Usage:
StreadmPlot4D[
{ vt, vx, vy, vz },
{ t, tmin, tmax },
{ x, xmin, xmax },
{ y, ymin, ymax },
{ z, zmin, zmax }
]
generates a stream plot of the vector field { vt, vx, vy, vz }
as a function of t, x, y, and z.
The 4D phasespace will be shown as a 3D perspective projection
where farther streams are shown in diferent colors.
For help, type ? StreamPlot4D in Mathematica.
In the following example, 4D phasespace is confined to a tesseract
with the color coding: blue = close, red = farther away.
The 3D axes are (x,y,z) and the fourth axis is t.
The shown vector field is:
vt = 1, vx = -1 - x^2 + y, vy = 1 + x - y^2, vz = 1
The code behind the plot is:
StreamPlot4D[
{1, -1 - x^2 + y, 1 + x - y^2, 1},
{t, -3, 3},
{x, -3, 3},
{y, -3, 3},
{z, -3, 3},
VectorPoints -> 0,
StreamColorFunction -> (Blend[{{-3, Blue}, {3, Red}}, #[[1]]] &),
ProjectionTo3D -> ({#[[2]], #[[3]], #[[4]]} (1 - 0.5 (#[[1]] + 3)/6) &),
StreamPoints -> Tuples[{{0}, Range[-3, 3, 1], Range[-3, 3, 1], {0}}],
StreamArrowheads -> Range[0, 1, 0.1],
PlotRange -> Automatic, PlotRangePadding -> Scaled[.2],
Boxed -> True,
ImageSize -> Scaled[1]
]
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