, eyes flicking down to her mouth as she licks her lips and draws in a shuddered breath. “I love you,” he tells her firmly, and she mumbles out that she knows, that she loves him too. “I don’t care what I did or didn’t do with her. I’m not with her. I don’t want to be. I’m with you.”

“But doesn’t it drive you crazy?” She finally asks - has wanted to ask since they found their way back to each other. “That you’ve been that intimate with someone who was just… using you?”

“If I let it, then yes. I suppose it would. But I can’t change what’s happened. I can either choose to wallow and feel sorry for myself, or I can let it go and move on. With you. If that’s still what you want, too.”

A small smile tugs at the corner’s of her mouth, and she nods, tells him, “Very much.”

“Why don’t we just… stop. See how things go. Stop putting pressure on ourselves for something that shouldn’t be stressful.”

She snorts out a laugh. “Robin Hood, are you saying sex with me is stressful?”

“I certainly am not,” he chuckles, leans in to touch their brows and rub their noses together. “But it’s not as fun if I know you’re heart isn’t quite in it yet.”

“It’s not that it’s not, I just…”

“You just need a little time, I know. I understand,” he tells her softly.

“I wanted to make you forget… about her,” Regina admits, looking down between them as she fiddles with her hands.

“Regina… I can assure you with all my heart, when I’m here with you, like this… that woman is the last thing on my mind.”

Jupiter Jones: Intuitive Detective

salamanderinspace posted the following tags in response to my gif set of Balem lashing out after Jupiter provokes him by suggesting why he killed his mother:

it just seems so unlikely to me that she could have deduced Balem’s guilt based on the tiny amount of information she is given unless some part of her really does remember subconsciously in intuition and the ghost of dreams the sticky silver cobwebs in the corners of the mind the diaphanous graves of spiders and their glittering dark eyesis this familliar mother

I think in order to understand why Jupiter reaches the conclusion that she does, it’s important to set out the context. So, the exchange runs like this:

(Balem has just explained space capitalism to Jupiter.)

Jupiter: If that’s what your mother taught you, then I can see why you hated her.

Balem: I loved my mother.

Jupiter: And yet you’re trying to kill me?

Balem: My mother made me understand that every human society is a pyramid, and that some loves will always matter more than others. It’s better to accept this than to pretend it isn't true.

Jupiter: Is that why you killed her?

Now, this exchange is important because it’s another example of Jupiter attempting to understand and figure things out; she uses her intuition and empathy to decipher the implications behind what she’s being told. 

Quite naturally, she assumes that Balem hated his mother - after all, to the best of her knowledge he’s been trying to kill her (the recurrence of his mother) relentlessly since discovering her existence. Unlike his siblings, no aspect of his behaviour suggests sentiment. Therefore, she’s surprised to discover that he claims to have loved his mother; it seems odd and illogical to Jupiter given his prior actions. In his next line, however, Balem gives Jupiter a lead by essentially explaining what she mustn’t do; she must not pretend that the hierarchy he advocates does not exist. From his speeches, Jupiter realises that Balem is very ideologically driven and is absolute in his beliefs; therefore, she appreciates that to diverge from those beliefs is dangerous. 

However, that is not to discredit your own thoughts. The film strongly hints at Jupiter having experiences and feelings in common with Seraphi; it’s not an accident that “I hate my life” echoes across both characters. A spiritual dimension is implied and I personally perceive Jupiter as an improved and purer version of Seraphi; whereas Seraphi could only wish for an end to harvesting, Jupiter is the one who actually sees the system begin to crumble. The implication for me is that she is poised to fulfil the destiny that Seraphi, despite her millennial existence, could not.


8/13/14                Spider of the Day

Theridiidae (Cobweb Spiders) - Neospintharus trigonum   Adult male- 3mm

3 species in BugGuide’s range (North America north of Mexico). All three species were previously genus Argyrodes.  All three species roughly 4mm or less in body size.  Males are much smaller than females.

Males have projections or modifications on their clypeus and/or eye region, females typically do not.

These small cobweb spiders can sometimes be kleptoparasitic and found in the webs of larger species like Nephila clavipes, Gasteracantha, and Argiope (to name a few).  They are so small they often go unnoticed by the web owner, thus allowing them to sneak away with the small insects that get caught in the web.  Sometimes more than one, or many, of these can be found in a single host web.  A variety of species can share the host web, as well.

Be careful in your ID, they also look a lot like these: Argyrodes/Faiditus/Neospintharus/Rhomphaea -

anonymous asked:

Isn't weird that Marilyn made her will at that time. I think she knew she would died young....

I guess, but due to her fame I don’t think it’s that surprising, she was planning on changing it though. Yeah, I think that’s true - to an extent. She did have lots of optimism for life though, as you can see by these quotes, she had a lot of mixed feelings during her lifetime.

“I’m thirty six years old, I’m just getting started!”

“When you’re young and healthy you can plan on Monday to commit suicide, and by Wednesday you’re laughing again.”

“Life —
I am of both of your directions
Somehow remaining hanging downward
the most
but strong as a cobweb in the
wind — I exist more with the cold glistening frost.
But my beaded rays have the colors I’ve
seen in a paintings — ah life they
have cheated you.”  

“Oh damn I wish that I were
dead — absolutely nonexistent —
gone away from here — from
everywhere but how would I do it
There is always bridges — the Brooklyn
bridge — no not the Brooklyn Bridge
because But I love that bridge (everything is beautiful from there and the air is so clean) walking it seems
peaceful there even with all those
cars going crazy underneath. So
it would have to be some other bridge
an ugly one and with no view — except
I particularly like in particular all bridges — there’s some-
thing about them and besides these I’ve
never seen an ugly bridge.”

last night i watched a moth die
before my eyes. it struggled against
the imminent stickiness of cobwebs, stopping
only to rest, and then flapping its wings violently
once more, one more time, just one more time.
then, the moth stopped struggling.
then, it stopped breathing.

sometimes, i feel as if i am a moth,
trapped in a sticky web of demons that are
trying to hold me down. i flap my wings desperately,
stopping only to rest. i try to escape,
but i cannot.

soon enough, i too will die. i fear i will
fade as quick as a final breath,
passing gently on.

—  the truth about death and the truth about me (m.m.)
Your heart is a house so full of cobwebs, I can’t tell if the lights are on, or if anyone is home. It’s time to clean house. Change the locks to your front door, so you can stop hoping that they kept your key and are coming back. Throw out their old sweaters and stop buying their favorite food. This is going to hurt and you are going to suffer for it, but like battling cancer, this is a fight you will win, because you have so much to live for, without them holding you down. Climb a mountain and see how the landscape is beautiful, scars and all. Beautiful. You are brighter than the farthest stars, so shine knowing that there are no words for describing your worth. It is just common knowledge.
Your heart is a house so full of cobwebs, I can’t tell if the lights are on, or if anyone is home. It’s time to clean house. Change the locks to your front door, so you can stop hoping that they kept your key and are coming back. Throw out their old sweaters and stop buying their favorite food. This is going to hurt and you are going to suffer for it, but like battling cancer, this is a fight you will win, because you have so much to live for, without them holding you down. Climb a mountain and see how the landscape is beautiful, scars and all. Beautiful. You are brighter than the farthest stars, so shine knowing that there are no words for describing your worth. It is just common knowledge.

Conversations in my head with myself be like

[p1: What’s the difference between a spiderweb and a cobweb? 
p2: I think it’s the frabric 
p1: I know! They both the same animal! ] 

There was a lot to love about Hot Topic in 2002. The cobweb tights, leather cuffs, neon mesh sleeves, so many shades of black nail polish that you never knew existed ’til you saw a cute goth girl wearing five different kinds on each hand. The mall goths and weekend punks, like me, who expressed their rebellious hearts through Rage Against The Machine flags and black band tees. Who knew being different was important but weren’t quite ready to go it alone. Then there were the broody, slightly intimidating sales staff, whose total indifference to their jobs and customers somehow made them the most attractive and desirable people in the world.

uhhh i almost cried…awkward