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This implicit function fascinates me. f(x, y) = sin(a · (x² + y²)) − cos(b · x · y)

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Joshua Guo

25,941 subscribers

26,348 次观看 • 10 个月前 •via X (Twitter)

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You don't like math because you don't follow me. Check out the beautiful, intricate pattern generated by this equation: sin (sin (x) + cos (y)) = cos (sin (x*y) + cos (x))
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You don't like math because you don't follow me. Check out the beautiful, intricate pattern generated by this equation: sin (sin (x) + cos (y)) = cos (sin (x*y) + cos (x))

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95,894 次观看 • 10 个月前

a=(x,y,d=5*cos(o=mag(k=x/8-25,e=y/8-25)/3.5))=>[(k*atan(3*cos(d*9))+x/2)*cos(c=(d+o)/4-t/8)+200,(k*d*cos(o-d+t)+y/2)*sin(c)+200] t=0,draw=$=>{t||createCanvas(w=400,w);background(6).stroke(255,96);for(t+=PI/60,y=99;y<300;y+=2)for(x=99;++x<300;)point(...a(x,y))} #つぶやきProcessing
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a=(x,y,d=5*cos(o=mag(k=x/8-25,e=y/8-25)/3.5))=>[(k*atan(3*cos(d*9))+x/2)*cos(c=(d+o)/4-t/8)+200,(k*d*cos(o-d+t)+y/2)*sin(c)+200] t=0,draw=$=>{t||createCanvas(w=400,w);background(6).stroke(255,96);for(t+=PI/60,y=99;y<300;y+=2)for(x=99;++x<300;)point(...a(x,y))} #つぶやきProcessing

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a=(x,y,d=mag(k=(4+cos(x/9-t))*cos(x/30),e=y/7-13)+sin(y/99+t/2)-4)=>point((q=3*sin(k*2)+sin(y/29)*k*(9+2*sin(cos(e)*9-d*4+t)))+40*cos(c=d-t)+200,q*sin(c)+d*35) t=0,draw=$=>{t||createCanvas(w=400,w);background(9).stroke(w,96);for(t+=PI/120,i=1e4;i--;)a(i,i/235)}#つぶやきProcessing
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a=(x,y,d=mag(k=(4+cos(x/9-t))*cos(x/30),e=y/7-13)+sin(y/99+t/2)-4)=>point((q=3*sin(k*2)+sin(y/29)*k*(9+2*sin(cos(e)*9-d*4+t)))+40*cos(c=d-t)+200,q*sin(c)+d*35) t=0,draw=$=>{t||createCanvas(w=400,w);background(9).stroke(w,96);for(t+=PI/120,i=1e4;i--;)a(i,i/235)}#つぶやきProcessing

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a=(x,y,k=x/8-12.5,d=abs(cos(k/2)+sin(y/4)))=> point((q=x/4+90+(d+.1)*k*cos(d-t*2+y/24))*.7*cos(c=y/99-t/8+d*d/32)+200,(q+y)*.7*sin(c)+(q-y)/2*cos(c*2)+200) t=0,draw=$=>{t||createCanvas(w=400,w);background(0).stroke(w,36);for(t+=PI/60,i=4e4;i--;)a(i%200,i/300)}#つぶやきProcessing
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a=(x,y,k=x/8-12.5,d=abs(cos(k/2)+sin(y/4)))=> point((q=x/4+90+(d+.1)*k*cos(d-t*2+y/24))*.7*cos(c=y/99-t/8+d*d/32)+200,(q+y)*.7*sin(c)+(q-y)/2*cos(c*2)+200) t=0,draw=$=>{t||createCanvas(w=400,w);background(0).stroke(w,36);for(t+=PI/60,i=4e4;i--;)a(i%200,i/300)}#つぶやきProcessing

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27,094 次观看 • 1 年前

t=0,draw=$=>{t||createCanvas(w=400,w);background(6).stroke(255,66);for(t+=PI/60,y=99;y<300;y+=3)for(x=99;++x<300;)o=mag(k=x/8-25,e=y/8-25)/4,point((q=x+y/3+k/cos(y/8)+1/k+o*k*cos(y/8-t)*sin(o*4-t))/3*atan(2*sin(c=o*e/50-t/8))+200,(y*tan(c)+q)/3*cos(c)+200)} //#つぶやきProcessing
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t=0,draw=$=>{t||createCanvas(w=400,w);background(6).stroke(255,66);for(t+=PI/60,y=99;y<300;y+=3)for(x=99;++x<300;)o=mag(k=x/8-25,e=y/8-25)/4,point((q=x+y/3+k/cos(y/8)+1/k+o*k*cos(y/8-t)*sin(o*4-t))/3*atan(2*sin(c=o*e/50-t/8))+200,(y*tan(c)+q)/3*cos(c)+200)} //#つぶやきProcessing

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50,717 次观看 • 1 年前

a=(x,y,d=mag(k=(4+sin(x/11+t*8))*cos(x/14),e=y/8-19)+sin(y/9+t*2))=>point((q=2*sin(k*2)+sin(y/17)*k*(9+2*sin(y-d*3)))+50*cos(c=d*d/49-t)+200,q*sin(c)+d*39-440) t=0,draw=$=>{t||createCanvas(w=400,w);background(9).stroke(w,96);for(t+=PI/240,i=1e4;i--;)a(i,i/235)}#つぶやきProcessing
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a=(x,y,d=mag(k=(4+sin(x/11+t*8))*cos(x/14),e=y/8-19)+sin(y/9+t*2))=>point((q=2*sin(k*2)+sin(y/17)*k*(9+2*sin(y-d*3)))+50*cos(c=d*d/49-t)+200,q*sin(c)+d*39-440) t=0,draw=$=>{t||createCanvas(w=400,w);background(9).stroke(w,96);for(t+=PI/240,i=1e4;i--;)a(i,i/235)}#つぶやきProcessing

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a=(x,y,k=x/12-12.5,d=2*abs(cos(k/2)+sin(y/4)+cos(k/8)))=>point((q=x/4+90+(d)*k*cos(d-t*2+y/24))*.7*cos(c=y/79-t/8+d/8)+q/8*sin(c*4)+200,(q)*.7*sin(c)+200) t=0,draw=$=>{t||createCanvas(w=400,w);background(0).stroke(w,36);for(t+=PI/60,i=4e4;i--;)a(i%300,i/300)}//#つぶやきProcessing
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a=(x,y,k=x/12-12.5,d=2*abs(cos(k/2)+sin(y/4)+cos(k/8)))=>point((q=x/4+90+(d)*k*cos(d-t*2+y/24))*.7*cos(c=y/79-t/8+d/8)+q/8*sin(c*4)+200,(q)*.7*sin(c)+200) t=0,draw=$=>{t||createCanvas(w=400,w);background(0).stroke(w,36);for(t+=PI/60,i=4e4;i--;)a(i%300,i/300)}//#つぶやきProcessing

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ffmpeg -i "/dev/video" -filter_complex \ "[0:v]split=2[orig][copy]; \ [copy]setpts=PTS+0.5/TB[delayed]; \ [orig][delayed]blend=all_expr='if(gt(mod(sin((X*X - Y*Y)/3000 + T*2)*cos((X+Y)/2000)\,1)\,0.5)\,A\,B)', \ hue=h='360*t/10':s=2,format=yuv420p[v]" \ -map "[v]" -map 0:a -c:v libx264 -crf 18 -preset fast -c:a

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a=(x,y,o=mag(k=x/4-12.5,e=y/9)/9)=>point((q=x+99+cos(9/k)+o*k*(cos(e*9)/3+cos(y/9)/.7)*sin(o*4-t))*.7*sin(c=o*e/30-t/8)+200,200+y/9*cos(c*4-t/2)-q/2*cos(c)) t=0,draw=$=>{t||createCanvas(w=400,w);background(6).stroke(w,46);for(t+=PI/60,i=3e4;i--;)a(i%100,i/150)}#つぶやきProcessing
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a=(x,y,o=mag(k=x/4-12.5,e=y/9)/9)=>point((q=x+99+cos(9/k)+o*k*(cos(e*9)/3+cos(y/9)/.7)*sin(o*4-t))*.7*sin(c=o*e/30-t/8)+200,200+y/9*cos(c*4-t/2)-q/2*cos(c)) t=0,draw=$=>{t||createCanvas(w=400,w);background(6).stroke(w,46);for(t+=PI/60,i=3e4;i--;)a(i%100,i/150)}#つぶやきProcessing

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a=(x,y,d=mag(k=(4+cos(y))*cos(x/4),e=y/8-20))=>point((q=sin(k*3)+sin(y/19+9)*k*(6+sin(e*14-d)))*cos(d/8+t/4)+50*cos(c=d-t)+200,q*sin(c)+d*7*sin(c/4)+200) t=0,draw=$=>{t||createCanvas(w=400,w);background(9).stroke(w,116);for(t+=PI/120,i=1e4;i--;)a(i,i/235)}//#つぶやきProcessing
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a=(x,y,d=mag(k=(4+cos(y))*cos(x/4),e=y/8-20))=>point((q=sin(k*3)+sin(y/19+9)*k*(6+sin(e*14-d)))*cos(d/8+t/4)+50*cos(c=d-t)+200,q*sin(c)+d*7*sin(c/4)+200) t=0,draw=$=>{t||createCanvas(w=400,w);background(9).stroke(w,116);for(t+=PI/120,i=1e4;i--;)a(i,i/235)}//#つぶやきProcessing

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a=(x,y,o=mag(k=x/4-12.5,e=y/9+9)/9)=>point((q=x+39+y+1/k+o*k*(cos(y)/4+cos(e))*sin(o*4-t))*.7*sin(c=o+e/99-t/8+i%2*3)+200,200+y/2*cos(c*4-o)-q/2*cos(c)) t=0,draw=$=>{t||createCanvas(w=400,w);background(6).stroke(w,46);for(t+=PI/60,i=4e4;i--;)a(i/2%100,i/350)}//#つぶやきProcessing
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a=(x,y,o=mag(k=x/4-12.5,e=y/9+9)/9)=>point((q=x+39+y+1/k+o*k*(cos(y)/4+cos(e))*sin(o*4-t))*.7*sin(c=o+e/99-t/8+i%2*3)+200,200+y/2*cos(c*4-o)-q/2*cos(c)) t=0,draw=$=>{t||createCanvas(w=400,w);background(6).stroke(w,46);for(t+=PI/60,i=4e4;i--;)a(i/2%100,i/350)}//#つぶやきProcessing

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a=(x,y,k=x/12-12.5,d=abs(cos(k/2)+sin(y/2)*cos(k/5)/2+1))=>point((q=x/4+99+(d+0)*k*(.5+cos(d*2-t+y/8)))*.8*cos(c=y/69-t/8+d/6)+200,q/2*cos(c+d/3+y/69)+200) t=0,draw=$=>{t||createCanvas(w=400,w);background(0).stroke(w,46);for(t+=PI/30,i=4e4;i--;)a(i%300,i/300)}#つぶやきProcessing
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a=(x,y,k=x/12-12.5,d=abs(cos(k/2)+sin(y/2)*cos(k/5)/2+1))=>point((q=x/4+99+(d+0)*k*(.5+cos(d*2-t+y/8)))*.8*cos(c=y/69-t/8+d/6)+200,q/2*cos(c+d/3+y/69)+200) t=0,draw=$=>{t||createCanvas(w=400,w);background(0).stroke(w,46);for(t+=PI/30,i=4e4;i--;)a(i%300,i/300)}#つぶやきProcessing

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a=(x,y,k=x/8-12.5,d=cos(k/2)+sin(y/3)-.5)=>point((q=x/4+60+d*k*(1+cos(d*4-t*2+y/14)))*.7*cos(c=y*d/169-t/8+d/9)+200+60*sin(t*3/32+c/4),(q+59)*.7*sin(c)+200) t=0,draw=$=>{t||createCanvas(w=400,w);background(0).stroke(w,36);for(t+=PI/30,i=4e4;i--;)a(i%200,i/400)}#つぶやきProcessing
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a=(x,y,k=x/8-12.5,d=cos(k/2)+sin(y/3)-.5)=>point((q=x/4+60+d*k*(1+cos(d*4-t*2+y/14)))*.7*cos(c=y*d/169-t/8+d/9)+200+60*sin(t*3/32+c/4),(q+59)*.7*sin(c)+200) t=0,draw=$=>{t||createCanvas(w=400,w);background(0).stroke(w,36);for(t+=PI/30,i=4e4;i--;)a(i%200,i/400)}#つぶやきProcessing

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ffmpeg -i /dev/video0 -filter_complex "[0:v]split[orig][copy];[copy]setpts=PTS+0.4/TB[delayed]; [orig][delayed]blend=all_expr='if(lt(mod(X*X+Y*Y\,2000)\,1000)\,A\,B)'" -f rawvideo -pix_fmt yuv420p - | ffplay -f rawvideo -video_size 640x480 -
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ffmpeg -i /dev/video0 -filter_complex "[0:v]split[orig][copy];[copy]setpts=PTS+0.4/TB[delayed]; [orig][delayed]blend=all_expr='if(lt(mod(X*X+Y*Y\,2000)\,1000)\,A\,B)'" -f rawvideo -pix_fmt yuv420p - | ffplay -f rawvideo -video_size 640x480 -

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I might not have mentioned it, but my wife has a PhD in quantum computing. She just told me a very cool mathematical function. ψₙₓ,ₙᵧ(x,y) = ψₙₓ(x) · ψₙᵧ(y) ψₙ(x) = e^(−x²/2) · Hₙ(x) / √(2ⁿ · n! · √π) Hₙ(x) = (−1)ⁿ · e^(x²) · dⁿ/dxⁿ [e^(−x²)] Eₙₓ,ₙᵧ = (nₓ + nᵧ + 1) · ħω gₙₓ₊ₙᵧ = nₓ + nᵧ + 1
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I might not have mentioned it, but my wife has a PhD in quantum computing. She just told me a very cool mathematical function. ψₙₓ,ₙᵧ(x,y) = ψₙₓ(x) · ψₙᵧ(y) ψₙ(x) = e^(−x²/2) · Hₙ(x) / √(2ⁿ · n! · √π) Hₙ(x) = (−1)ⁿ · e^(x²) · dⁿ/dxⁿ [e^(−x²)] Eₙₓ,ₙᵧ = (nₓ + nᵧ + 1) · ħω gₙₓ₊ₙᵧ = nₓ + nᵧ + 1

Joshua Guo

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a=(x,y,d=mag(k=(5+sin(y))*cos(x*2),e=y/6-13)-3)=>point((q=3*sin(k*2)+k/19*y*(e+d/3*sin(e-d*4+t))+99)*sin(c=d-t/4+i%2*8)*cos(c/4+e/3)+200,q*d/9*cos(c/2+7)+200) t=0,draw=$=>{t||createCanvas(w=400,w);background(9).stroke(w,126);for(t+=PI/30,i=2e4;i--;)a(i,i/1e3)}#つぶやきProcessing
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a=(x,y,d=mag(k=(5+sin(y))*cos(x*2),e=y/6-13)-3)=>point((q=3*sin(k*2)+k/19*y*(e+d/3*sin(e-d*4+t))+99)*sin(c=d-t/4+i%2*8)*cos(c/4+e/3)+200,q*d/9*cos(c/2+7)+200) t=0,draw=$=>{t||createCanvas(w=400,w);background(9).stroke(w,126);for(t+=PI/30,i=2e4;i--;)a(i,i/1e3)}#つぶやきProcessing

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a=(x,y,d=mag(k=(4+sin(y*2-t)*3)*cos(x/29),e=y/8-13))=>point((q=3*sin(k*2)+.3/k+sin(y/25)*k*(9+4*sin(e*9-d*3+t*2)))+30*cos(c=d-t)+200,q*sin(c)+d*39-220) t=0,draw=$=>{t||createCanvas(w=400,w);background(9).stroke(w,96);for(t+=PI/240,i=1e4;i--;)a(i,i/235)}//#つぶやきProcessing
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a=(x,y,d=mag(k=(4+sin(y*2-t)*3)*cos(x/29),e=y/8-13))=>point((q=3*sin(k*2)+.3/k+sin(y/25)*k*(9+4*sin(e*9-d*3+t*2)))+30*cos(c=d-t)+200,q*sin(c)+d*39-220) t=0,draw=$=>{t||createCanvas(w=400,w);background(9).stroke(w,96);for(t+=PI/240,i=1e4;i--;)a(i,i/235)}//#つぶやきProcessing

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a=(x,y,d=mag(k=5*cos(x/19)*cos(y/30),e=y/8-12)**2/59+2)=>point((q=4*sin(atan2(k,e)*9)+9*sin(d-t)-k/d*(9+sin(d*9-t*16)*3))+50*cos(c=d*d/7-t)+200,q*sin(c)+d*45-9) t=0,draw=$=>{t||createCanvas(w=400,w);background(9).stroke(w,36);for(t+=PI/240,i=1e4;i--;)a(i,i/41)}#つぶやきProcessing
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a=(x,y,d=mag(k=5*cos(x/19)*cos(y/30),e=y/8-12)**2/59+2)=>point((q=4*sin(atan2(k,e)*9)+9*sin(d-t)-k/d*(9+sin(d*9-t*16)*3))+50*cos(c=d*d/7-t)+200,q*sin(c)+d*45-9) t=0,draw=$=>{t||createCanvas(w=400,w);background(9).stroke(w,36);for(t+=PI/240,i=1e4;i--;)a(i,i/41)}#つぶやきProcessing

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39,971 次观看 • 1 年前

a=(x,y,d=5*cos(mag(k=x/8-12.5,e=y/8-12.5)/3))=>stroke(99+99/abs(k*sin(k))*sin(t*4+e)**2,96).point((x+(d*k+k*3)*sin(d*2.5-t))/2+150,d*13+(d*3+12)*(3+cos(d*3-t))+d*e+150) t=0,draw=$=>{t||createCanvas(w=400,w);background(6);for(t+=PI/60,i=4e4;i--;)a(i%200,i/200)} #つぶやきProcessing
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a=(x,y,d=5*cos(mag(k=x/8-12.5,e=y/8-12.5)/3))=>stroke(99+99/abs(k*sin(k))*sin(t*4+e)**2,96).point((x+(d*k+k*3)*sin(d*2.5-t))/2+150,d*13+(d*3+12)*(3+cos(d*3-t))+d*e+150) t=0,draw=$=>{t||createCanvas(w=400,w);background(6);for(t+=PI/60,i=4e4;i--;)a(i%200,i/200)} #つぶやきProcessing

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42,188 次观看 • 1 年前