DescriptionStreaklines and pathlines animation.gif	English: The plot shows fluid flow under the velocity field ${\displaystyle \mathbf {u} (\mathbf {x} ,t)=(1,xt)}$. The red dot represents a particle released from the origin at time ${\displaystyle t=0}$, tracing out its pathline in red. As it moves, it leaves behind a trail of blue ink (released from the origin), which starts on the pathline, but is carried up by the fluid flow. The velocity is represented twice, with flow vectors, and the grey dashed streamlines, which connect the flow vectors. Deutsch: Die Grafik zeigt Fluid-Strömung in einem Geschwindigkeitsfeld ${\displaystyle \mathbf {u} (\mathbf {x} ,t)=(1,xt)}$. Der rote Punkt wird zum Zeitpunkt ${\displaystyle t=0}$ im Ursprung ins Feld gesetzt und zeichnet eine rote Bahnlinie. In seiner Bewegung hinterlässt er eine blaue Spur, die Streichlinie, die mit der Bahnlinie im Ursprung beginnt, aber die Punkte der Bahnlinie zeigt, wie sie von der Strömung des Fluids mitgenommen werden. Die Geschwindigkeit wird zweifach dargestellt; mit Strömungs-Vektoren und mit grau gestrichelten Stromlinien, die die Strömungs-Vektoren verbinden.
Date	5 February 2009
Source	Own work   This diagram was created with Mathematica.
Author	Fi1Kaiv8
Other versions	Streaklines and pathlines animation (low).gif

p = Join[{
   If[x < t, 1/3 x^3, 100],
   If[x < t, 1/2 t x^2 - 1/6 x^3, 100]},
  Table[1/2 (x^2) t + y0, {y0, -10, 40, 0.9}]];
Export["plot.gif",
Table[Plot[p, {x, 0, 10.6},
  PlotRange -> {0, 10.6},
  AspectRatio -> 1,
  PlotRangeClipping -> True,
  PlotStyle ->
   PadRight[{Directive[Thickness[Medium], Red],
     Directive[Thickness[Medium], Green]}, 60,
    Directive[Gray, Dashed]],
  Exclusions -> {t},
  ExclusionsStyle -> None,
  ImageSize -> 500,
  AxesLabel -> {x, y},
  Epilog ->
   {Line[Flatten[
      With[{\[Epsilon] = 0.025},
       Table[{{x - \[Epsilon]/Sqrt[1 + x^2 t^2],
          y - x t \[Epsilon]/Sqrt[1 + x^2 t^2]}, {x + \[Epsilon]/
            Sqrt[1 + x^2 t^2],
          y + x t \[Epsilon]/Sqrt[1 + x^2 t^2]}}, {x, 0.1, 4,
         0.1}, {y, 0.1, 4, 0.1}]]
      , 1]],
    PointSize[0.015], Red, Point[{t, 1/3 t^3}]}
  ], {t, 0, 1.6, 0.025}],
AnimationRepetitions -> Infinity,
"DisplayDurations" -> PadLeft[{1.5}, 65, 0.1]
]

I, the copyright holder of this work, hereby publish it under the following licenses:

This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.

You are free:

• to share – to copy, distribute and transmit the work
• to remix – to adapt the work

Under the following conditions:

• attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
• share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

https://creativecommons.org/licenses/by-sa/3.0CC BY-SA 3.0 Creative Commons Attribution-Share Alike 3.0 truetrue

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue

You may select the license of your choice.