I was dicking around in polar coordinates last night and I found something... extensible.
r = sqrt(sec(2θ)), an ordinary hyperbola. One of the five conic sections. In Cartesian coordinates x^2 = y^2 + 1.
r = sqrt(sec(3θ)), a triperbola :)
And now here's r = sqrt(sec(aθ)) for some other values of a:
a = [1/2 2/7 6/1 5/2 3/5 5/9]
5x5 Diamond rule, iterates 1-32
Iterates 40, 48, 56
Iterate 64
Iterate 128
This is a 2D cellular automaton generating a 3D fractal layer by layer. I coded it in Microsoft Excel - each pixel is 1 cell.
See more MSExcel fractals
michael sheen: they're best buddies!
david tennant: they're married
parents got a new cat they named lord montague and this morning i heard my dad in the other room say "i would have to advise against that decision, my lord" followed by a crashing sound
Quote from Ncuti Gatwa's recent interview in Rolling Stone UK:
“My Doctor is emotionally vulnerable. He hides it with humour, but he’s lonely,” says Gatwa of his forthcoming reinvention of the ever-changing Doctor.
I'm gonna hold out the teensiest-tiniest bit of hope that they'll make some sort of reference to the Doctor losing Yaz as a reason for this loneliness.
if i was a scientist it would be so tempting to form conclusions based on my gut feeling and then work backwards to support them... it would feel sooo good
what the fuck is morbius even about
A/C unit failed. Repair scheduled for Tuesday.
Questions:
Will it have an appreciable effect?
Will my cat die?
I spit out my drink lmao
i…. i love it… λ 🥲
is this a valid notation? i wish it were, ill definitely be using it
What’s the worst thing about limits?
• Is it always having to amplify by the conjugate to eliminate indeterminate forms? NO.
• Is it having to learn some limits by heart (especially for trig functions)? NO.
• Is it having to sometimes use L’Hôpital-Bernoulli’s rule over and over again? NO.
• Is it having to just write “lim” before each line? YES. FUCKING YES. WHY OH GOD WHY I HATE THE NOTATION.
The most infuriating part of it is that it’s just a notation and it could so easily be changed, BUT NO, we’re stuck with this shit.