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:ashow more

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 -show more

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

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

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

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

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

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

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

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

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

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

a=(x,y,d=mag(k=5*cos(x/14)*cos(y/30),e=y/8-13)**2/59+4)=>point((q=60-3*sin(atan2(k,e)*e)+k*(3+4/d*sin(d*d-t*2)))*sin(c=d/2+e/99-t/18)+200,(q+d*9)*cos(c)+200) t=0,draw=$=>{t||createCanvas(w=400,w);background(9).stroke(w,66);for(t+=PI/20,i=1e4;i--;)a(i%200,i/43)}#つぶやきProcessing

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

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

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

1. Spatial Constraints & Magnitude: K(u) = A₁ *... cos(u / λ₁) E(v) = (v / λ₂) - δ_offset Distance Driver: D(u,v) = √( K(u)² + E(v)² ) 2. Pulsation Kinematics: Q(u,v,t) = αsin(2K) + (β/K) + sin(v/λ₃) * K * [γ + εsin(ω₁E - ω₂D + ω₃t)] ↳ The (β/K) term creates the asymptotic stretch of the tentacles, while the nested sine waves act as a damped harmonic oscillator for the contraction of the bell. pause - push - pause - push (action) 3. Polar-to-Cartesian Mapping Rotational Phase: θ(u,v,t) = D(u,v) - t X(u,v,t) = Q * cos(θ) * S_x + C_x Y(u,v,t) = Q * sin(θ) + S_y * D - C_y 4. Particle Sizing Filter: Radius = K(u)² > τ ? 2 : 1 Alpha-Blended Buffer: C_final = (1 - ρ) * C_new + ρ * C_buffer (u,v = particle indices, t = continuous time, ρ = retention rate for trails)show more

Abracadabra 🪄 #define t (t+fract(1e4*sin(dot(FC.xy,vec2(137,-13))))/6e1) #define S smoothstep float... i,d,s,m,l,x=abs(mod(t/4.,2.)-1.),a=x 6.)break;l=length(.2*k.xy-vec2(sin(t)/9.,.6+sin(t+t)/9.));k.y<-5.?k.y=-k.y-10.,m=.5:m=1.;k.xz*=mat2(cos(a*6.28+k.y*.3*S(.2,.5,x)*S(.7,.5,x)+vec4(0,33,11,0)));for(p=k*.5,s=.01;s<1.;s+=s)p.y+=.95+abs(dot(sin(p.x+2.*t+p/s),.2+p-p))*s;l=mix(sin(length(k*k.x)),mix(sin(length(p)),l,.5-l),S(5.5,6.,p.y));p=abs(k);d+=s=.012+.09*abs(max(sin(length(k)+l),max(max(max(p.x,p.y),p.z),dot(p,vec3(.577))*mix(.5,.9,a))-3.)-i/1e2);}o=tanh(o*o/1e6)*m;show more

Following many two-dimensional turbulence animations, it is time to... share computer code! Implementation of a vorticity-streamfunction method with a pseudo-spectral discretization + third-order Runge-Kutta for time integration (our CFD class semester project). The MATLAB code: M = 256; % number of points N = M; Lx = 2*pi; Ly = 2*pi; nu = 5e-4; % kinematic viscosity Sc = 0.7; % Schmidt number beta = 0; % meridional gradient of Coriolis parameter ar = 0.02; %random number amplitude b = 1; % mean scalar gradient CFLmax = 0.8; tend = 200; % end time x=linspace(0,Lx,M+1); x(end)=[]; dx = Lx/M; kx=[0:M/2 -M/2+1:-1]*2*pi/Lx; y=linspace(0,Ly,N+1); y(end)=[]; ky=[0:N/2 -N/2+1:-1]*2*pi/Ly; dy = Ly/N; time = 0; index_kmax = ceil(M/3); kmax = kx(index_kmax); filter = ones(M,N); filter(index_kmax+1:2*index_kmax+3,index_kmax+1:2*index_kmax+3)=0; rng(64); [u, v, omega, psi, ddx, ddy, idel2, kk, k2]=deal(zeros(M,N)); for j=1:N ddx(:,j)=1i*kx; end for i=1:M ddy(i,:)=1i*ky; end for i=1:M for j=1:N idel2(i,j)=-kx(i)^2-ky(j)^2; end end idel2=1./idel2; idel2(1,1)=0; for i=1:M for j=1:N kk(i,j)=kx(i)^2+ky(j)^2; k2(i,j)=kx(i)^2+ky(j)^2; if kk(i,j) >= 6^2 && kk(i,j) <= 7^2 % forcing kk(i,j) = -kk(i,j); end if kk(i,j) <= 2^2 kk(i,j) = 8*kk(i,j); % large-scale dissipation end end end for i=1:M for j=1:N u(i,j) = cos(2*x(i))*sin(2*y(j))+ar*rand; v(i,j) = -sin(2*x(i))*cos(2*y(j))+ar*rand; end end uhat = fft2(u); vhat = fft2(v); omegahat = ddx.*vhat - ddy.*uhat; % make vorticity phi = rand(size(u)); phihat = fft2(phi); ncid = netcdf.create(' 'CLOBBER'); dimid_x = netcdf.defDim(ncid, 'x', M); dimid_y = netcdf.defDim(ncid, 'y', N); dimid_time = netcdf.defDim(ncid, 'time', netcdf.getConstant('NC_UNLIMITED')); varid_x = netcdf.defVar(ncid, 'x', 'NC_FLOAT', [dimid_x]); varid_y = netcdf.defVar(ncid, 'y', 'NC_FLOAT', [dimid_y]); varid_u = netcdf.defVar(ncid, 'u', 'NC_FLOAT', [dimid_x, dimid_y, dimid_time]); varid_v = netcdf.defVar(ncid, 'v', 'NC_FLOAT', [dimid_x, dimid_y, dimid_time]); varid_omega = netcdf.defVar(ncid, 'vorticity', 'NC_FLOAT', [dimid_x, dimid_y, dimid_time]); varid_phi = netcdf.defVar(ncid, 'scalar', 'NC_FLOAT', [dimid_x, dimid_y, dimid_time]); varid_dissipation = netcdf.defVar(ncid, 'dissipation', 'NC_FLOAT', [dimid_x, dimid_y, dimid_time]); varid_time = netcdf.defVar(ncid, 'time', 'NC_FLOAT', [dimid_time]); netcdf.endDef(ncid); netcdf.putVar(ncid, varid_time, 0, 1, time); netcdf.putVar(ncid, varid_x, 0, M, x); netcdf.putVar(ncid, varid_y, 0, N, y); netcdf.putVar(ncid, varid_phi, [0, 0, 0], [M, N, 1], phi); netcdf.putVar(ncid, varid_u, [0, 0, 0], [M, N, 1], u); netcdf.putVar(ncid, varid_v, [0, 0, 0], [M, N, 1], v); netcdf.putVar(ncid, varid_omega, [0, 0, 0], [M, N, 1], omega); netcdf.putVar(ncid, varid_dissipation, [0, 0, 0], [M, N, 1], 0*omega); dt = 0.5*min([dx dy]); nstep = 1; while time < tend psihat = -idel2.*omegahat; uhat = ddy.*psihat; vhat = -ddx.*psihat; u = real(ifft2(uhat)); v = real(ifft2(vhat)); omegadx = real(ifft2(ddx.*omegahat)); omegady = real(ifft2(ddy.*omegahat)); facto = exp(-nu*8/15*dt*kk); factp = exp(-nu/Sc*8/15*dt*k2); r0o = -fft2(u.*omegadx+v.*omegady)+beta*vhat; r0p = -fft2(u.*real(ifft2(ddx.*phihat))+v.*real(ifft2(ddy.*phihat)))+b*vhat; omegahat = facto.*(omegahat + dt*8/15*r0o); % update omega phihat = factp.*(phihat + dt*8/15*r0p); % update phi %%%% Substep 2 psihat = -idel2.*omegahat; uhat = ddy.*psihat; vhat = -ddx.*psihat; u = real(ifft2(uhat)); v = real(ifft2(vhat)); omegadx = real(ifft2(ddx.*omegahat)); omegady = real(ifft2(ddy.*omegahat)); r1o = -fft2(u.*omegadx+v.*omegady)+beta*vhat; r1p = -fft2(u.*real(ifft2(ddx.*phihat))+v.*real(ifft2(ddy.*phihat)))+b*vhat; omegahat = omegahat + dt*(-17/60*facto.*r0o + 5/12*r1o); phihat = phihat + dt*(-17/60*factp.*r0p + 5/12*r1p); facto = exp(-nu*(-17/60+5/12)*dt*kk); factp = exp(-nu/Sc*(-17/60+5/12)*dt*k2); omegahat = omegahat.*facto; phihat = phihat.*factp; %%%% Substep 3 psihat = -idel2.*omegahat; uhat = ddy.*psihat; vhat = -ddx.*psihat; % max(max(abs(real(ifft2(1i*ddx.*uhat+1i*ddy.*vhat))))) % divergence u = real(ifft2(uhat)); v = real(ifft2(vhat)); omegadx = real(ifft2(ddx.*omegahat)); omegady = real(ifft2(ddy.*omegahat)); r2o = -fft2(u.*omegadx+v.*omegady)+beta*vhat; r2p = -fft2(u.*real(ifft2(ddx.*phihat))+v.*real(ifft2(ddy.*phihat)))+b*vhat; omegahat = omegahat + dt*(-5/12*facto.*r1o + 3/4*r2o); phihat = phihat + dt*(-5/12*factp.*r1p + 3/4*r2p); facto = exp(-nu*(-5/12+3/4)*dt*kk); factp = exp(-nu/Sc*(-5/12+3/4)*dt*kk); omegahat = omegahat.*facto; phihat = phihat.*factp; phihat = filter.*phihat; omegahat = filter.*omegahat; time = time + dt; nstep = nstep + 1; CFL = max(max(abs(u)))/dx*dt+max(max(abs(v)))/dy*dt; if mod(nstep,20)==0 phi = real(ifft2(phihat)); omega = real(ifft2(omegahat)); dissipation = 2*nu*(real(ifft2(ddx.*uhat)).^2 + real(ifft2(ddy.*uhat)).^2 + real(ifft2(ddx.*vhat)).^2 + real(ifft2(ddy.*vhat)).^2); eta = (nu^3/mean(dissipation,'all'))^0.25; subplot(221); pcolor(x,y,omega'); title('Vorticity'); shading flat; axis equal tight; colorbar; drawnow subplot(222); pcolor(x,y,phi'); title('Scalar'); shading flat; axis equal tight; colorbar; drawnow subplot(223); pcolor(x,y,dissipation'); title('Dissipation'); shading flat; axis equal tight; colorbar; drawnow subplot(224); pcolor(x,y,u); title('u-velocity'); shading flat; axis equal tight; colorbar; drawnow fprintf(1,'step = %d time = %g dt = %g CFL = %g kmax*eta = %g %g\n', nstep, time, dt, CFL, eta.*kmax, eta.*kmax/sqrt(Sc)); [~, dim_time_len] = netcdf.inqDim(ncid,dimid_time); netcdf.putVar(ncid, varid_time, [dim_time_len], [1], time); netcdf.putVar(ncid, varid_phi, [0, 0, dim_time_len], [M, N, 1], phi); netcdf.putVar(ncid, varid_u, [0, 0, dim_time_len], [M, N, 1], u); netcdf.putVar(ncid, varid_v, [0, 0, dim_time_len], [M, N, 1], v); netcdf.putVar(ncid, varid_omega, [0, 0, dim_time_len], [M, N, 1], omega); netcdf.putVar(ncid, varid_dissipation, [0, 0, dim_time_len], [M, N, 1], dissipation); netcdf.sync(ncid); end dt = CFLmax/CFL*dt; %0.0005; end netcdf.close(ncid);show more

[Backpropagation] by Hand✍️ [1] Forward Pass ↳ Given a... multi layer perceptron (3 levels), an input vector X, predictions Y^{Pred} = [0.5, 0.5, 0], and ground truth label Y^{Target} = [0, 1, 0]. [2] Backpropagation ↳ Insert cells to hold our calculations. [3] Layer 3 - Softmax (blue) ↳ Calculate ∂L / ∂z3 directly using the simple equation: Y^{Pred} - Y^{Target} = [0.5, -0.5, 0]. ↳ This simple equation is the benefit of using Softmax and Cross Entropy Loss together. [4] Layer 3 - Weights (orange) & Biases (black) ↳ Calculate ∂L / ∂W3 and ∂L / ∂b3 by multiplying ∂L / ∂z3 and [ a2 | 1 ]. [5] Layer 2 - Activations (green) ↳ Calculate ∂L / ∂a2 by multiplying ∂L / ∂z3 and W3. [6] Layer 2 - ReLU (blue) ↳ Calculate ∂L / ∂z2 by multiplying ∂L / ∂a2 with 1 for positive values and 0 otherwise. [7] Layer 2 - Weights (orange) & Biases (black) ↳ Calculate ∂L / ∂W2 and ∂L / ∂b2 by multiplying ∂L / ∂z2 and [ a1 | 1 ]. [8] Layer 1 - Activations (green) ↳ Calculate ∂L / ∂a1 by multiplying ∂L / ∂z2 and W2. [9] Layer 1 - ReLU (blue) ↳ Calculate ∂L / ∂z1 by multiplying ∂L / ∂a1 with 1 for positive values and 0 otherwise. [10] Layer 1 - Weights (orange) & Biases (black) ↳ Calculate ∂L / ∂W1 and ∂L / ∂b1 by multiplying ∂L / ∂z1 and [ x | 1 ]. [11] Gradient Descent ↳ Update weights and biases (typically a learning rate is applied here). 💡 Matrix Multiplication is All You Need: Just like in the forward pass, backpropagation is all about matrix multiplications. You can definitely do everything by hand as I demonstrated in this exercise, albeit slow and imperfect. This is why GPU's ability to multiply matrices efficiently plays such an important role in the deep learning evolution. This is why NVIDIA is now close to $1 trillion in valuation. 💡Exploding Gradients: We can already see the gradients are getting larger as we back-propagate up, even in this simple 3-layer network. This motivates using methods like skip connections to handle exploding (or diminishing) gradients as in the ResNet. I did the calculations entirely by hand. Please let me know if you spot any error or have any questions!show more

In 2020 I entered a summer shredding contest. This... was my gameplan to go from 18% body fat to 10% or less body fat in 12 weeks: (Applicable no matter where you’re starting, bookmark this) 1. Eat bodyweight (in lbs) x 10-12 calories daily (more on higher activity days, less on lower) 2. Eat 1g of protein per pound of bodyweight (if you’re starting more overweight you can aim for goal bodyweight) 3. 10K+ steps daily and progressively more cardio sessions (0 - month 1, 2-3x45 minutes/wk month 2, 5-6x45 minutes month 3) 4. Lifted 5x/week on a push, pull, legs, rest, upper, lower, rest split with a focus on: - every set ending near failure - fighting to get stronger week by week - managing volume (less volume towards end of the cut for recovery) 5. Limited alcohol to only a few drinks/month 6. Slept 7 hours/night minimum 7. 5g creatine daily 8. Drank around a .75-1 gallon of water + electrolytes daily 9. Refeed days (bodyweight x 15 calorie goal), 1x/wk in month 3 The framework is really this simple to drop body fat. Adjustments will need to be made based on biofeedback & weight data. If you aren’t losing at a rate of 0.5-1% bodyweight per week, you must: - increase your average weekly movement (steps or cardio minutes) - and/or decrease your average weekly calorie intake. Hope this helps guide you to a leaner version of yourself. 🤝show more