New #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) {

f=j=>x.fillRect(448+(j&255)*4,(j>>8)*4,4,4)
t||(p=Array(N=4**8).fill(n=1),f(0),f(1))
if(p[++n])for(i=1;(q=++i*n)<N;)p[q]=0,f(q),M=n;throw M

Jun 19 2019 2:39 AM UTC

}// 139/140

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Sieve of Eratosthenes. Throws primes less than 65536. Row Y Column X stays unfilled if 256*Y+X is prime. #math

u/Xen

clever
u/donbright

#primes #numbertheory
u/taupelink

maybe #sieve is a worthwhile hashtag too!

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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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katkip

function u(t) {

t||(z=0);for(i=999;i--;){x=Math.random()+1;if((r=(x**2)/(x**x))>z)z=r}
throw z

Jun 17 2019 6:54 AM UTC

}// 78/140

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Approximating maxima of (x^2)/(x^x)

u/katkip

#math

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taupelink

function u(t) {

f=(a,b,n)=>b?(a>=b?
(x.fillStyle=R(25*n),
x.fillRect(X,Y,b,b),X+=d?0:b,Y+=d?b:0,f(a-b,b,n+1))
:(d=!d,f(b,a,n+1))
):0
d=X=Y=0;f(1920,1080,0)

Jun 13 2019 1:58 AM UTC

}// 139/140

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GCD(1920,1080)=120, the size of the smallest reddest square. Demonstration of Euclidean algorithm by subtraction, cf. https://en.wikipedia.org/wiki/Euclidean_algo… #math

u/taupelink

#recursive #recursion
u/taupelink

(120 is the side length, not the size)
u/donbright

#numbertheory
u/donbright

this is super interesting

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taupelink

remix of d/14533 by u/rodrigo.siqueira

function u(t) {

m=1e3;n=100;R=Math.random()*3;X=R*C(v=t*n);Y=R*S(v);Q=R*R*S(3/R);x.moveTo(A=960+m*X,B=540+m*Y);x.lineTo(A+(-Y+X*Q)*n,B+(X+Y*Q)*n);x.stroke()

Jun 12 2019 9:29 PM UTC

}// 140/140

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Slow-building remix with polar coordinates and random r #math

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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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username

function u(t) {

t?onmousemove=_=>e=_:e={x:666,y:420}
x.beginPath()
for(i=c.width+=0;i--;x.lineWidth=14)x.lineTo(i,542+e.y*S(6.283*(t-i/e.x)))
x.stroke()

Jun 10 2019 12:46 PM UTC

}// 136/140

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harmonic wave equation (in javascript notation y=(x,y)=>A*S(2*Math.PI*(t/T-x/λ))) - move mouse to change wave length and amplitude (period is fixed at T=1 for simplicity)

u/aleamb

#interactive
u/aleamb

#math
u/marc8

Remixes https://www.dwitter.net/d/10105
u/username

u/marc8 I guess we had the same idea. However, my intention was to show a harmonic wave equation using d/14535 and then I just remixed that
u/username

actually, d/14535 does not do that. I did not post the dweet I had originally drafted. it used the above equation (in my very first comment) in code and that is exactly like that

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taupelink

remix of d/11655 by u/Undefined

function u(t) {

l=(n,a)=>(a.push(n),n-1?l(n%2?n*3+1:n/2,a):a)
c.width|=0,k=0,b=l(~~t+2,[]),m=(Math.max(...b)/99)|1
b.forEach(X=>x.fillRect(k++*20,0,20,X/m))

Jun 7 2019 2:21 AM UTC

}// 140/140

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Mini #collatz, adapted for column graphs #math

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KilledByAPixel

function u(t) {

for(s="",a=[i=1];i++<300;s+=a[i-2]+"/"+a[i-1]+"&emsp;")i%2?(n=(i-1)/2,m=n+1,a.push(a[n-1]+a[m-1])):(n=i/2,a.push(a[n-1]))
t?0:c.outerHTML=s

Jun 5 2019 8:36 PM UTC

}// 139/140

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Generating every fraction in order using the Stern–Brocot sequence.

u/KilledByAPixel

Minified version of this https://jan.jarfalk.se/infinite-fractions/
u/taupelink

#math
u/taupelink

#numbertheory
u/KilledByAPixel

https://en.wikipedia.org/wiki/Stern%E2%80%93…

dwitter.net | #Math