I'm hoping to animate the trajectory of a 2D Brownian Motion. Here's my attempt, which is based on what I've read in Mathematica's documentation:
SeedRandom[666];
Animate[ListLinePlot[
Transpose[RandomFunction[WienerProcess[], {0, T, .001}, 2]["ValueList"]]],
{T, 0, 0.04},
AnimationRunning -> False]
There are two things that I'm seeking help with:
It doesn't look like the seed is fixed. When I animate the parameter T (the ending time of the Brownian Motion), it appears as though I get a different trajectory after each time step.
I'd like the window to be of fixed size. For example, having each of the horizontal and vertical axes to range from -1 to 1.
Please let me know if you can help with either of these two items.