Is this what my brain looks like?

Jules | adult | all pronouns | aroace | multi-fandom blog

[amphibianshaped]

apparatus

[frcz78]

Ok, it's finally done. Home is a place, home is a person.

This story is my first major piece after several years of art block, and I'm so glad I could finally get back to drawing.

Huge thanks to my dear friend @chancekey for the support.

[thepiratefish]

Haven't seen a 2026 version so I made it myself

[night-at-the-musian]

IT’S THAT TIME OF YEAR AGAIN, FOLKS!

[thebreakfastgenie]

Quand il faut expliquer la pâtisserie à un Américain: imaginez un hamburger

[paperpatchnotes]

Ok someone has to take this away from me before I drive myself insane attmepting to idk art better 🙈

Idk how long I'll be on this murderbot train but these ARE my new favorite books to ever.

[theoneofwhomisblue]

Mouse MD

[owlservice]

He needs mouse bites to live

[pul5e-m3tal]

mouth bites

[annabelle--cane]

so she's legally basically its mother and she was game for that kind of dynamic at first but it was violently like Absolutely Not and now neither of them are into it but on paper that's still what they have to be to each other. thiago seemed to almost think it was her toxic/abusive gold digging sugar baby or something. amena calls it her third mom. it most commonly thinks of her as its client and itself as her security guard. she is the only one it will let touch it in any kind of unnecessary and emotionally intimate way. she bought it. it manipulated her into getting ptsd treatment. its situationship desperately wants her approval and to show her that it's an upstanding young research transport who can be entrusted with the safety of her dear [redacted]. they hold hands to avoid looking suspicious. what are they.

[be-kind-recklessly]

I got such a great prompt for @mutualrapport but I've been so busy I haven't been able to work on it :(

So many ideas in my brain, I can't wait for next week when most of my deadlines are over

[girlnephew]

[ryanthedemiguy]

I don't think this is possible????

[physicallyimprobable]

Hello Ryan I am here to help. So the first step is pretty easy: Three cheeseburgers are worth 18, so each one is worth 6. If these are dollars, that's a steal!

From the second equation we get that cheeseburger plus fries-squared is five. Subtracting cheeseburger, which is six, from both sides, we get that fries-squared is negative-one. Math fans will know that there are two solutions to this; either fries are the "imaginary unit" 𝒾 or they are its negative, -𝒾. We'll do the rest of the problem with 𝒾, keeping in mind that at the end we should also take the complex conjugates as solutions.

Finally, we have that cup to the power of fries, minus cup, equals three. Replacing fries with 𝒾, and moving a cup to the other side, we get that cup-to-the-𝒾 is equal to cup-plus-three.

Now, the weird part about this is the cup-to-the-i. The problem with this is that complex exponentiation is technically not a thing. That is to say, there is no one function which is mathematically equal to "input-to-the-power-of-𝒾". In fact, there are infinitely many such functions.

Fortunately, due to reasons that take about six pages to explain (trust me I've done it), there is one particular function that many people have agreed is "the most reasonable one". This is not a mathematical notion, but a human preference. Seeing as this question was presumably written by a human, I am comfortable with using this function.

So, what function is this? Well, given a complex number r∠θ written in polar form (if you don't know what that means don't worry), where -π < θ ≤ π, then (r∠θ)^𝒾 = e^(-θ)∠ln(r).

Applying this to our problem a value r∠θ will be a possible solution for cup if e^(-θ)∠ln(r) = r∠θ + 3. Splitting this into real and imaginary parts, we get two equations: e^(-θ) cos(ln(r)) = r cos(θ) + 3 and e^(-θ) sin(ln(r)) = r sin(θ). We can graph these equations on Desmos:

The possible values of cup are the intersections between the red, green, and purple. There are infinitely many of these which have an angle of around -π/3, and there are two weirdos: One which is a complex number very close to -2.98, and one which is somewhere around -25. The possible values for cup are all of these infinitely many solutions, and also all of their complex conjugates.

[sharkgirldick]

They were right, 99% of people can't solve it.

[peelerofpotatoes]

i've actually been working on some formulae to give all possible solutions to complex exponentiation problems recently, so here's my take on this:

let the value of the glass = z, for z ∈ ℂ:

z^(±i) = 3+z

let z = r·e^(iθ) for r,θ ∈ ℝ, -π < θ ≤ π

∴ z = r·e^i(θ+2πn) for all n ∈ ℤ

∴ (r·e^i(θ+2πn))^(±i) = 3+r·e^i(θ+2πn)

distribute powers (apologies for the use of ∓):

r^(±i)·e^(∓(θ+2πn)) = 3+r·e^i(θ+2πn)

convert to the same base:

e^i(±ln(r))·e^(∓(θ+2πn)) = 3+r·e^i(θ+2πn)

split into real and imaginary components:

re: cos(±ln(r))·e^(∓(θ+2πn)) = 3+r·cos(θ)

im: sin(±ln(r))·e^(∓(θ+2πn)) = r·sin(θ)

in effect, all this changes is the restriction on the domain of theta to be between -pi and pi, so you can just ignore that constraint.

[inthefallofasparrow]

[lilkakow]

Soviet swimmer Maria Havrish congratulates her rival Elena Kovalenko, who defeated her in the breaststroke competition at the Spartakiad of the Peoples of the USSR in Moscow, 1956 (photo by Lisa Larsen)

[lilkakow]

[fabrickind]

oobh i got plany off bobbin thread

[boomer-mythology-destroyer]

[jadeharleyinc]

hey sorry. can you stand a little further back and we try again

[aro-narcissus]

Starting a collection

[charlesoberonn]

♫ It's fun to stay at the ♫

[be-kind-recklessly]

The first 1-2 pages of All Systems Red, inspired by @nothingiswrongwithyourarmrests's post about how tmbd should have been adapted into a graphic novel.

Version where every tab is readable below the cut, because I spent way too much time on those things for no one to be able to see them

[jomatinsims]

india  foxtrot   yankee  oscar  uniform   charlie  alpha  november   romeo  echo  alpha  delta   tango  hotel  india  sierra   yankee  oscar  uniform    hotel  echo  lima lima  oscar   juliett  oscar  november. alpha  papa  oscar  lima  oscar  golf  india  echo  sierra   foxtrot  oscar  romeo   tango  hotel  echo   delta  echo  charlie  echo  papa  tango  india  oscar  november   bravo  uniform  tango  i  whiskey  alpha  november  tango  echo  delta   tango  oscar   mike  alpha  kilo  echo   sierra  uniform  romeo  echo   yankee  oscar  uniform   sierra  tango  alpha  romeo  tango  echo  delta   romeo  echo  alpha  delta  india  november  golf ,  sierra  oscar  i  tango  hotel  oscar  uniform  golf  hotel  tango   india  tango   bravo  echo  sierra  tango   november  oscar  tango tango  oscar   alpha  november november  oscar  uniform  november  charlie  echo   mike  yankee  sierra

[targetedknowledge]

[still-asunbeam]

actually i don't want to talk about my feelings i'd rather engage in hand to hand combat