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    $\begingroup$ Have you tried changing the PlotRange option in ParametricPlot3D? Perhaps try something like PlotRange -> {{0,1},{0,0.2},{0,1}} $\endgroup$ Commented Jun 23, 2021 at 15:56
  • $\begingroup$ @bRost03: I tried using the option you suggested but it does not cover the whole space. The whole space I intend to cover is $x,y,z \geq 0$ and $x+y+z \leq 1.$ $\endgroup$ Commented Jun 23, 2021 at 16:17
  • $\begingroup$ So you want the plot to be some sort of pyramid shape? $\endgroup$ Commented Jun 23, 2021 at 16:22
  • $\begingroup$ @bRost03: Yes, something like that (pyramid shape). I would ideally want to have a bunch of random initial condition points on the pyramid and then trace their trajectory. $\endgroup$ Commented Jun 23, 2021 at 16:27
  • $\begingroup$ @egt123, thus you should use the RegionFunctions with you formulas of volume $\endgroup$ Commented Jun 23, 2021 at 16:29