Top #math dweets

function u(t) {

c.width=1920 // clear the canvas
for(i=0;i<9;i++)
x.fillRect(400+i*100+S(t)*300,400,50,200) // draw 50x200 rects

} // 122/140

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    u(t) is called 60 times per second.
    t: Elapsed time in seconds.
    S: Shorthand for Math.sin.
    C: Shorthand for Math.cos.
    T: Shorthand for Math.tan.
    R: Function that generates rgba-strings, usage ex.: R(255, 255, 255, 0.5)
    c: A 1920x1080 canvas.
    x: A 2D context for that canvas.

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rodrigo.siqueira

function u(t) {

for(c.width=w=i=2e3;i--;)
X=S(i*i),Y=S(i),ℵ=C(Math.atan2(X,Y)-t)*Math.hypot(X,Y),
K=w/2,x.fillRect(w*ℵ/(Z=4+C(t)+X*X-Y*Y)+K,w+K*(ℵ-6)/Z,7,8)

Jun 26 2019 7:01 PM UTC

}// 140/140

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The Hyperbolic Paraboloid (z=x²-y²). The S(i*i) and S(i) are random number generators between -1 and +1. The atan2 and hypot are used to calculate 3d object rotation (Euler equations could also be used, as seen on /d/12086). Thanks to u/cantelope for the Tiny 3D Engine Tutorials: https://cantelope.org/tiny_3D/ and https://cantelope.org/3D/ #math #hypot #D3 #hyperbolic #surface

u/cantelope

:D
u/rodrigo.siqueira

There is an interesting fact that the Pringles potato chips are a truncated hyperbolic paraboloid. The strength of the shape helps to prevent them from breaking while stacked. The curvature of the shape improves resistance to tension and compression forces. Remember this next time you eat a hyperbolic paraboloid.

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taupelink

function u(t) {

t||(a=[[]],r=k=0);x.font=`3em"`
a[r][k]=k%r?a[r-1][k-1]+a[r-1][k]:1
r<16&&x.fillText(a[r][k],960-60*r+120*k,60*r+60)
++k>r&&(a[++r]=[],k=0)

Jun 18 2019 1:17 AM UTC

}// 139/140

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Pascal's Triangle #math #recursive #recursion

u/katkip

Awesome!
u/donbright

#numbertheory

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taupelink

function u(t) {

c.width|=0;f=X=>{for(i=2;i*i<=X;i++)if(X%i==0)return i+'*'+f(X/i);return X};k=frame/6|0;x.font='5em"';x.fillText(k+'='+f(k),0,540)

Jun 28 2019 1:01 AM UTC

}// 130/140

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factorization into #prime products. #math

u/taupelink

simple #recursion #recursive
u/Xen

very clever
u/katkip

wow
u/donbright

#numbertheory

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donbright

function u(t) {

w=(c.width=999)/2
for(i=-t;i<t;i+=.1)for(j=-t;j<t;j+=.1){
B=1+i*i+j*j
X=S(t)*i/B
Y=j/B
Z=(B-2)/B/2
x.fillRect(w+(X+Y+Z)*w,w+(Y-Z-X)*w,2,2)}

Nov 8 2021 6:45 AM UTC

}// 139/140

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stereographic projection of the plane (in this case, a 0.1 grid to infinity) onto the sphere. aka Moebius Transformation. see also https://hyrodium.tumblr.com/post/13708635481… and https://en.wikipedia.org/wiki/Stereographic_…

u/donbright

#math #stereographic

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taupelink

function u(t) {

t||(x.font=`30em"`,x.fillText("1+",40,620),x.fillText("1",1050,400),x.fillRect(570,b=450,1200,24))
x.drawImage(c,0,0,2e3,1e3,650,b,1100,550)

Jul 24 2019 3:24 AM UTC

}// 140/140

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Continued fraction for the golden ratio, 1+sqrt(5)/2. #math #numbertheory https://en.wikipedia.org/wiki/Golden_ratio

u/taupelink

hmm, doesn't seem to work on iOS Safari
u/taupelink

to get it to work on iOS/MacOS, replace 2e3 with 1920 and 1100 with 1e3.
u/taupelink

* maybe it's a safari issue rather than an OS issue. * on my iOS device, that adjustment seems to work temporarily, but then the browser has to reload the screen. ¯\_(ツ)_/¯

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rodrigo.siqueira

remix of d/14530 by u/rodrigo.siqueira

function u(t) {

c.width|=0;for(X=-3;X<3;X+=.1){for(Y=-3;Y<3;Y+=.1){
Q=(P=-t%27+X*X+Y*Y)*S(3/P**1)
Dx=-Y+X*Q
Dy=X+Y*Q
x.fillRect(960+Dx*40,550+Dy*40,5,5)}}

Jun 11 2019 1:44 AM UTC

}// 138/140

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Differential Equation Slope Field - My second attempt to model this system of nonlinear differential equations: https://imgur.com/gallery/jpAn7tX

u/aleamb

love it!
u/aleamb

#math #system #nonlinear #de #modeling
u/artfarnaa

Hi Rodrigo. Love your work. Can you give a small summary of yourself, or link? Very impressive body of work.
u/rodrigo.siqueira

@artfarnaa, I work with artificial intelligence and natural language processing, developing new algorithms to improve customer interaction with companies and services. I get inspiration from theoretical neuroscience to create AI tools, chatbot frameworks and search engines. I also create fractals, here is my gallery: https://www.fractarte.com.br/galeria2/galeri… Here, I dive into the depth of chaos equations to find unexplored patterns, geometries and emergent properties. My Twitter is https://twitter.com/rsiqueira

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rodrigo.siqueira

function u(t) {

c.width|=σ=(X)=>{return 1/(1+Math.pow(Math.E,-X))}
for(i=-500;i<500;i++)
x.fillRect(i+950,820-σ(i/30*C(t*2)+Math.random()*2)*400,5,5)

Mar 4 2019 8:41 PM UTC

}// 133/140

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Sigmoid activation function used in Artificial Neural Networks. Animation shows changes of neural weights plus a random bias.

u/pavel

I often use sigmoids for movement. The ease-out / ease-in looks great. I used 1/(1+1e9**(.5-t%1)) in d/11146 for the 'jumps'.
u/katkip

#sigmoid #math
u/katkip

also #ai
u/rodrigo.siqueira

also #neural

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iverjo

remix of d/257 by u/iverjo

function u(t) {

x.fillStyle=R(249,183,227,.01);X=S(t);x.lineTo(960+512*X*X*X,480-32*(13*C(t)-5*C(2*t)-2*C(3*t)-C(4*t)));x.fill()

Dec 31 2016 3:17 PM UTC

}// 112/140

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u/BriSeven

nice maths
u/iverjo

Found the mathematic formula online somewhere ^^
u/joeytwiddle

Wait, there's a mathematical formula for love? :-O
u/iverjo

#heart
u/katkip

<3 #math

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marc8

function u(t) {

c.width|=0
with(x)for(j=3;j;j--){beginPath()
for(i=-4;i<9-C(t)*10;i+=.02)arc(a=i*99,q=-150+j*350,j*50,i-.01,i)
arc(a,q,99,i,i+6)
stroke()}

Mar 31 2019 5:06 PM UTC

}// 138/140

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Curtate, common and prolate throcoid

u/joeytwiddle

#math

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katkip

remix of d/12347 by u/katkip

function u(t) {

c.width*=1;t||(a=b=5);for(i=999;i--;)a+=S(b+C(a+i/9999)),b+=C(a+C(b+t*i)),x.fillRect(a*590-1800,b*290-300,9,9)

Feb 14 2019 6:13 PM UTC

}// 110/140

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Chaotic #attractor in motion #math (quarc in string theory)

dwitter.net | #math