Mathematica code for this animation: https://twitter.com/bencbartlett/status/1440039445261029377

lorenz_many_particles.nb

SetDirectory[NotebookDirectory[]];

\[Sigma] = 10;
\[Rho] = 28;
\[Beta] = 8/3;
Tmax = 10;

eqn = {
   x'[t] == \[Sigma] (-x[t] + y[t]),
   y'[t] == \[Rho]* x[t] - y[t] - x[t]*z[t],
   z'[t] == x[t]*y[t] - \[Beta]*z[t]
   };

trange = 0.1;
soln = ParametricNDSolveValue[
   Join[eqn, {x[0] == x0, y[0] == y0, z[0] == z0}], {x[t], y[t], 
    z[t]}, {t, -1.1*trange, Tmax}, {x0, y0, z0}];

nParticles = 2500;
boxRange = 30;
icRange = 0.8;
center = {0, 0, 25};
initalConditions = 
  center + RandomReal[{-boxRange*icRange, boxRange*icRange}, {3, 
     nParticles}];

allPoints = Evaluate[MapThread[soln, initalConditions]];
drawplot[tt_, imagesize_ : 1080] := Module[{t0, t1},
   t0 = Max[0, 0 + tt];
   t1 = Min[Tmax, trange + tt];
   Show[
    Graphics3D[{
      PointSize -> .004,
      Opacity[0.9],
      White,
      Glow[White],
      Point[allPoints /. t -> tt + trange]
      }],
    ParametricPlot3D[
     allPoints, {t, t0, t1},
     (*PlotPoints\[Rule]200,MaxRecursion\[Rule]6,*)
     
     ColorFunction -> 
      Function[{x, y, z, t}, 
       Directive[
        ColorData["SolarColors"][(*.05+.85**)((t - tt)/trange)^4], 
        Opacity[0.5*(t - tt)/trange]^1]],
     ColorFunctionScaling -> False],
    PlotRange -> 
     center + {{-boxRange, boxRange}, {-boxRange, 
        boxRange}, {-boxRange, boxRange}},
    BoxRatios -> {1, 1, 1},
    ImagePadding -> 50,
    PlotRangeClipping -> False,
    Axes -> False,
    Background -> Black,
    Boxed -> True, BoxStyle -> White,
    ImageSize -> imagesize,
    ViewPoint -> 5*{1.3, -2.4, 1.},
    ViewVertical -> {0, 0, 1}
    ]
   ];
pointsAppear[numPoints_, imagesize_ : 1080] := Module[{},
   Graphics3D[{
     PointSize -> .004,
     White,
     Opacity[0.9],
     Point[allPoints[[;; numPoints]] /. t -> 1*^-6],
     Opacity[0.0],
     Point[allPoints[[numPoints + 1 ;;]] /. t -> 1*^-6]
     },
    PlotRange -> 
     center + {{-boxRange, boxRange}, {-boxRange, 
        boxRange}, {-boxRange, boxRange}},
    BoxRatios -> {1, 1, 1},
    ImagePadding -> 50,
    Axes -> False,
    Background -> Black,
    Boxed -> True, BoxStyle -> White,
    ImageSize -> imagesize,
    ViewPoint -> 5*{1.3, -2.4, 1.},
    ViewVertical -> {0, 0, 1}
    ]
   ];
renderFrame[ttt_, imagesize_ : 1080] := Module[{numPoints},
   numPoints = 
    Ceiling[nParticles*(1 + ((ttt + 
            trange)/.05))]; (*0 to max in \[Delta]t=0.05*)
   
   numPoints = Clip[numPoints, {1, nParticles}];
   If[ttt + trange < 0, pointsAppear[numPoints, imagesize], 
    drawplot[ttt, imagesize]]
   ];

saveframe[ttt_] := Module[{frame, title},
   frame = renderFrame[ttt - trange + 1*^-6];
   title = IntegerString[Floor[(ttt + 1)*10000], 10, 9] <> ".png";
   Export["frames/" <> title, frame];
   Print[title];
   ];

duration = 15;
nFrames = 60 * duration;
dt = (0.7 - (-0.05))/nFrames;