Top #Bifurcation 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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Current theme challenge: #Opposites

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rodrigo.siqueira

remix of d/12440 by u/rodrigo.siqueira

function u(t) {

t||(a=b=0)
for(i=5e3;i--;)x.fillStyle=R(C(a)*200,S(a)*b/3,t*42),x.fillRect(960+b*S(a*.8),540-b*C(a*.8),1,1),a+=1.9*C(2.5*a)+C(t/5),b+=.00076

Jul 7 2019 9:15 PM UTC

}// 140/140

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Feigenbaum Flower. Homage to Mitchell Feigenbaum (1944-2019). He demonstrated the universal character of dynamical non-linear systems, which has made possible the systematic study of chaos. In 1975, using the small HP-65 calculator, he discovered that the ratio of successive distances between bifurcation events tends to a constant δ ≈ 4.66920... This "ratio of convergence" of period-doubling bifurcations is now known as the first Feigenbaum constant. #bifurcation #attractor #fractal #chaos #math

u/taupelink

This is a great tribute. RIP.
u/donbright

really nice
u/artfarnaa

Rodrigo - are you working full time on this fractal stuff? Super impressive if its only a hobby. Great work.
u/rodrigo.siqueira

#tribute

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rodrigo.siqueira

remix of d/25376 by u/rodrigo.siqueira

function u(t) {

f=(x,y,n=3)=>y<Math.random()*X-x?f(x*x-y*y+.3,3*x*S(y),n+1):S(n/5)**2
for(i=2e4;i--;x.fillRect(X=u&2047,u>>11,f(X/990-1,u/2e6-1.1),1))u=-~u

Apr 27 2022 8:03 PM UTC

}// 139/140

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Electric #fractal with rays and bifurcations #bifurcation

u/magna

wow!
u/pavel

Brainy!
u/rep_movsd

Galaxy brain

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rodrigo.siqueira

remix of d/25337 by u/rodrigo.siqueira

function u(t) {

f=(x,y,n=0)=>y<X/S(y)**2?f(x*x-y*y-.8,2*x*S(y)+.2,n+t/4+2):S(n/9)
for(i=2e4;i--;x.fillRect(X=u&2047,u>>11,f(X/480-2,u/1e6-1.15),1))u=-~u

Apr 18 2022 2:39 PM UTC

}// 137/140

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#fractal with electrical #bifurcation rays

u/donbright

legend. how does this even work?

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rodrigo.siqueira

remix of d/26492 by u/rodrigo.siqueira

function u(t) {

x.fillRect(0,0,2e3,2e3)
for(Z=Y=i=-1;i<1;i=i+.001)
X=i*4.5+S(Z/52)/5,
Y=4*C(i*Y-2),
Z=(8+Y*S(3*i+t))*60,
x.clearRect(980+150*X,Z+Y,2,5)

Nov 21 2022 3:38 PM UTC

}// 135/140

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Liquid #bifurcation

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rodrigo.siqueira

remix of d/26470 by u/rodrigo.siqueira

function u(t) {

c.style.filter=`invert(`
a=0;for(X=1920;X--;)x.fillStyle=R(a*X,a*130,9/X),a+=C(a*((X/160-3+C(X/t)/t)*5+25)/16),x.fillRect(X,a*630+190,1,.2)

Nov 15 2022 2:51 PM UTC

}// 139/140

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Neon #bifurcation "A bifurcation occurs when a small smooth change made to the parameter values (the bifurcation parameters) of a system causes a sudden qualitative or topological change in its behavior." (from the Bifurcation Theory)

u/leafyvez

amazing!
u/Xen

Siick!
u/Joachim

Beautiful!
u/magna

So glowy!

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rodrigo.siqueira

remix of d/12440 by u/rodrigo.siqueira

function u(t) {

t||(a=b=0)
for(i=5e3;i--;)x.fillStyle=`hsl(9,45%,${S(t*4)*50}%)`,x.fillRect(960+b*S(a*1.5),540-b*C(a*2),1,2),a+=1.8*C(2.6*a)+C(t/4),b+=.001

Feb 21 2019 2:18 PM UTC

}// 139/140

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Emergent eagle from bifurcation. Using Katip's Attractor. #chaos, #bifurcation

u/katkip

This is so beautiful!!! #art
u/donbright

this is remarkable. #tshirt

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rodrigo.siqueira

remix of d/12434 by u/katkip

function u(t) {

t||(a=b=0)
for(i=8000;i--;)x.fillRect(560+b*C(a),540+b*S(a),1,1),a+=.847*C(t+5*a)+C(t),b+=.002

Feb 20 2019 9:25 PM UTC

}// 94/140

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The Eye of Bifurcation #bifurcation

u/geb

All I see is the number triangle https://www.dwitter.net/d/10794

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rodrigo.siqueira

remix of d/12129 by u/rodrigo.siqueira

function u(t) {

c.width^=Y=0
for(X=2e3;X--;)
 Y=C(Y+t)*X/450,
 x.fillRect(X,540+Y*120,5,5)

Feb 4 2019 2:12 PM UTC

}// 74/140

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A very small bifurcation equation. #attractor

u/rodrigo.siqueira

Animated #bifurcation

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rodrigo.siqueira

remix of d/12001 by u/thorbear

function u(t) {

X=t/6;Y=2;s=999;x.globalAlpha=.05;for(i=3e3;i--;)
Y=1.66-2*(.1*X-S(1.2*Y)),
x.fillRect(X*s,Y*s-700,3,3)

Jan 31 2019 2:25 PM UTC

}// 103/140

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Bifurcation diagram attractor of the logistic map. xₙ₊₁ = r * xₙ(1-xₙ). Bifurcation diagrams enable the visualization of bifurcation theory. #fractal

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rodrigo.siqueira

remix of d/26459 by u/rodrigo.siqueira

function u(t) {

c.style.filter=`invert(`
a=0;for(X=1920;X--;)for(i=11;i--;)
a+=C(a*((X/210-2)*5+30+C(i+t/3.5)*9)/16),x.fillRect(X,a*700+210,t<3.5,.2)

Nov 9 2022 1:39 PM UTC

}// 133/140

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#bifurcation fibers x-ray

dwitter.net | #Bifurcation